torch.nn¶
Parameters¶

class
torch.nn.
Parameter
[source]¶ A kind of Tensor that is to be considered a module parameter.
Parameters are
Tensor
subclasses, that have a very special property when used withModule
s  when they’re assigned as Module attributes they are automatically added to the list of its parameters, and will appear e.g. inparameters()
iterator. Assigning a Tensor doesn’t have such effect. This is because one might want to cache some temporary state, like last hidden state of the RNN, in the model. If there was no such class asParameter
, these temporaries would get registered too. Parameters
data (Tensor) – parameter tensor.
requires_grad (bool, optional) – if the parameter requires gradient. See Excluding subgraphs from backward for more details. Default: True
Containers¶
Module¶

class
torch.nn.
Module
[source]¶ Base class for all neural network modules.
Your models should also subclass this class.
Modules can also contain other Modules, allowing to nest them in a tree structure. You can assign the submodules as regular attributes:
import torch.nn as nn import torch.nn.functional as F class Model(nn.Module): def __init__(self): super(Model, self).__init__() self.conv1 = nn.Conv2d(1, 20, 5) self.conv2 = nn.Conv2d(20, 20, 5) def forward(self, x): x = F.relu(self.conv1(x)) return F.relu(self.conv2(x))
Submodules assigned in this way will be registered, and will have their parameters converted too when you call
to()
, etc.
add_module
(name, module)[source]¶ Adds a child module to the current module.
The module can be accessed as an attribute using the given name.
 Parameters
name (string) – name of the child module. The child module can be accessed from this module using the given name
module (Module) – child module to be added to the module.

apply
(fn)[source]¶ Applies
fn
recursively to every submodule (as returned by.children()
) as well as self. Typical use includes initializing the parameters of a model (see also torchnninit). Parameters
fn (
Module
> None) – function to be applied to each submodule Returns
self
 Return type
Example:
>>> def init_weights(m): >>> print(m) >>> if type(m) == nn.Linear: >>> m.weight.data.fill_(1.0) >>> print(m.weight) >>> net = nn.Sequential(nn.Linear(2, 2), nn.Linear(2, 2)) >>> net.apply(init_weights) Linear(in_features=2, out_features=2, bias=True) Parameter containing: tensor([[ 1., 1.], [ 1., 1.]]) Linear(in_features=2, out_features=2, bias=True) Parameter containing: tensor([[ 1., 1.], [ 1., 1.]]) Sequential( (0): Linear(in_features=2, out_features=2, bias=True) (1): Linear(in_features=2, out_features=2, bias=True) ) Sequential( (0): Linear(in_features=2, out_features=2, bias=True) (1): Linear(in_features=2, out_features=2, bias=True) )

buffers
(recurse=True)[source]¶ Returns an iterator over module buffers.
 Parameters
recurse (bool) – if True, then yields buffers of this module and all submodules. Otherwise, yields only buffers that are direct members of this module.
 Yields
torch.Tensor – module buffer
Example:
>>> for buf in model.buffers(): >>> print(type(buf.data), buf.size()) <class 'torch.FloatTensor'> (20L,) <class 'torch.FloatTensor'> (20L, 1L, 5L, 5L)

children
()[source]¶ Returns an iterator over immediate children modules.
 Yields
Module – a child module

cuda
(device=None)[source]¶ Moves all model parameters and buffers to the GPU.
This also makes associated parameters and buffers different objects. So it should be called before constructing optimizer if the module will live on GPU while being optimized.

double
()[source]¶ Casts all floating point parameters and buffers to
double
datatype. Returns
self
 Return type

dump_patches
= False¶ This allows better BC support for
load_state_dict()
. Instate_dict()
, the version number will be saved as in the attribute _metadata of the returned state dict, and thus pickled. _metadata is a dictionary with keys that follow the naming convention of state dict. See_load_from_state_dict
on how to use this information in loading.If new parameters/buffers are added/removed from a module, this number shall be bumped, and the module’s _load_from_state_dict method can compare the version number and do appropriate changes if the state dict is from before the change.

eval
()[source]¶ Sets the module in evaluation mode.
This has any effect only on certain modules. See documentations of particular modules for details of their behaviors in training/evaluation mode, if they are affected, e.g.
Dropout
,BatchNorm
, etc.

extra_repr
()[source]¶ Set the extra representation of the module
To print customized extra information, you should reimplement this method in your own modules. Both singleline and multiline strings are acceptable.

float
()[source]¶ Casts all floating point parameters and buffers to float datatype.
 Returns
self
 Return type

forward
(*input)[source]¶ Defines the computation performed at every call.
Should be overridden by all subclasses.
Note
Although the recipe for forward pass needs to be defined within this function, one should call the
Module
instance afterwards instead of this since the former takes care of running the registered hooks while the latter silently ignores them.

half
()[source]¶ Casts all floating point parameters and buffers to
half
datatype. Returns
self
 Return type

load_state_dict
(state_dict, strict=True)[source]¶ Copies parameters and buffers from
state_dict
into this module and its descendants. Ifstrict
isTrue
, then the keys ofstate_dict
must exactly match the keys returned by this module’sstate_dict()
function. Parameters
state_dict (dict) – a dict containing parameters and persistent buffers.
strict (bool, optional) – whether to strictly enforce that the keys in
state_dict
match the keys returned by this module’sstate_dict()
function. Default:True
 Returns
missing_keys is a list of str containing the missing keys
unexpected_keys is a list of str containing the unexpected keys
 Return type
NamedTuple
withmissing_keys
andunexpected_keys
fields

modules
()[source]¶ Returns an iterator over all modules in the network.
 Yields
Module – a module in the network
Note
Duplicate modules are returned only once. In the following example,
l
will be returned only once.Example:
>>> l = nn.Linear(2, 2) >>> net = nn.Sequential(l, l) >>> for idx, m in enumerate(net.modules()): print(idx, '>', m) 0 > Sequential( (0): Linear(in_features=2, out_features=2, bias=True) (1): Linear(in_features=2, out_features=2, bias=True) ) 1 > Linear(in_features=2, out_features=2, bias=True)

named_buffers
(prefix='', recurse=True)[source]¶ Returns an iterator over module buffers, yielding both the name of the buffer as well as the buffer itself.
 Parameters
 Yields
(string, torch.Tensor) – Tuple containing the name and buffer
Example:
>>> for name, buf in self.named_buffers(): >>> if name in ['running_var']: >>> print(buf.size())

named_children
()[source]¶ Returns an iterator over immediate children modules, yielding both the name of the module as well as the module itself.
 Yields
(string, Module) – Tuple containing a name and child module
Example:
>>> for name, module in model.named_children(): >>> if name in ['conv4', 'conv5']: >>> print(module)

named_modules
(memo=None, prefix='')[source]¶ Returns an iterator over all modules in the network, yielding both the name of the module as well as the module itself.
 Yields
(string, Module) – Tuple of name and module
Note
Duplicate modules are returned only once. In the following example,
l
will be returned only once.Example:
>>> l = nn.Linear(2, 2) >>> net = nn.Sequential(l, l) >>> for idx, m in enumerate(net.named_modules()): print(idx, '>', m) 0 > ('', Sequential( (0): Linear(in_features=2, out_features=2, bias=True) (1): Linear(in_features=2, out_features=2, bias=True) )) 1 > ('0', Linear(in_features=2, out_features=2, bias=True))

named_parameters
(prefix='', recurse=True)[source]¶ Returns an iterator over module parameters, yielding both the name of the parameter as well as the parameter itself.
 Parameters
 Yields
(string, Parameter) – Tuple containing the name and parameter
Example:
>>> for name, param in self.named_parameters(): >>> if name in ['bias']: >>> print(param.size())

parameters
(recurse=True)[source]¶ Returns an iterator over module parameters.
This is typically passed to an optimizer.
 Parameters
recurse (bool) – if True, then yields parameters of this module and all submodules. Otherwise, yields only parameters that are direct members of this module.
 Yields
Parameter – module parameter
Example:
>>> for param in model.parameters(): >>> print(type(param.data), param.size()) <class 'torch.FloatTensor'> (20L,) <class 'torch.FloatTensor'> (20L, 1L, 5L, 5L)

register_backward_hook
(hook)[source]¶ Registers a backward hook on the module.
The hook will be called every time the gradients with respect to module inputs are computed. The hook should have the following signature:
hook(module, grad_input, grad_output) > Tensor or None
The
grad_input
andgrad_output
may be tuples if the module has multiple inputs or outputs. The hook should not modify its arguments, but it can optionally return a new gradient with respect to input that will be used in place ofgrad_input
in subsequent computations. Returns
a handle that can be used to remove the added hook by calling
handle.remove()
 Return type
torch.utils.hooks.RemovableHandle
Warning
The current implementation will not have the presented behavior for complex
Module
that perform many operations. In some failure cases,grad_input
andgrad_output
will only contain the gradients for a subset of the inputs and outputs. For suchModule
, you should usetorch.Tensor.register_hook()
directly on a specific input or output to get the required gradients.

register_buffer
(name, tensor)[source]¶ Adds a persistent buffer to the module.
This is typically used to register a buffer that should not to be considered a model parameter. For example, BatchNorm’s
running_mean
is not a parameter, but is part of the persistent state.Buffers can be accessed as attributes using given names.
 Parameters
name (string) – name of the buffer. The buffer can be accessed from this module using the given name
tensor (Tensor) – buffer to be registered.
Example:
>>> self.register_buffer('running_mean', torch.zeros(num_features))

register_forward_hook
(hook)[source]¶ Registers a forward hook on the module.
The hook will be called every time after
forward()
has computed an output. It should have the following signature:hook(module, input, output) > None
The hook should not modify the input or output.
 Returns
a handle that can be used to remove the added hook by calling
handle.remove()
 Return type
torch.utils.hooks.RemovableHandle

register_forward_pre_hook
(hook)[source]¶ Registers a forward prehook on the module.
The hook will be called every time before
forward()
is invoked. It should have the following signature:hook(module, input) > None
The hook should not modify the input.
 Returns
a handle that can be used to remove the added hook by calling
handle.remove()
 Return type
torch.utils.hooks.RemovableHandle

register_parameter
(name, param)[source]¶ Adds a parameter to the module.
The parameter can be accessed as an attribute using given name.
 Parameters
name (string) – name of the parameter. The parameter can be accessed from this module using the given name
param (Parameter) – parameter to be added to the module.

state_dict
(destination=None, prefix='', keep_vars=False)[source]¶ Returns a dictionary containing a whole state of the module.
Both parameters and persistent buffers (e.g. running averages) are included. Keys are corresponding parameter and buffer names.
 Returns
a dictionary containing a whole state of the module
 Return type
Example:
>>> module.state_dict().keys() ['bias', 'weight']

to
(*args, **kwargs)[source]¶ Moves and/or casts the parameters and buffers.
This can be called as

to
(device=None, dtype=None, non_blocking=False)[source]

to
(dtype, non_blocking=False)[source]

to
(tensor, non_blocking=False)[source]
Its signature is similar to
torch.Tensor.to()
, but only accepts floating point desireddtype
s. In addition, this method will only cast the floating point parameters and buffers todtype
(if given). The integral parameters and buffers will be moveddevice
, if that is given, but with dtypes unchanged. Whennon_blocking
is set, it tries to convert/move asynchronously with respect to the host if possible, e.g., moving CPU Tensors with pinned memory to CUDA devices.See below for examples.
Note
This method modifies the module inplace.
 Parameters
device (
torch.device
) – the desired device of the parameters and buffers in this moduledtype (
torch.dtype
) – the desired floating point type of the floating point parameters and buffers in this moduletensor (torch.Tensor) – Tensor whose dtype and device are the desired dtype and device for all parameters and buffers in this module
 Returns
self
 Return type
Example:
>>> linear = nn.Linear(2, 2) >>> linear.weight Parameter containing: tensor([[ 0.1913, 0.3420], [0.5113, 0.2325]]) >>> linear.to(torch.double) Linear(in_features=2, out_features=2, bias=True) >>> linear.weight Parameter containing: tensor([[ 0.1913, 0.3420], [0.5113, 0.2325]], dtype=torch.float64) >>> gpu1 = torch.device("cuda:1") >>> linear.to(gpu1, dtype=torch.half, non_blocking=True) Linear(in_features=2, out_features=2, bias=True) >>> linear.weight Parameter containing: tensor([[ 0.1914, 0.3420], [0.5112, 0.2324]], dtype=torch.float16, device='cuda:1') >>> cpu = torch.device("cpu") >>> linear.to(cpu) Linear(in_features=2, out_features=2, bias=True) >>> linear.weight Parameter containing: tensor([[ 0.1914, 0.3420], [0.5112, 0.2324]], dtype=torch.float16)


train
(mode=True)[source]¶ Sets the module in training mode.
This has any effect only on certain modules. See documentations of particular modules for details of their behaviors in training/evaluation mode, if they are affected, e.g.
Dropout
,BatchNorm
, etc. Returns
self
 Return type

Sequential¶

class
torch.nn.
Sequential
(*args)[source]¶ A sequential container. Modules will be added to it in the order they are passed in the constructor. Alternatively, an ordered dict of modules can also be passed in.
To make it easier to understand, here is a small example:
# Example of using Sequential model = nn.Sequential( nn.Conv2d(1,20,5), nn.ReLU(), nn.Conv2d(20,64,5), nn.ReLU() ) # Example of using Sequential with OrderedDict model = nn.Sequential(OrderedDict([ ('conv1', nn.Conv2d(1,20,5)), ('relu1', nn.ReLU()), ('conv2', nn.Conv2d(20,64,5)), ('relu2', nn.ReLU()) ]))
ModuleList¶

class
torch.nn.
ModuleList
(modules=None)[source]¶ Holds submodules in a list.
ModuleList
can be indexed like a regular Python list, but modules it contains are properly registered, and will be visible by allModule
methods. Parameters
modules (iterable, optional) – an iterable of modules to add
Example:
class MyModule(nn.Module): def __init__(self): super(MyModule, self).__init__() self.linears = nn.ModuleList([nn.Linear(10, 10) for i in range(10)]) def forward(self, x): # ModuleList can act as an iterable, or be indexed using ints for i, l in enumerate(self.linears): x = self.linears[i // 2](x) + l(x) return x

append
(module)[source]¶ Appends a given module to the end of the list.
 Parameters
module (nn.Module) – module to append
ModuleDict¶

class
torch.nn.
ModuleDict
(modules=None)[source]¶ Holds submodules in a dictionary.
ModuleDict
can be indexed like a regular Python dictionary, but modules it contains are properly registered, and will be visible by allModule
methods.ModuleDict
is an ordered dictionary that respectsthe order of insertion, and
in
update()
, the order of the mergedOrderedDict
or anotherModuleDict
(the argument toupdate()
).
Note that
update()
with other unordered mapping types (e.g., Python’s plaindict
) does not preserve the order of the merged mapping. Parameters
modules (iterable, optional) – a mapping (dictionary) of (string: module) or an iterable of keyvalue pairs of type (string, module)
Example:
class MyModule(nn.Module): def __init__(self): super(MyModule, self).__init__() self.choices = nn.ModuleDict({ 'conv': nn.Conv2d(10, 10, 3), 'pool': nn.MaxPool2d(3) }) self.activations = nn.ModuleDict([ ['lrelu', nn.LeakyReLU()], ['prelu', nn.PReLU()] ]) def forward(self, x, choice, act): x = self.choices[choice](x) x = self.activations[act](x) return x

pop
(key)[source]¶ Remove key from the ModuleDict and return its module.
 Parameters
key (string) – key to pop from the ModuleDict

update
(modules)[source]¶ Update the
ModuleDict
with the keyvalue pairs from a mapping or an iterable, overwriting existing keys.Note
If
modules
is anOrderedDict
, aModuleDict
, or an iterable of keyvalue pairs, the order of new elements in it is preserved.
ParameterList¶

class
torch.nn.
ParameterList
(parameters=None)[source]¶ Holds parameters in a list.
ParameterList
can be indexed like a regular Python list, but parameters it contains are properly registered, and will be visible by allModule
methods. Parameters
parameters (iterable, optional) – an iterable of
Parameter
to add
Example:
class MyModule(nn.Module): def __init__(self): super(MyModule, self).__init__() self.params = nn.ParameterList([nn.Parameter(torch.randn(10, 10)) for i in range(10)]) def forward(self, x): # ParameterList can act as an iterable, or be indexed using ints for i, p in enumerate(self.params): x = self.params[i // 2].mm(x) + p.mm(x) return x

append
(parameter)[source]¶ Appends a given parameter at the end of the list.
 Parameters
parameter (nn.Parameter) – parameter to append
ParameterDict¶

class
torch.nn.
ParameterDict
(parameters=None)[source]¶ Holds parameters in a dictionary.
ParameterDict can be indexed like a regular Python dictionary, but parameters it contains are properly registered, and will be visible by all Module methods.
ParameterDict
is an ordered dictionary that respectsthe order of insertion, and
in
update()
, the order of the mergedOrderedDict
or anotherParameterDict
(the argument toupdate()
).
Note that
update()
with other unordered mapping types (e.g., Python’s plaindict
) does not preserve the order of the merged mapping. Parameters
parameters (iterable, optional) – a mapping (dictionary) of (string :
Parameter
) or an iterable of keyvalue pairs of type (string,Parameter
)
Example:
class MyModule(nn.Module): def __init__(self): super(MyModule, self).__init__() self.params = nn.ParameterDict({ 'left': nn.Parameter(torch.randn(5, 10)), 'right': nn.Parameter(torch.randn(5, 10)) }) def forward(self, x, choice): x = self.params[choice].mm(x) return x

pop
(key)[source]¶ Remove key from the ParameterDict and return its parameter.
 Parameters
key (string) – key to pop from the ParameterDict

update
(parameters)[source]¶ Update the
ParameterDict
with the keyvalue pairs from a mapping or an iterable, overwriting existing keys.Note
If
parameters
is anOrderedDict
, aParameterDict
, or an iterable of keyvalue pairs, the order of new elements in it is preserved.
Convolution layers¶
Conv1d¶

class
torch.nn.
Conv1d
(in_channels, out_channels, kernel_size, stride=1, padding=0, dilation=1, groups=1, bias=True, padding_mode='zeros')[source]¶ Applies a 1D convolution over an input signal composed of several input planes.
In the simplest case, the output value of the layer with input size \((N, C_{\text{in}}, L)\) and output \((N, C_{\text{out}}, L_{\text{out}})\) can be precisely described as:
\[\text{out}(N_i, C_{\text{out}_j}) = \text{bias}(C_{\text{out}_j}) + \sum_{k = 0}^{C_{in}  1} \text{weight}(C_{\text{out}_j}, k) \star \text{input}(N_i, k) \]where \(\star\) is the valid crosscorrelation operator, \(N\) is a batch size, \(C\) denotes a number of channels, \(L\) is a length of signal sequence.
stride
controls the stride for the crosscorrelation, a single number or a oneelement tuple.padding
controls the amount of implicit zeropaddings on both sides forpadding
number of points.dilation
controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but this link has a nice visualization of whatdilation
does.groups
controls the connections between inputs and outputs.in_channels
andout_channels
must both be divisible bygroups
. For example,At groups=1, all inputs are convolved to all outputs.
At groups=2, the operation becomes equivalent to having two conv layers side by side, each seeing half the input channels, and producing half the output channels, and both subsequently concatenated.
At groups=
in_channels
, each input channel is convolved with its own set of filters, of size \(\left\lfloor\frac{out\_channels}{in\_channels}\right\rfloor\).
Note
Depending of the size of your kernel, several (of the last) columns of the input might be lost, because it is a valid crosscorrelation, and not a full crosscorrelation. It is up to the user to add proper padding.
Note
When groups == in_channels and out_channels == K * in_channels, where K is a positive integer, this operation is also termed in literature as depthwise convolution.
In other words, for an input of size \((N, C_{in}, L_{in})\), a depthwise convolution with a depthwise multiplier K, can be constructed by arguments \((C_\text{in}=C_{in}, C_\text{out}=C_{in} \times K, ..., \text{groups}=C_{in})\).
Note
In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting
torch.backends.cudnn.deterministic = True
. Please see the notes on Reproducibility for background. Parameters
in_channels (int) – Number of channels in the input image
out_channels (int) – Number of channels produced by the convolution
stride (int or tuple, optional) – Stride of the convolution. Default: 1
padding (int or tuple, optional) – Zeropadding added to both sides of the input. Default: 0
padding_mode (string, optional) – zeros
dilation (int or tuple, optional) – Spacing between kernel elements. Default: 1
groups (int, optional) – Number of blocked connections from input channels to output channels. Default: 1
bias (bool, optional) – If
True
, adds a learnable bias to the output. Default:True
 Shape:
Input: \((N, C_{in}, L_{in})\)
Output: \((N, C_{out}, L_{out})\) where
\[L_{out} = \left\lfloor\frac{L_{in} + 2 \times \text{padding}  \text{dilation} \times (\text{kernel\_size}  1)  1}{\text{stride}} + 1\right\rfloor \]
 Variables
~Conv1d.weight (Tensor) – the learnable weights of the module of shape \((\text{out\_channels}, \frac{\text{in\_channels}}{\text{groups}}, \text{kernel\_size})\). The values of these weights are sampled from \(\mathcal{U}(\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{C_\text{in} * \text{kernel\_size}}\)
~Conv1d.bias (Tensor) – the learnable bias of the module of shape (out_channels). If
bias
isTrue
, then the values of these weights are sampled from \(\mathcal{U}(\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{C_\text{in} * \text{kernel\_size}}\)
Examples:
>>> m = nn.Conv1d(16, 33, 3, stride=2) >>> input = torch.randn(20, 16, 50) >>> output = m(input)
Conv2d¶

class
torch.nn.
Conv2d
(in_channels, out_channels, kernel_size, stride=1, padding=0, dilation=1, groups=1, bias=True, padding_mode='zeros')[source]¶ Applies a 2D convolution over an input signal composed of several input planes.
In the simplest case, the output value of the layer with input size \((N, C_{\text{in}}, H, W)\) and output \((N, C_{\text{out}}, H_{\text{out}}, W_{\text{out}})\) can be precisely described as:
\[\text{out}(N_i, C_{\text{out}_j}) = \text{bias}(C_{\text{out}_j}) + \sum_{k = 0}^{C_{\text{in}}  1} \text{weight}(C_{\text{out}_j}, k) \star \text{input}(N_i, k) \]where \(\star\) is the valid 2D crosscorrelation operator, \(N\) is a batch size, \(C\) denotes a number of channels, \(H\) is a height of input planes in pixels, and \(W\) is width in pixels.
stride
controls the stride for the crosscorrelation, a single number or a tuple.padding
controls the amount of implicit zeropaddings on both sides forpadding
number of points for each dimension.dilation
controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but this link has a nice visualization of whatdilation
does.groups
controls the connections between inputs and outputs.in_channels
andout_channels
must both be divisible bygroups
. For example,At groups=1, all inputs are convolved to all outputs.
At groups=2, the operation becomes equivalent to having two conv layers side by side, each seeing half the input channels, and producing half the output channels, and both subsequently concatenated.
At groups=
in_channels
, each input channel is convolved with its own set of filters, of size: \(\left\lfloor\frac{out\_channels}{in\_channels}\right\rfloor\).
The parameters
kernel_size
,stride
,padding
,dilation
can either be:a single
int
– in which case the same value is used for the height and width dimensiona
tuple
of two ints – in which case, the first int is used for the height dimension, and the second int for the width dimension
Note
Depending of the size of your kernel, several (of the last) columns of the input might be lost, because it is a valid crosscorrelation, and not a full crosscorrelation. It is up to the user to add proper padding.
Note
When groups == in_channels and out_channels == K * in_channels, where K is a positive integer, this operation is also termed in literature as depthwise convolution.
In other words, for an input of size \((N, C_{in}, H_{in}, W_{in})\), a depthwise convolution with a depthwise multiplier K, can be constructed by arguments \((in\_channels=C_{in}, out\_channels=C_{in} \times K, ..., groups=C_{in})\).
Note
In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting
torch.backends.cudnn.deterministic = True
. Please see the notes on Reproducibility for background. Parameters
in_channels (int) – Number of channels in the input image
out_channels (int) – Number of channels produced by the convolution
stride (int or tuple, optional) – Stride of the convolution. Default: 1
padding (int or tuple, optional) – Zeropadding added to both sides of the input. Default: 0
padding_mode (string, optional) – zeros
dilation (int or tuple, optional) – Spacing between kernel elements. Default: 1
groups (int, optional) – Number of blocked connections from input channels to output channels. Default: 1
bias (bool, optional) – If
True
, adds a learnable bias to the output. Default:True
 Shape:
Input: \((N, C_{in}, H_{in}, W_{in})\)
Output: \((N, C_{out}, H_{out}, W_{out})\) where
\[H_{out} = \left\lfloor\frac{H_{in} + 2 \times \text{padding}[0]  \text{dilation}[0] \times (\text{kernel\_size}[0]  1)  1}{\text{stride}[0]} + 1\right\rfloor \]\[W_{out} = \left\lfloor\frac{W_{in} + 2 \times \text{padding}[1]  \text{dilation}[1] \times (\text{kernel\_size}[1]  1)  1}{\text{stride}[1]} + 1\right\rfloor \]
 Variables
~Conv2d.weight (Tensor) – the learnable weights of the module of shape \((\text{out\_channels}, \frac{\text{in\_channels}}{\text{groups}},\) \(\text{kernel\_size[0]}, \text{kernel\_size[1]})\). The values of these weights are sampled from \(\mathcal{U}(\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{C_\text{in} * \prod_{i=0}^{1}\text{kernel\_size}[i]}\)
~Conv2d.bias (Tensor) – the learnable bias of the module of shape (out_channels). If
bias
isTrue
, then the values of these weights are sampled from \(\mathcal{U}(\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{C_\text{in} * \prod_{i=0}^{1}\text{kernel\_size}[i]}\)
Examples:
>>> # With square kernels and equal stride >>> m = nn.Conv2d(16, 33, 3, stride=2) >>> # nonsquare kernels and unequal stride and with padding >>> m = nn.Conv2d(16, 33, (3, 5), stride=(2, 1), padding=(4, 2)) >>> # nonsquare kernels and unequal stride and with padding and dilation >>> m = nn.Conv2d(16, 33, (3, 5), stride=(2, 1), padding=(4, 2), dilation=(3, 1)) >>> input = torch.randn(20, 16, 50, 100) >>> output = m(input)
Conv3d¶

class
torch.nn.
Conv3d
(in_channels, out_channels, kernel_size, stride=1, padding=0, dilation=1, groups=1, bias=True, padding_mode='zeros')[source]¶ Applies a 3D convolution over an input signal composed of several input planes.
In the simplest case, the output value of the layer with input size \((N, C_{in}, D, H, W)\) and output \((N, C_{out}, D_{out}, H_{out}, W_{out})\) can be precisely described as:
\[out(N_i, C_{out_j}) = bias(C_{out_j}) + \sum_{k = 0}^{C_{in}  1} weight(C_{out_j}, k) \star input(N_i, k) \]where \(\star\) is the valid 3D crosscorrelation operator
stride
controls the stride for the crosscorrelation.padding
controls the amount of implicit zeropaddings on both sides forpadding
number of points for each dimension.dilation
controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but this link has a nice visualization of whatdilation
does.groups
controls the connections between inputs and outputs.in_channels
andout_channels
must both be divisible bygroups
. For example,At groups=1, all inputs are convolved to all outputs.
At groups=2, the operation becomes equivalent to having two conv layers side by side, each seeing half the input channels, and producing half the output channels, and both subsequently concatenated.
At groups=
in_channels
, each input channel is convolved with its own set of filters, of size \(\left\lfloor\frac{out\_channels}{in\_channels}\right\rfloor\).
The parameters
kernel_size
,stride
,padding
,dilation
can either be:a single
int
– in which case the same value is used for the depth, height and width dimensiona
tuple
of three ints – in which case, the first int is used for the depth dimension, the second int for the height dimension and the third int for the width dimension
Note
Depending of the size of your kernel, several (of the last) columns of the input might be lost, because it is a valid crosscorrelation, and not a full crosscorrelation. It is up to the user to add proper padding.
Note
When groups == in_channels and out_channels == K * in_channels, where K is a positive integer, this operation is also termed in literature as depthwise convolution.
In other words, for an input of size \((N, C_{in}, D_{in}, H_{in}, W_{in})\), a depthwise convolution with a depthwise multiplier K, can be constructed by arguments \((in\_channels=C_{in}, out\_channels=C_{in} \times K, ..., groups=C_{in})\).
Note
In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting
torch.backends.cudnn.deterministic = True
. Please see the notes on Reproducibility for background. Parameters
in_channels (int) – Number of channels in the input image
out_channels (int) – Number of channels produced by the convolution
stride (int or tuple, optional) – Stride of the convolution. Default: 1
padding (int or tuple, optional) – Zeropadding added to all three sides of the input. Default: 0
padding_mode (string, optional) – zeros
dilation (int or tuple, optional) – Spacing between kernel elements. Default: 1
groups (int, optional) – Number of blocked connections from input channels to output channels. Default: 1
bias (bool, optional) – If
True
, adds a learnable bias to the output. Default:True
 Shape:
Input: \((N, C_{in}, D_{in}, H_{in}, W_{in})\)
Output: \((N, C_{out}, D_{out}, H_{out}, W_{out})\) where
\[D_{out} = \left\lfloor\frac{D_{in} + 2 \times \text{padding}[0]  \text{dilation}[0] \times (\text{kernel\_size}[0]  1)  1}{\text{stride}[0]} + 1\right\rfloor \]\[H_{out} = \left\lfloor\frac{H_{in} + 2 \times \text{padding}[1]  \text{dilation}[1] \times (\text{kernel\_size}[1]  1)  1}{\text{stride}[1]} + 1\right\rfloor \]\[W_{out} = \left\lfloor\frac{W_{in} + 2 \times \text{padding}[2]  \text{dilation}[2] \times (\text{kernel\_size}[2]  1)  1}{\text{stride}[2]} + 1\right\rfloor \]
 Variables
~Conv3d.weight (Tensor) – the learnable weights of the module of shape \((\text{out\_channels}, \frac{\text{in\_channels}}{\text{groups}},\) \(\text{kernel\_size[0]}, \text{kernel\_size[1]}, \text{kernel\_size[2]})\). The values of these weights are sampled from \(\mathcal{U}(\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{C_\text{in} * \prod_{i=0}^{2}\text{kernel\_size}[i]}\)
~Conv3d.bias (Tensor) – the learnable bias of the module of shape (out_channels). If
bias
isTrue
, then the values of these weights are sampled from \(\mathcal{U}(\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{C_\text{in} * \prod_{i=0}^{2}\text{kernel\_size}[i]}\)
Examples:
>>> # With square kernels and equal stride >>> m = nn.Conv3d(16, 33, 3, stride=2) >>> # nonsquare kernels and unequal stride and with padding >>> m = nn.Conv3d(16, 33, (3, 5, 2), stride=(2, 1, 1), padding=(4, 2, 0)) >>> input = torch.randn(20, 16, 10, 50, 100) >>> output = m(input)
ConvTranspose1d¶

class
torch.nn.
ConvTranspose1d
(in_channels, out_channels, kernel_size, stride=1, padding=0, output_padding=0, groups=1, bias=True, dilation=1, padding_mode='zeros')[source]¶ Applies a 1D transposed convolution operator over an input image composed of several input planes.
This module can be seen as the gradient of Conv1d with respect to its input. It is also known as a fractionallystrided convolution or a deconvolution (although it is not an actual deconvolution operation).
stride
controls the stride for the crosscorrelation.padding
controls the amount of implicit zeropaddings on both sides fordilation * (kernel_size  1)  padding
number of points. See note below for details.output_padding
controls the additional size added to one side of the output shape. See note below for details.dilation
controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but this link has a nice visualization of whatdilation
does.groups
controls the connections between inputs and outputs.in_channels
andout_channels
must both be divisible bygroups
. For example,At groups=1, all inputs are convolved to all outputs.
At groups=2, the operation becomes equivalent to having two conv layers side by side, each seeing half the input channels, and producing half the output channels, and both subsequently concatenated.
At groups=
in_channels
, each input channel is convolved with its own set of filters (of size \(\left\lfloor\frac{out\_channels}{in\_channels}\right\rfloor\)).
Note
Depending of the size of your kernel, several (of the last) columns of the input might be lost, because it is a valid crosscorrelation, and not a full crosscorrelation. It is up to the user to add proper padding.
Note
The
padding
argument effectively addsdilation * (kernel_size  1)  padding
amount of zero padding to both sizes of the input. This is set so that when aConv1d
and aConvTranspose1d
are initialized with same parameters, they are inverses of each other in regard to the input and output shapes. However, whenstride > 1
,Conv1d
maps multiple input shapes to the same output shape.output_padding
is provided to resolve this ambiguity by effectively increasing the calculated output shape on one side. Note thatoutput_padding
is only used to find output shape, but does not actually add zeropadding to output.Note
In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting
torch.backends.cudnn.deterministic = True
. Please see the notes on Reproducibility for background. Parameters
in_channels (int) – Number of channels in the input image
out_channels (int) – Number of channels produced by the convolution
stride (int or tuple, optional) – Stride of the convolution. Default: 1
padding (int or tuple, optional) –
dilation * (kernel_size  1)  padding
zeropadding will be added to both sides of the input. Default: 0output_padding (int or tuple, optional) – Additional size added to one side of the output shape. Default: 0
groups (int, optional) – Number of blocked connections from input channels to output channels. Default: 1
bias (bool, optional) – If
True
, adds a learnable bias to the output. Default:True
dilation (int or tuple, optional) – Spacing between kernel elements. Default: 1
 Shape:
Input: \((N, C_{in}, L_{in})\)
Output: \((N, C_{out}, L_{out})\) where
\[L_{out} = (L_{in}  1) \times \text{stride}  2 \times \text{padding} + \text{dilation} \times (\text{kernel\_size}  1) + \text{output\_padding} + 1 \]
 Variables
~ConvTranspose1d.weight (Tensor) – the learnable weights of the module of shape \((\text{in\_channels}, \frac{\text{out\_channels}}{\text{groups}},\) \(\text{kernel\_size})\). The values of these weights are sampled from \(\mathcal{U}(\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{C_\text{in} * \text{kernel\_size}}\)
~ConvTranspose1d.bias (Tensor) – the learnable bias of the module of shape (out_channels). If
bias
isTrue
, then the values of these weights are sampled from \(\mathcal{U}(\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{C_\text{in} * \text{kernel\_size}}\)
ConvTranspose2d¶

class
torch.nn.
ConvTranspose2d
(in_channels, out_channels, kernel_size, stride=1, padding=0, output_padding=0, groups=1, bias=True, dilation=1, padding_mode='zeros')[source]¶ Applies a 2D transposed convolution operator over an input image composed of several input planes.
This module can be seen as the gradient of Conv2d with respect to its input. It is also known as a fractionallystrided convolution or a deconvolution (although it is not an actual deconvolution operation).
stride
controls the stride for the crosscorrelation.padding
controls the amount of implicit zeropaddings on both sides fordilation * (kernel_size  1)  padding
number of points. See note below for details.output_padding
controls the additional size added to one side of the output shape. See note below for details.dilation
controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but this link has a nice visualization of whatdilation
does.groups
controls the connections between inputs and outputs.in_channels
andout_channels
must both be divisible bygroups
. For example,At groups=1, all inputs are convolved to all outputs.
At groups=2, the operation becomes equivalent to having two conv layers side by side, each seeing half the input channels, and producing half the output channels, and both subsequently concatenated.
At groups=
in_channels
, each input channel is convolved with its own set of filters (of size \(\left\lfloor\frac{out\_channels}{in\_channels}\right\rfloor\)).
The parameters
kernel_size
,stride
,padding
,output_padding
can either be:a single
int
– in which case the same value is used for the height and width dimensionsa
tuple
of two ints – in which case, the first int is used for the height dimension, and the second int for the width dimension
Note
Depending of the size of your kernel, several (of the last) columns of the input might be lost, because it is a valid crosscorrelation, and not a full crosscorrelation. It is up to the user to add proper padding.
Note
The
padding
argument effectively addsdilation * (kernel_size  1)  padding
amount of zero padding to both sizes of the input. This is set so that when aConv2d
and aConvTranspose2d
are initialized with same parameters, they are inverses of each other in regard to the input and output shapes. However, whenstride > 1
,Conv2d
maps multiple input shapes to the same output shape.output_padding
is provided to resolve this ambiguity by effectively increasing the calculated output shape on one side. Note thatoutput_padding
is only used to find output shape, but does not actually add zeropadding to output.Note
In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting
torch.backends.cudnn.deterministic = True
. Please see the notes on Reproducibility for background. Parameters
in_channels (int) – Number of channels in the input image
out_channels (int) – Number of channels produced by the convolution
stride (int or tuple, optional) – Stride of the convolution. Default: 1
padding (int or tuple, optional) –
dilation * (kernel_size  1)  padding
zeropadding will be added to both sides of each dimension in the input. Default: 0output_padding (int or tuple, optional) – Additional size added to one side of each dimension in the output shape. Default: 0
groups (int, optional) – Number of blocked connections from input channels to output channels. Default: 1
bias (bool, optional) – If
True
, adds a learnable bias to the output. Default:True
dilation (int or tuple, optional) – Spacing between kernel elements. Default: 1
 Shape:
Input: \((N, C_{in}, H_{in}, W_{in})\)
Output: \((N, C_{out}, H_{out}, W_{out})\) where
\[H_{out} = (H_{in}  1) \times \text{stride}[0]  2 \times \text{padding}[0] + \text{dilation}[0] \times (\text{kernel\_size}[0]  1) + \text{output\_padding}[0] + 1 \]\[W_{out} = (W_{in}  1) \times \text{stride}[1]  2 \times \text{padding}[1] + \text{dilation}[1] \times (\text{kernel\_size}[1]  1) + \text{output\_padding}[1] + 1 \]
 Variables
~ConvTranspose2d.weight (Tensor) – the learnable weights of the module of shape \((\text{in\_channels}, \frac{\text{out\_channels}}{\text{groups}},\) \(\text{kernel\_size[0]}, \text{kernel\_size[1]})\). The values of these weights are sampled from \(\mathcal{U}(\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{C_\text{in} * \prod_{i=0}^{1}\text{kernel\_size}[i]}\)
~ConvTranspose2d.bias (Tensor) – the learnable bias of the module of shape (out_channels) If
bias
isTrue
, then the values of these weights are sampled from \(\mathcal{U}(\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{C_\text{in} * \prod_{i=0}^{1}\text{kernel\_size}[i]}\)
Examples:
>>> # With square kernels and equal stride >>> m = nn.ConvTranspose2d(16, 33, 3, stride=2) >>> # nonsquare kernels and unequal stride and with padding >>> m = nn.ConvTranspose2d(16, 33, (3, 5), stride=(2, 1), padding=(4, 2)) >>> input = torch.randn(20, 16, 50, 100) >>> output = m(input) >>> # exact output size can be also specified as an argument >>> input = torch.randn(1, 16, 12, 12) >>> downsample = nn.Conv2d(16, 16, 3, stride=2, padding=1) >>> upsample = nn.ConvTranspose2d(16, 16, 3, stride=2, padding=1) >>> h = downsample(input) >>> h.size() torch.Size([1, 16, 6, 6]) >>> output = upsample(h, output_size=input.size()) >>> output.size() torch.Size([1, 16, 12, 12])
ConvTranspose3d¶

class
torch.nn.
ConvTranspose3d
(in_channels, out_channels, kernel_size, stride=1, padding=0, output_padding=0, groups=1, bias=True, dilation=1, padding_mode='zeros')[source]¶ Applies a 3D transposed convolution operator over an input image composed of several input planes. The transposed convolution operator multiplies each input value elementwise by a learnable kernel, and sums over the outputs from all input feature planes.
This module can be seen as the gradient of Conv3d with respect to its input. It is also known as a fractionallystrided convolution or a deconvolution (although it is not an actual deconvolution operation).
stride
controls the stride for the crosscorrelation.padding
controls the amount of implicit zeropaddings on both sides fordilation * (kernel_size  1)  padding
number of points. See note below for details.output_padding
controls the additional size added to one side of the output shape. See note below for details.dilation
controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but this link has a nice visualization of whatdilation
does.groups
controls the connections between inputs and outputs.in_channels
andout_channels
must both be divisible bygroups
. For example,At groups=1, all inputs are convolved to all outputs.
At groups=2, the operation becomes equivalent to having two conv layers side by side, each seeing half the input channels, and producing half the output channels, and both subsequently concatenated.
At groups=
in_channels
, each input channel is convolved with its own set of filters (of size \(\left\lfloor\frac{out\_channels}{in\_channels}\right\rfloor\)).
The parameters
kernel_size
,stride
,padding
,output_padding
can either be:a single
int
– in which case the same value is used for the depth, height and width dimensionsa
tuple
of three ints – in which case, the first int is used for the depth dimension, the second int for the height dimension and the third int for the width dimension
Note
Depending of the size of your kernel, several (of the last) columns of the input might be lost, because it is a valid crosscorrelation, and not a full crosscorrelation. It is up to the user to add proper padding.
Note
The
padding
argument effectively addsdilation * (kernel_size  1)  padding
amount of zero padding to both sizes of the input. This is set so that when aConv3d
and aConvTranspose3d
are initialized with same parameters, they are inverses of each other in regard to the input and output shapes. However, whenstride > 1
,Conv3d
maps multiple input shapes to the same output shape.output_padding
is provided to resolve this ambiguity by effectively increasing the calculated output shape on one side. Note thatoutput_padding
is only used to find output shape, but does not actually add zeropadding to output.Note
In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting
torch.backends.cudnn.deterministic = True
. Please see the notes on Reproducibility for background. Parameters
in_channels (int) – Number of channels in the input image
out_channels (int) – Number of channels produced by the convolution
stride (int or tuple, optional) – Stride of the convolution. Default: 1
padding (int or tuple, optional) –
dilation * (kernel_size  1)  padding
zeropadding will be added to both sides of each dimension in the input. Default: 0output_padding (int or tuple, optional) – Additional size added to one side of each dimension in the output shape. Default: 0
groups (int, optional) – Number of blocked connections from input channels to output channels. Default: 1
bias (bool, optional) – If
True
, adds a learnable bias to the output. Default:True
dilation (int or tuple, optional) – Spacing between kernel elements. Default: 1
 Shape:
Input: \((N, C_{in}, D_{in}, H_{in}, W_{in})\)
Output: \((N, C_{out}, D_{out}, H_{out}, W_{out})\) where
\[D_{out} = (D_{in}  1) \times \text{stride}[0]  2 \times \text{padding}[0] + \text{dilation}[0] \times (\text{kernel\_size}[0]  1) + \text{output\_padding}[0] + 1 \]\[H_{out} = (H_{in}  1) \times \text{stride}[1]  2 \times \text{padding}[1] + \text{dilation}[1] \times (\text{kernel\_size}[1]  1) + \text{output\_padding}[1] + 1 \]\[W_{out} = (W_{in}  1) \times \text{stride}[2]  2 \times \text{padding}[2] + \text{dilation}[2] \times (\text{kernel\_size}[2]  1) + \text{output\_padding}[2] + 1 \]
 Variables
~ConvTranspose3d.weight (Tensor) – the learnable weights of the module of shape \((\text{in\_channels}, \frac{\text{out\_channels}}{\text{groups}},\) \(\text{kernel\_size[0]}, \text{kernel\_size[1]}, \text{kernel\_size[2]})\). The values of these weights are sampled from \(\mathcal{U}(\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{C_\text{in} * \prod_{i=0}^{2}\text{kernel\_size}[i]}\)
~ConvTranspose3d.bias (Tensor) – the learnable bias of the module of shape (out_channels) If
bias
isTrue
, then the values of these weights are sampled from \(\mathcal{U}(\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{C_\text{in} * \prod_{i=0}^{2}\text{kernel\_size}[i]}\)
Examples:
>>> # With square kernels and equal stride >>> m = nn.ConvTranspose3d(16, 33, 3, stride=2) >>> # nonsquare kernels and unequal stride and with padding >>> m = nn.ConvTranspose3d(16, 33, (3, 5, 2), stride=(2, 1, 1), padding=(0, 4, 2)) >>> input = torch.randn(20, 16, 10, 50, 100) >>> output = m(input)
Unfold¶

class
torch.nn.
Unfold
(kernel_size, dilation=1, padding=0, stride=1)[source]¶ Extracts sliding local blocks from a batched input tensor.
Consider an batched
input
tensor of shape \((N, C, *)\), where \(N\) is the batch dimension, \(C\) is the channel dimension, and \(*\) represent arbitrary spatial dimensions. This operation flattens each slidingkernel_size
sized block within the spatial dimensions ofinput
into a column (i.e., last dimension) of a 3Doutput
tensor of shape \((N, C \times \prod(\text{kernel\_size}), L)\), where \(C \times \prod(\text{kernel\_size})\) is the total number of values within each block (a block has \(\prod(\text{kernel\_size})\) spatial locations each containing a \(C\)channeled vector), and \(L\) is the total number of such blocks:\[L = \prod_d \left\lfloor\frac{\text{spatial\_size}[d] + 2 \times \text{padding}[d] %  \text{dilation}[d] \times (\text{kernel\_size}[d]  1)  1}{\text{stride}[d]} + 1\right\rfloor, \]where \(\text{spatial\_size}\) is formed by the spatial dimensions of
input
(\(*\) above), and \(d\) is over all spatial dimensions.Therefore, indexing
output
at the last dimension (column dimension) gives all values within a certain block.The
padding
,stride
anddilation
arguments specify how the sliding blocks are retrieved.stride
controls the stride for the sliding blocks.padding
controls the amount of implicit zeropaddings on both sides forpadding
number of points for each dimension before reshaping.dilation
controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but this link has a nice visualization of whatdilation
does.
 Parameters
stride (int or tuple, optional) – the stride of the sliding blocks in the input spatial dimensions. Default: 1
padding (int or tuple, optional) – implicit zero padding to be added on both sides of input. Default: 0
dilation (int or tuple, optional) – a parameter that controls the stride of elements within the neighborhood. Default: 1
If
kernel_size
,dilation
,padding
orstride
is an int or a tuple of length 1, their values will be replicated across all spatial dimensions.For the case of two input spatial dimensions this operation is sometimes called
im2col
.
Note
Fold
calculates each combined value in the resulting large tensor by summing all values from all containing blocks.Unfold
extracts the values in the local blocks by copying from the large tensor. So, if the blocks overlap, they are not inverses of each other.Warning
Currently, only 4D input tensors (batched imagelike tensors) are supported.
 Shape:
Input: \((N, C, *)\)
Output: \((N, C \times \prod(\text{kernel\_size}), L)\) as described above
Examples:
>>> unfold = nn.Unfold(kernel_size=(2, 3)) >>> input = torch.randn(2, 5, 3, 4) >>> output = unfold(input) >>> # each patch contains 30 values (2x3=6 vectors, each of 5 channels) >>> # 4 blocks (2x3 kernels) in total in the 3x4 input >>> output.size() torch.Size([2, 30, 4]) >>> # Convolution is equivalent with Unfold + Matrix Multiplication + Fold (or view to output shape) >>> inp = torch.randn(1, 3, 10, 12) >>> w = torch.randn(2, 3, 4, 5) >>> inp_unf = torch.nn.functional.unfold(inp, (4, 5)) >>> out_unf = inp_unf.transpose(1, 2).matmul(w.view(w.size(0), 1).t()).transpose(1, 2) >>> out = torch.nn.functional.fold(out_unf, (7, 8), (1, 1)) >>> # or equivalently (and avoiding a copy), >>> # out = out_unf.view(1, 2, 7, 8) >>> (torch.nn.functional.conv2d(inp, w)  out).abs().max() tensor(1.9073e06)
Fold¶

class
torch.nn.
Fold
(output_size, kernel_size, dilation=1, padding=0, stride=1)[source]¶ Combines an array of sliding local blocks into a large containing tensor.
Consider a batched
input
tensor containing sliding local blocks, e.g., patches of images, of shape \((N, C \times \prod(\text{kernel\_size}), L)\), where \(N\) is batch dimension, \(C \times \prod(\text{kernel\_size})\) is the number of values within a block (a block has \(\prod(\text{kernel\_size})\) spatial locations each containing a \(C\)channeled vector), and \(L\) is the total number of blocks. (This is exactly the same specification as the output shape ofUnfold
.) This operation combines these local blocks into the largeoutput
tensor of shape \((N, C, \text{output\_size}[0], \text{output\_size}[1], \dots)\) by summing the overlapping values. Similar toUnfold
, the arguments must satisfy\[L = \prod_d \left\lfloor\frac{\text{output\_size}[d] + 2 \times \text{padding}[d] %  \text{dilation}[d] \times (\text{kernel\_size}[d]  1)  1}{\text{stride}[d]} + 1\right\rfloor, \]where \(d\) is over all spatial dimensions.
output_size
describes the spatial shape of the large containing tensor of the sliding local blocks. It is useful to resolve the ambiguity when multiple input shapes map to same number of sliding blocks, e.g., withstride > 0
.
The
padding
,stride
anddilation
arguments specify how the sliding blocks are retrieved.stride
controls the stride for the sliding blocks.padding
controls the amount of implicit zeropaddings on both sides forpadding
number of points for each dimension before reshaping.dilation
controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but this link has a nice visualization of whatdilation
does.
 Parameters
output_size (int or tuple) – the shape of the spatial dimensions of the output (i.e.,
output.sizes()[2:]
)stride (int or tuple) – the stride of the sliding blocks in the input spatial dimensions. Default: 1
padding (int or tuple, optional) – implicit zero padding to be added on both sides of input. Default: 0
dilation (int or tuple, optional) – a parameter that controls the stride of elements within the neighborhood. Default: 1
If
output_size
,kernel_size
,dilation
,padding
orstride
is an int or a tuple of length 1 then their values will be replicated across all spatial dimensions.For the case of two output spatial dimensions this operation is sometimes called
col2im
.
Note
Fold
calculates each combined value in the resulting large tensor by summing all values from all containing blocks.Unfold
extracts the values in the local blocks by copying from the large tensor. So, if the blocks overlap, they are not inverses of each other.Warning
Currently, only 4D output tensors (batched imagelike tensors) are supported.
 Shape:
Input: \((N, C \times \prod(\text{kernel\_size}), L)\)
Output: \((N, C, \text{output\_size}[0], \text{output\_size}[1], \dots)\) as described above
Examples:
>>> fold = nn.Fold(output_size=(4, 5), kernel_size=(2, 2)) >>> input = torch.randn(1, 3 * 2 * 2, 12) >>> output = fold(input) >>> output.size() torch.Size([1, 3, 4, 5])
Pooling layers¶
MaxPool1d¶

class
torch.nn.
MaxPool1d
(kernel_size, stride=None, padding=0, dilation=1, return_indices=False, ceil_mode=False)[source]¶ Applies a 1D max pooling over an input signal composed of several input planes.
In the simplest case, the output value of the layer with input size \((N, C, L)\) and output \((N, C, L_{out})\) can be precisely described as:
\[out(N_i, C_j, k) = \max_{m=0, \ldots, \text{kernel\_size}  1} input(N_i, C_j, stride \times k + m) \]If
padding
is nonzero, then the input is implicitly zeropadded on both sides forpadding
number of points.dilation
controls the spacing between the kernel points. It is harder to describe, but this link has a nice visualization of whatdilation
does. Parameters
kernel_size – the size of the window to take a max over
stride – the stride of the window. Default value is
kernel_size
padding – implicit zero padding to be added on both sides
dilation – a parameter that controls the stride of elements in the window
return_indices – if
True
, will return the max indices along with the outputs. Useful fortorch.nn.MaxUnpool1d
laterceil_mode – when True, will use ceil instead of floor to compute the output shape
 Shape:
Input: \((N, C, L_{in})\)
Output: \((N, C, L_{out})\), where
\[L_{out} = \left\lfloor \frac{L_{in} + 2 \times \text{padding}  \text{dilation} \times (\text{kernel\_size}  1)  1}{\text{stride}} + 1\right\rfloor \]
Examples:
>>> # pool of size=3, stride=2 >>> m = nn.MaxPool1d(3, stride=2) >>> input = torch.randn(20, 16, 50) >>> output = m(input)
MaxPool2d¶

class
torch.nn.
MaxPool2d
(kernel_size, stride=None, padding=0, dilation=1, return_indices=False, ceil_mode=False)[source]¶ Applies a 2D max pooling over an input signal composed of several input planes.
In the simplest case, the output value of the layer with input size \((N, C, H, W)\), output \((N, C, H_{out}, W_{out})\) and
kernel_size
\((kH, kW)\) can be precisely described as:\[\begin{aligned} out(N_i, C_j, h, w) ={} & \max_{m=0, \ldots, kH1} \max_{n=0, \ldots, kW1} \\ & \text{input}(N_i, C_j, \text{stride[0]} \times h + m, \text{stride[1]} \times w + n) \end{aligned} \]If
padding
is nonzero, then the input is implicitly zeropadded on both sides forpadding
number of points.dilation
controls the spacing between the kernel points. It is harder to describe, but this link has a nice visualization of whatdilation
does.The parameters
kernel_size
,stride
,padding
,dilation
can either be:a single
int
– in which case the same value is used for the height and width dimensiona
tuple
of two ints – in which case, the first int is used for the height dimension, and the second int for the width dimension
 Parameters
kernel_size – the size of the window to take a max over
stride – the stride of the window. Default value is
kernel_size
padding – implicit zero padding to be added on both sides
dilation – a parameter that controls the stride of elements in the window
return_indices – if
True
, will return the max indices along with the outputs. Useful fortorch.nn.MaxUnpool2d
laterceil_mode – when True, will use ceil instead of floor to compute the output shape
 Shape:
Input: \((N, C, H_{in}, W_{in})\)
Output: \((N, C, H_{out}, W_{out})\), where
\[H_{out} = \left\lfloor\frac{H_{in} + 2 * \text{padding[0]}  \text{dilation[0]} \times (\text{kernel\_size[0]}  1)  1}{\text{stride[0]}} + 1\right\rfloor \]\[W_{out} = \left\lfloor\frac{W_{in} + 2 * \text{padding[1]}  \text{dilation[1]} \times (\text{kernel\_size[1]}  1)  1}{\text{stride[1]}} + 1\right\rfloor \]
Examples:
>>> # pool of square window of size=3, stride=2 >>> m = nn.MaxPool2d(3, stride=2) >>> # pool of nonsquare window >>> m = nn.MaxPool2d((3, 2), stride=(2, 1)) >>> input = torch.randn(20, 16, 50, 32) >>> output = m(input)
MaxPool3d¶

class
torch.nn.
MaxPool3d
(kernel_size, stride=None, padding=0, dilation=1, return_indices=False, ceil_mode=False)[source]¶ Applies a 3D max pooling over an input signal composed of several input planes.
In the simplest case, the output value of the layer with input size \((N, C, D, H, W)\), output \((N, C, D_{out}, H_{out}, W_{out})\) and
kernel_size
\((kD, kH, kW)\) can be precisely described as:\[\begin{aligned} \text{out}(N_i, C_j, d, h, w) ={} & \max_{k=0, \ldots, kD1} \max_{m=0, \ldots, kH1} \max_{n=0, \ldots, kW1} \\ & \text{input}(N_i, C_j, \text{stride[0]} \times d + k, \text{stride[1]} \times h + m, \text{stride[2]} \times w + n) \end{aligned} \]If
padding
is nonzero, then the input is implicitly zeropadded on both sides forpadding
number of points.dilation
controls the spacing between the kernel points. It is harder to describe, but this link has a nice visualization of whatdilation
does.The parameters
kernel_size
,stride
,padding
,dilation
can either be:a single
int
– in which case the same value is used for the depth, height and width dimensiona
tuple
of three ints – in which case, the first int is used for the depth dimension, the second int for the height dimension and the third int for the width dimension
 Parameters
kernel_size – the size of the window to take a max over
stride – the stride of the window. Default value is
kernel_size
padding – implicit zero padding to be added on all three sides
dilation – a parameter that controls the stride of elements in the window
return_indices – if
True
, will return the max indices along with the outputs. Useful fortorch.nn.MaxUnpool3d
laterceil_mode – when True, will use ceil instead of floor to compute the output shape
 Shape:
Input: \((N, C, D_{in}, H_{in}, W_{in})\)
Output: \((N, C, D_{out}, H_{out}, W_{out})\), where
\[D_{out} = \left\lfloor\frac{D_{in} + 2 \times \text{padding}[0]  \text{dilation}[0] \times (\text{kernel\_size}[0]  1)  1}{\text{stride}[0]} + 1\right\rfloor \]\[H_{out} = \left\lfloor\frac{H_{in} + 2 \times \text{padding}[1]  \text{dilation}[1] \times (\text{kernel\_size}[1]  1)  1}{\text{stride}[1]} + 1\right\rfloor \]\[W_{out} = \left\lfloor\frac{W_{in} + 2 \times \text{padding}[2]  \text{dilation}[2] \times (\text{kernel\_size}[2]  1)  1}{\text{stride}[2]} + 1\right\rfloor \]
Examples:
>>> # pool of square window of size=3, stride=2 >>> m = nn.MaxPool3d(3, stride=2) >>> # pool of nonsquare window >>> m = nn.MaxPool3d((3, 2, 2), stride=(2, 1, 2)) >>> input = torch.randn(20, 16, 50,44, 31) >>> output = m(input)
MaxUnpool1d¶

class
torch.nn.
MaxUnpool1d
(kernel_size, stride=None, padding=0)[source]¶ Computes a partial inverse of
MaxPool1d
.MaxPool1d
is not fully invertible, since the nonmaximal values are lost.MaxUnpool1d
takes in as input the output ofMaxPool1d
including the indices of the maximal values and computes a partial inverse in which all nonmaximal values are set to zero.Note
MaxPool1d
can map several input sizes to the same output sizes. Hence, the inversion process can get ambiguous. To accommodate this, you can provide the needed output size as an additional argumentoutput_size
in the forward call. See the Inputs and Example below. Parameters
 Inputs:
input: the input Tensor to invert
indices: the indices given out by
MaxPool1d
output_size (optional): the targeted output size
 Shape:
Input: \((N, C, H_{in})\)
Output: \((N, C, H_{out})\), where
\[H_{out} = (H_{in}  1) \times \text{stride}[0]  2 \times \text{padding}[0] + \text{kernel\_size}[0] \]or as given by
output_size
in the call operator
Example:
>>> pool = nn.MaxPool1d(2, stride=2, return_indices=True) >>> unpool = nn.MaxUnpool1d(2, stride=2) >>> input = torch.tensor([[[1., 2, 3, 4, 5, 6, 7, 8]]]) >>> output, indices = pool(input) >>> unpool(output, indices) tensor([[[ 0., 2., 0., 4., 0., 6., 0., 8.]]]) >>> # Example showcasing the use of output_size >>> input = torch.tensor([[[1., 2, 3, 4, 5, 6, 7, 8, 9]]]) >>> output, indices = pool(input) >>> unpool(output, indices, output_size=input.size()) tensor([[[ 0., 2., 0., 4., 0., 6., 0., 8., 0.]]]) >>> unpool(output, indices) tensor([[[ 0., 2., 0., 4., 0., 6., 0., 8.]]])
MaxUnpool2d¶

class
torch.nn.
MaxUnpool2d
(kernel_size, stride=None, padding=0)[source]¶ Computes a partial inverse of
MaxPool2d
.MaxPool2d
is not fully invertible, since the nonmaximal values are lost.MaxUnpool2d
takes in as input the output ofMaxPool2d
including the indices of the maximal values and computes a partial inverse in which all nonmaximal values are set to zero.Note
MaxPool2d
can map several input sizes to the same output sizes. Hence, the inversion process can get ambiguous. To accommodate this, you can provide the needed output size as an additional argumentoutput_size
in the forward call. See the Inputs and Example below. Parameters
 Inputs:
input: the input Tensor to invert
indices: the indices given out by
MaxPool2d
output_size (optional): the targeted output size
 Shape:
Input: \((N, C, H_{in}, W_{in})\)
Output: \((N, C, H_{out}, W_{out})\), where
\[H_{out} = (H_{in}  1) \times \text{stride[0]}  2 \times \text{padding[0]} + \text{kernel\_size[0]} \]\[W_{out} = (W_{in}  1) \times \text{stride[1]}  2 \times \text{padding[1]} + \text{kernel\_size[1]} \]or as given by
output_size
in the call operator
Example:
>>> pool = nn.MaxPool2d(2, stride=2, return_indices=True) >>> unpool = nn.MaxUnpool2d(2, stride=2) >>> input = torch.tensor([[[[ 1., 2, 3, 4], [ 5, 6, 7, 8], [ 9, 10, 11, 12], [13, 14, 15, 16]]]]) >>> output, indices = pool(input) >>> unpool(output, indices) tensor([[[[ 0., 0., 0., 0.], [ 0., 6., 0., 8.], [ 0., 0., 0., 0.], [ 0., 14., 0., 16.]]]]) >>> # specify a different output size than input size >>> unpool(output, indices, output_size=torch.Size([1, 1, 5, 5])) tensor([[[[ 0., 0., 0., 0., 0.], [ 6., 0., 8., 0., 0.], [ 0., 0., 0., 14., 0.], [ 16., 0., 0., 0., 0.], [ 0., 0., 0., 0., 0.]]]])
MaxUnpool3d¶

class
torch.nn.
MaxUnpool3d
(kernel_size, stride=None, padding=0)[source]¶ Computes a partial inverse of
MaxPool3d
.MaxPool3d
is not fully invertible, since the nonmaximal values are lost.MaxUnpool3d
takes in as input the output ofMaxPool3d
including the indices of the maximal values and computes a partial inverse in which all nonmaximal values are set to zero.Note
MaxPool3d
can map several input sizes to the same output sizes. Hence, the inversion process can get ambiguous. To accommodate this, you can provide the needed output size as an additional argumentoutput_size
in the forward call. See the Inputs section below. Parameters
 Inputs:
input: the input Tensor to invert
indices: the indices given out by
MaxPool3d
output_size (optional): the targeted output size
 Shape:
Input: \((N, C, D_{in}, H_{in}, W_{in})\)
Output: \((N, C, D_{out}, H_{out}, W_{out})\), where
\[D_{out} = (D_{in}  1) \times \text{stride[0]}  2 \times \text{padding[0]} + \text{kernel\_size[0]} \]\[H_{out} = (H_{in}  1) \times \text{stride[1]}  2 \times \text{padding[1]} + \text{kernel\_size[1]} \]\[W_{out} = (W_{in}  1) \times \text{stride[2]}  2 \times \text{padding[2]} + \text{kernel\_size[2]} \]or as given by
output_size
in the call operator
Example:
>>> # pool of square window of size=3, stride=2 >>> pool = nn.MaxPool3d(3, stride=2, return_indices=True) >>> unpool = nn.MaxUnpool3d(3, stride=2) >>> output, indices = pool(torch.randn(20, 16, 51, 33, 15)) >>> unpooled_output = unpool(output, indices) >>> unpooled_output.size() torch.Size([20, 16, 51, 33, 15])
AvgPool1d¶

class
torch.nn.
AvgPool1d
(kernel_size, stride=None, padding=0, ceil_mode=False, count_include_pad=True)[source]¶ Applies a 1D average pooling over an input signal composed of several input planes.
In the simplest case, the output value of the layer with input size \((N, C, L)\), output \((N, C, L_{out})\) and
kernel_size
\(k\) can be precisely described as:\[\text{out}(N_i, C_j, l) = \frac{1}{k} \sum_{m=0}^{k1} \text{input}(N_i, C_j, \text{stride} \times l + m)\]If
padding
is nonzero, then the input is implicitly zeropadded on both sides forpadding
number of points.The parameters
kernel_size
,stride
,padding
can each be anint
or a oneelement tuple. Parameters
kernel_size – the size of the window
stride – the stride of the window. Default value is
kernel_size
padding – implicit zero padding to be added on both sides
ceil_mode – when True, will use ceil instead of floor to compute the output shape
count_include_pad – when True, will include the zeropadding in the averaging calculation
 Shape:
Input: \((N, C, L_{in})\)
Output: \((N, C, L_{out})\), where
\[L_{out} = \left\lfloor \frac{L_{in} + 2 \times \text{padding}  \text{kernel\_size}}{\text{stride}} + 1\right\rfloor \]
Examples:
>>> # pool with window of size=3, stride=2 >>> m = nn.AvgPool1d(3, stride=2) >>> m(torch.tensor([[[1.,2,3,4,5,6,7]]])) tensor([[[ 2., 4., 6.]]])
AvgPool2d¶

class
torch.nn.
AvgPool2d
(kernel_size, stride=None, padding=0, ceil_mode=False, count_include_pad=True)[source]¶ Applies a 2D average pooling over an input signal composed of several input planes.
In the simplest case, the output value of the layer with input size \((N, C, H, W)\), output \((N, C, H_{out}, W_{out})\) and
kernel_size
\((kH, kW)\) can be precisely described as:\[out(N_i, C_j, h, w) = \frac{1}{kH * kW} \sum_{m=0}^{kH1} \sum_{n=0}^{kW1} input(N_i, C_j, stride[0] \times h + m, stride[1] \times w + n)\]If
padding
is nonzero, then the input is implicitly zeropadded on both sides forpadding
number of points.The parameters
kernel_size
,stride
,padding
can either be:a single
int
– in which case the same value is used for the height and width dimensiona
tuple
of two ints – in which case, the first int is used for the height dimension, and the second int for the width dimension
 Parameters
kernel_size – the size of the window
stride – the stride of the window. Default value is
kernel_size
padding – implicit zero padding to be added on both sides
ceil_mode – when True, will use ceil instead of floor to compute the output shape
count_include_pad – when True, will include the zeropadding in the averaging calculation
 Shape:
Input: \((N, C, H_{in}, W_{in})\)
Output: \((N, C, H_{out}, W_{out})\), where
\[H_{out} = \left\lfloor\frac{H_{in} + 2 \times \text{padding}[0]  \text{kernel\_size}[0]}{\text{stride}[0]} + 1\right\rfloor \]\[W_{out} = \left\lfloor\frac{W_{in} + 2 \times \text{padding}[1]  \text{kernel\_size}[1]}{\text{stride}[1]} + 1\right\rfloor \]
Examples:
>>> # pool of square window of size=3, stride=2 >>> m = nn.AvgPool2d(3, stride=2) >>> # pool of nonsquare window >>> m = nn.AvgPool2d((3, 2), stride=(2, 1)) >>> input = torch.randn(20, 16, 50, 32) >>> output = m(input)
AvgPool3d¶

class
torch.nn.
AvgPool3d
(kernel_size, stride=None, padding=0, ceil_mode=False, count_include_pad=True)[source]¶ Applies a 3D average pooling over an input signal composed of several input planes.
In the simplest case, the output value of the layer with input size \((N, C, D, H, W)\), output \((N, C, D_{out}, H_{out}, W_{out})\) and
kernel_size
\((kD, kH, kW)\) can be precisely described as:\[\begin{aligned} \text{out}(N_i, C_j, d, h, w) ={} & \sum_{k=0}^{kD1} \sum_{m=0}^{kH1} \sum_{n=0}^{kW1} \\ & \frac{\text{input}(N_i, C_j, \text{stride}[0] \times d + k, \text{stride}[1] \times h + m, \text{stride}[2] \times w + n)} {kD \times kH \times kW} \end{aligned} \]If
padding
is nonzero, then the input is implicitly zeropadded on all three sides forpadding
number of points.The parameters
kernel_size
,stride
can either be:a single
int
– in which case the same value is used for the depth, height and width dimensiona
tuple
of three ints – in which case, the first int is used for the depth dimension, the second int for the height dimension and the third int for the width dimension
 Parameters
kernel_size – the size of the window
stride – the stride of the window. Default value is
kernel_size
padding – implicit zero padding to be added on all three sides
ceil_mode – when True, will use ceil instead of floor to compute the output shape
count_include_pad – when True, will include the zeropadding in the averaging calculation
 Shape:
Input: \((N, C, D_{in}, H_{in}, W_{in})\)
Output: \((N, C, D_{out}, H_{out}, W_{out})\), where
\[D_{out} = \left\lfloor\frac{D_{in} + 2 \times \text{padding}[0]  \text{kernel\_size}[0]}{\text{stride}[0]} + 1\right\rfloor \]\[H_{out} = \left\lfloor\frac{H_{in} + 2 \times \text{padding}[1]  \text{kernel\_size}[1]}{\text{stride}[1]} + 1\right\rfloor \]\[W_{out} = \left\lfloor\frac{W_{in} + 2 \times \text{padding}[2]  \text{kernel\_size}[2]}{\text{stride}[2]} + 1\right\rfloor \]
Examples:
>>> # pool of square window of size=3, stride=2 >>> m = nn.AvgPool3d(3, stride=2) >>> # pool of nonsquare window >>> m = nn.AvgPool3d((3, 2, 2), stride=(2, 1, 2)) >>> input = torch.randn(20, 16, 50,44, 31) >>> output = m(input)
FractionalMaxPool2d¶

class
torch.nn.
FractionalMaxPool2d
(kernel_size, output_size=None, output_ratio=None, return_indices=False, _random_samples=None)[source]¶ Applies a 2D fractional max pooling over an input signal composed of several input planes.
Fractional MaxPooling is described in detail in the paper Fractional MaxPooling by Ben Graham
The maxpooling operation is applied in \(kH \times kW\) regions by a stochastic step size determined by the target output size. The number of output features is equal to the number of input planes.
 Parameters
kernel_size – the size of the window to take a max over. Can be a single number k (for a square kernel of k x k) or a tuple (kh, kw)
output_size – the target output size of the image of the form oH x oW. Can be a tuple (oH, oW) or a single number oH for a square image oH x oH
output_ratio – If one wants to have an output size as a ratio of the input size, this option can be given. This has to be a number or tuple in the range (0, 1)
return_indices – if
True
, will return the indices along with the outputs. Useful to pass tonn.MaxUnpool2d()
. Default:False
Examples
>>> # pool of square window of size=3, and target output size 13x12 >>> m = nn.FractionalMaxPool2d(3, output_size=(13, 12)) >>> # pool of square window and target output size being half of input image size >>> m = nn.FractionalMaxPool2d(3, output_ratio=(0.5, 0.5)) >>> input = torch.randn(20, 16, 50, 32) >>> output = m(input)
LPPool1d¶

class
torch.nn.
LPPool1d
(norm_type, kernel_size, stride=None, ceil_mode=False)[source]¶ Applies a 1D poweraverage pooling over an input signal composed of several input planes.
On each window, the function computed is:
\[f(X) = \sqrt[p]{\sum_{x \in X} x^{p}} \]At p = \(\infty\), one gets Max Pooling
At p = 1, one gets Sum Pooling (which is proportional to Average Pooling)
Note
If the sum to the power of p is zero, the gradient of this function is not defined. This implementation will set the gradient to zero in this case.
 Parameters
kernel_size – a single int, the size of the window
stride – a single int, the stride of the window. Default value is
kernel_size
ceil_mode – when True, will use ceil instead of floor to compute the output shape
 Shape:
Input: \((N, C, L_{in})\)
Output: \((N, C, L_{out})\), where
\[L_{out} = \left\lfloor\frac{L_{in} + 2 \times \text{padding}  \text{kernel\_size}}{\text{stride}} + 1\right\rfloor \]
 Examples::
>>> # power2 pool of window of length 3, with stride 2. >>> m = nn.LPPool1d(2, 3, stride=2) >>> input = torch.randn(20, 16, 50) >>> output = m(input)
LPPool2d¶

class
torch.nn.
LPPool2d
(norm_type, kernel_size, stride=None, ceil_mode=False)[source]¶ Applies a 2D poweraverage pooling over an input signal composed of several input planes.
On each window, the function computed is:
\[f(X) = \sqrt[p]{\sum_{x \in X} x^{p}} \]At p = \(\infty\), one gets Max Pooling
At p = 1, one gets Sum Pooling (which is proportional to average pooling)
The parameters
kernel_size
,stride
can either be:a single
int
– in which case the same value is used for the height and width dimensiona
tuple
of two ints – in which case, the first int is used for the height dimension, and the second int for the width dimension
Note
If the sum to the power of p is zero, the gradient of this function is not defined. This implementation will set the gradient to zero in this case.
 Parameters
kernel_size – the size of the window
stride – the stride of the window. Default value is
kernel_size
ceil_mode – when True, will use ceil instead of floor to compute the output shape
 Shape:
Input: \((N, C, H_{in}, W_{in})\)
Output: \((N, C, H_{out}, W_{out})\), where
\[H_{out} = \left\lfloor\frac{H_{in} + 2 \times \text{padding}[0]  \text{dilation}[0] \times (\text{kernel\_size}[0]  1)  1}{\text{stride}[0]} + 1\right\rfloor \]\[W_{out} = \left\lfloor\frac{W_{in} + 2 \times \text{padding}[1]  \text{dilation}[1] \times (\text{kernel\_size}[1]  1)  1}{\text{stride}[1]} + 1\right\rfloor \]
Examples:
>>> # power2 pool of square window of size=3, stride=2 >>> m = nn.LPPool2d(2, 3, stride=2) >>> # pool of nonsquare window of power 1.2 >>> m = nn.LPPool2d(1.2, (3, 2), stride=(2, 1)) >>> input = torch.randn(20, 16, 50, 32) >>> output = m(input)
AdaptiveMaxPool1d¶

class
torch.nn.
AdaptiveMaxPool1d
(output_size, return_indices=False)[source]¶ Applies a 1D adaptive max pooling over an input signal composed of several input planes.
The output size is H, for any input size. The number of output features is equal to the number of input planes.
 Parameters
output_size – the target output size H
return_indices – if
True
, will return the indices along with the outputs. Useful to pass to nn.MaxUnpool1d. Default:False
Examples
>>> # target output size of 5 >>> m = nn.AdaptiveMaxPool1d(5) >>> input = torch.randn(1, 64, 8) >>> output = m(input)
AdaptiveMaxPool2d¶

class
torch.nn.
AdaptiveMaxPool2d
(output_size, return_indices=False)[source]¶ Applies a 2D adaptive max pooling over an input signal composed of several input planes.
The output is of size H x W, for any input size. The number of output features is equal to the number of input planes.
 Parameters
output_size – the target output size of the image of the form H x W. Can be a tuple (H, W) or a single H for a square image H x H. H and W can be either a
int
, orNone
which means the size will be the same as that of the input.return_indices – if
True
, will return the indices along with the outputs. Useful to pass to nn.MaxUnpool2d. Default:False
Examples
>>> # target output size of 5x7 >>> m = nn.AdaptiveMaxPool2d((5,7)) >>> input = torch.randn(1, 64, 8, 9) >>> output = m(input) >>> # target output size of 7x7 (square) >>> m = nn.AdaptiveMaxPool2d(7) >>> input = torch.randn(1, 64, 10, 9) >>> output = m(input) >>> # target output size of 10x7 >>> m = nn.AdaptiveMaxPool2d((None, 7)) >>> input = torch.randn(1, 64, 10, 9) >>> output = m(input)
AdaptiveMaxPool3d¶

class
torch.nn.
AdaptiveMaxPool3d
(output_size, return_indices=False)[source]¶ Applies a 3D adaptive max pooling over an input signal composed of several input planes.
The output is of size D x H x W, for any input size. The number of output features is equal to the number of input planes.
 Parameters
output_size – the target output size of the image of the form D x H x W. Can be a tuple (D, H, W) or a single D for a cube D x D x D. D, H and W can be either a
int
, orNone
which means the size will be the same as that of the input.return_indices – if
True
, will return the indices along with the outputs. Useful to pass to nn.MaxUnpool3d. Default:False
Examples
>>> # target output size of 5x7x9 >>> m = nn.AdaptiveMaxPool3d((5,7,9)) >>> input = torch.randn(1, 64, 8, 9, 10) >>> output = m(input) >>> # target output size of 7x7x7 (cube) >>> m = nn.AdaptiveMaxPool3d(7) >>> input = torch.randn(1, 64, 10, 9, 8) >>> output = m(input) >>> # target output size of 7x9x8 >>> m = nn.AdaptiveMaxPool3d((7, None, None)) >>> input = torch.randn(1, 64, 10, 9, 8) >>> output = m(input)
AdaptiveAvgPool1d¶

class
torch.nn.
AdaptiveAvgPool1d
(output_size)[source]¶ Applies a 1D adaptive average pooling over an input signal composed of several input planes.
The output size is H, for any input size. The number of output features is equal to the number of input planes.
 Parameters
output_size – the target output size H
Examples
>>> # target output size of 5 >>> m = nn.AdaptiveAvgPool1d(5) >>> input = torch.randn(1, 64, 8) >>> output = m(input)
AdaptiveAvgPool2d¶

class
torch.nn.
AdaptiveAvgPool2d
(output_size)[source]¶ Applies a 2D adaptive average pooling over an input signal composed of several input planes.
The output is of size H x W, for any input size. The number of output features is equal to the number of input planes.
 Parameters
output_size – the target output size of the image of the form H x W. Can be a tuple (H, W) or a single H for a square image H x H. H and W can be either a
int
, orNone
which means the size will be the same as that of the input.
Examples
>>> # target output size of 5x7 >>> m = nn.AdaptiveAvgPool2d((5,7)) >>> input = torch.randn(1, 64, 8, 9) >>> output = m(input) >>> # target output size of 7x7 (square) >>> m = nn.AdaptiveAvgPool2d(7) >>> input = torch.randn(1, 64, 10, 9) >>> output = m(input) >>> # target output size of 10x7 >>> m = nn.AdaptiveMaxPool2d((None, 7)) >>> input = torch.randn(1, 64, 10, 9) >>> output = m(input)
AdaptiveAvgPool3d¶

class
torch.nn.
AdaptiveAvgPool3d
(output_size)[source]¶ Applies a 3D adaptive average pooling over an input signal composed of several input planes.
The output is of size D x H x W, for any input size. The number of output features is equal to the number of input planes.
 Parameters
output_size – the target output size of the form D x H x W. Can be a tuple (D, H, W) or a single number D for a cube D x D x D. D, H and W can be either a
int
, orNone
which means the size will be the same as that of the input.
Examples
>>> # target output size of 5x7x9 >>> m = nn.AdaptiveAvgPool3d((5,7,9)) >>> input = torch.randn(1, 64, 8, 9, 10) >>> output = m(input) >>> # target output size of 7x7x7 (cube) >>> m = nn.AdaptiveAvgPool3d(7) >>> input = torch.randn(1, 64, 10, 9, 8) >>> output = m(input) >>> # target output size of 7x9x8 >>> m = nn.AdaptiveMaxPool3d((7, None, None)) >>> input = torch.randn(1, 64, 10, 9, 8) >>> output = m(input)
Padding layers¶
ReflectionPad1d¶

class
torch.nn.
ReflectionPad1d
(padding)[source]¶ Pads the input tensor using the reflection of the input boundary.
For Ndimensional padding, use
torch.nn.functional.pad()
. Parameters
padding (int, tuple) – the size of the padding. If is int, uses the same padding in all boundaries. If a 2tuple, uses (\(\text{padding\_left}\), \(\text{padding\_right}\))
 Shape:
Input: \((N, C, W_{in})\)
Output: \((N, C, W_{out})\) where
\(W_{out} = W_{in} + \text{padding\_left} + \text{padding\_right}\)
Examples:
>>> m = nn.ReflectionPad1d(2) >>> input = torch.arange(8, dtype=torch.float).reshape(1, 2, 4) >>> input tensor([[[0., 1., 2., 3.], [4., 5., 6., 7.]]]) >>> m(input) tensor([[[2., 1., 0., 1., 2., 3., 2., 1.], [6., 5., 4., 5., 6., 7., 6., 5.]]]) >>> # using different paddings for different sides >>> m = nn.ReflectionPad1d((3, 1)) >>> m(input) tensor([[[3., 2., 1., 0., 1., 2., 3., 2.], [7., 6., 5., 4., 5., 6., 7., 6.]]])
ReflectionPad2d¶

class
torch.nn.
ReflectionPad2d
(padding)[source]¶ Pads the input tensor using the reflection of the input boundary.
For Ndimensional padding, use
torch.nn.functional.pad()
. Parameters
padding (int, tuple) – the size of the padding. If is int, uses the same padding in all boundaries. If a 4tuple, uses (\(\text{padding\_left}\), \(\text{padding\_right}\), \(\text{padding\_top}\), \(\text{padding\_bottom}\))
 Shape:
Input: \((N, C, H_{in}, W_{in})\)
Output: \((N, C, H_{out}, W_{out})\) where
\(H_{out} = H_{in} + \text{padding\_top} + \text{padding\_bottom}\)
\(W_{out} = W_{in} + \text{padding\_left} + \text{padding\_right}\)
Examples:
>>> m = nn.ReflectionPad2d(2) >>> input = torch.arange(9, dtype=torch.float).reshape(1, 1, 3, 3) >>> input tensor([[[[0., 1., 2.], [3., 4., 5.], [6., 7., 8.]]]]) >>> m(input) tensor([[[[8., 7., 6., 7., 8., 7., 6.], [5., 4., 3., 4., 5., 4., 3.], [2., 1., 0., 1., 2., 1., 0.], [5., 4., 3., 4., 5., 4., 3.], [8., 7., 6., 7., 8., 7., 6.], [5., 4., 3., 4., 5., 4., 3.], [2., 1., 0., 1., 2., 1., 0.]]]]) >>> # using different paddings for different sides >>> m = nn.ReflectionPad2d((1, 1, 2, 0)) >>> m(input) tensor([[[[7., 6., 7., 8., 7.], [4., 3., 4., 5., 4.], [1., 0., 1., 2., 1.], [4., 3., 4., 5., 4.], [7., 6., 7., 8., 7.]]]])
ReplicationPad1d¶

class
torch.nn.
ReplicationPad1d
(padding)[source]¶ Pads the input tensor using replication of the input boundary.
For Ndimensional padding, use
torch.nn.functional.pad()
. Parameters
padding (int, tuple) – the size of the padding. If is int, uses the same padding in all boundaries. If a 2tuple, uses (\(\text{padding\_left}\), \(\text{padding\_right}\))
 Shape:
Input: \((N, C, W_{in})\)
Output: \((N, C, W_{out})\) where
\(W_{out} = W_{in} + \text{padding\_left} + \text{padding\_right}\)
Examples:
>>> m = nn.ReplicationPad1d(2) >>> input = torch.arange(8, dtype=torch.float).reshape(1, 2, 4) >>> input tensor([[[0., 1., 2., 3.], [4., 5., 6., 7.]]]) >>> m(input) tensor([[[0., 0., 0., 1., 2., 3., 3., 3.], [4., 4., 4., 5., 6., 7., 7., 7.]]]) >>> # using different paddings for different sides >>> m = nn.ReplicationPad1d((3, 1)) >>> m(input) tensor([[[0., 0., 0., 0., 1., 2., 3., 3.], [4., 4., 4., 4., 5., 6., 7., 7.]]])
ReplicationPad2d¶

class
torch.nn.
ReplicationPad2d
(padding)[source]¶ Pads the input tensor using replication of the input boundary.
For Ndimensional padding, use
torch.nn.functional.pad()
. Parameters
padding (int, tuple) – the size of the padding. If is int, uses the same padding in all boundaries. If a 4tuple, uses (\(\text{padding\_left}\), \(\text{padding\_right}\), \(\text{padding\_top}\), \(\text{padding\_bottom}\))
 Shape:
Input: \((N, C, H_{in}, W_{in})\)
Output: \((N, C, H_{out}, W_{out})\) where
\(H_{out} = H_{in} + \text{padding\_top} + \text{padding\_bottom}\)
\(W_{out} = W_{in} + \text{padding\_left} + \text{padding\_right}\)
Examples:
>>> m = nn.ReplicationPad2d(2) >>> input = torch.arange(9, dtype=torch.float).reshape(1, 1, 3, 3) >>> input tensor([[[[0., 1., 2.], [3., 4., 5.], [6., 7., 8.]]]]) >>> m(input) tensor([[[[0., 0., 0., 1., 2., 2., 2.], [0., 0., 0., 1., 2., 2., 2.], [0., 0., 0., 1., 2., 2., 2.], [3., 3., 3., 4., 5., 5., 5.], [6., 6., 6., 7., 8., 8., 8.], [6., 6., 6., 7., 8., 8., 8.], [6., 6., 6., 7., 8., 8., 8.]]]]) >>> # using different paddings for different sides >>> m = nn.ReplicationPad2d((1, 1, 2, 0)) >>> m(input) tensor([[[[0., 0., 1., 2., 2.], [0., 0., 1., 2., 2.], [0., 0., 1., 2., 2.], [3., 3., 4., 5., 5.], [6., 6., 7., 8., 8.]]]])
ReplicationPad3d¶

class
torch.nn.
ReplicationPad3d
(padding)[source]¶ Pads the input tensor using replication of the input boundary.
For Ndimensional padding, use
torch.nn.functional.pad()
. Parameters
padding (int, tuple) – the size of the padding. If is int, uses the same padding in all boundaries. If a 6tuple, uses (\(\text{padding\_left}\), \(\text{padding\_right}\), \(\text{padding\_top}\), \(\text{padding\_bottom}\), \(\text{padding\_front}\), \(\text{padding\_back}\))
 Shape:
Input: \((N, C, D_{in}, H_{in}, W_{in})\)
Output: \((N, C, D_{out}, H_{out}, W_{out})\) where
\(D_{out} = D_{in} + \text{padding\_front} + \text{padding\_back}\)
\(H_{out} = H_{in} + \text{padding\_top} + \text{padding\_bottom}\)
\(W_{out} = W_{in} + \text{padding\_left} + \text{padding\_right}\)
Examples:
>>> m = nn.ReplicationPad3d(3) >>> input = torch.randn(16, 3, 8, 320, 480) >>> output = m(input) >>> # using different paddings for different sides >>> m = nn.ReplicationPad3d((3, 3, 6, 6, 1, 1)) >>> output = m(input)
ZeroPad2d¶

class
torch.nn.
ZeroPad2d
(padding)[source]¶ Pads the input tensor boundaries with zero.
For Ndimensional padding, use
torch.nn.functional.pad()
. Parameters
padding (int, tuple) – the size of the padding. If is int, uses the same padding in all boundaries. If a 4tuple, uses (\(\text{padding\_left}\), \(\text{padding\_right}\), \(\text{padding\_top}\), \(\text{padding\_bottom}\))
 Shape:
Input: \((N, C, H_{in}, W_{in})\)
Output: \((N, C, H_{out}, W_{out})\) where
\(H_{out} = H_{in} + \text{padding\_top} + \text{padding\_bottom}\)
\(W_{out} = W_{in} + \text{padding\_left} + \text{padding\_right}\)
Examples:
>>> m = nn.ZeroPad2d(2) >>> input = torch.randn(1, 1, 3, 3) >>> input tensor([[[[0.1678, 0.4418, 1.9466], [ 0.9604, 0.4219, 0.5241], [0.9162, 0.5436, 0.6446]]]]) >>> m(input) tensor([[[[ 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000], [ 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000], [ 0.0000, 0.0000, 0.1678, 0.4418, 1.9466, 0.0000, 0.0000], [ 0.0000, 0.0000, 0.9604, 0.4219, 0.5241, 0.0000, 0.0000], [ 0.0000, 0.0000, 0.9162, 0.5436, 0.6446, 0.0000, 0.0000], [ 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000], [ 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000]]]]) >>> # using different paddings for different sides >>> m = nn.ZeroPad2d((1, 1, 2, 0)) >>> m(input) tensor([[[[ 0.0000, 0.0000, 0.0000, 0.0000, 0.0000], [ 0.0000, 0.0000, 0.0000, 0.0000, 0.0000], [ 0.0000, 0.1678, 0.4418, 1.9466, 0.0000], [ 0.0000, 0.9604, 0.4219, 0.5241, 0.0000], [ 0.0000, 0.9162, 0.5436, 0.6446, 0.0000]]]])
ConstantPad1d¶

class
torch.nn.
ConstantPad1d
(padding, value)[source]¶ Pads the input tensor boundaries with a constant value.
For Ndimensional padding, use
torch.nn.functional.pad()
. Parameters
padding (int, tuple) – the size of the padding. If is int, uses the same padding in both boundaries. If a 2tuple, uses (\(\text{padding\_left}\), \(\text{padding\_right}\))
 Shape:
Input: \((N, C, W_{in})\)
Output: \((N, C, W_{out})\) where
\(W_{out} = W_{in} + \text{padding\_left} + \text{padding\_right}\)
Examples:
>>> m = nn.ConstantPad1d(2, 3.5) >>> input = torch.randn(1, 2, 4) >>> input tensor([[[1.0491, 0.7152, 0.0749, 0.8530], [1.3287, 1.8966, 0.1466, 0.2771]]]) >>> m(input) tensor([[[ 3.5000, 3.5000, 1.0491, 0.7152, 0.0749, 0.8530, 3.5000, 3.5000], [ 3.5000, 3.5000, 1.3287, 1.8966, 0.1466, 0.2771, 3.5000, 3.5000]]]) >>> m = nn.ConstantPad1d(2, 3.5) >>> input = torch.randn(1, 2, 3) >>> input tensor([[[ 1.6616, 1.4523, 1.1255], [3.6372, 0.1182, 1.8652]]]) >>> m(input) tensor([[[ 3.5000, 3.5000, 1.6616, 1.4523, 1.1255, 3.5000, 3.5000], [ 3.5000, 3.5000, 3.6372, 0.1182, 1.8652, 3.5000, 3.5000]]]) >>> # using different paddings for different sides >>> m = nn.ConstantPad1d((3, 1), 3.5) >>> m(input) tensor([[[ 3.5000, 3.5000, 3.5000, 1.6616, 1.4523, 1.1255, 3.5000], [ 3.5000, 3.5000, 3.5000, 3.6372, 0.1182, 1.8652, 3.5000]]])
ConstantPad2d¶

class
torch.nn.
ConstantPad2d
(padding, value)[source]¶ Pads the input tensor boundaries with a constant value.
For Ndimensional padding, use
torch.nn.functional.pad()
. Parameters
padding (int, tuple) – the size of the padding. If is int, uses the same padding in all boundaries. If a 4tuple, uses (\(\text{padding\_left}\), \(\text{padding\_right}\), \(\text{padding\_top}\), \(\text{padding\_bottom}\))
 Shape:
Input: \((N, C, H_{in}, W_{in})\)
Output: \((N, C, H_{out}, W_{out})\) where
\(H_{out} = H_{in} + \text{padding\_top} + \text{padding\_bottom}\)
\(W_{out} = W_{in} + \text{padding\_left} + \text{padding\_right}\)
Examples:
>>> m = nn.ConstantPad2d(2, 3.5) >>> input = torch.randn(1, 2, 2) >>> input tensor([[[ 1.6585, 0.4320], [0.8701, 0.4649]]]) >>> m(input) tensor([[[ 3.5000, 3.5000, 3.5000, 3.5000, 3.5000, 3.5000], [ 3.5000, 3.5000, 3.5000, 3.5000, 3.5000, 3.5000], [ 3.5000, 3.5000, 1.6585, 0.4320, 3.5000, 3.5000], [ 3.5000, 3.5000, 0.8701, 0.4649, 3.5000, 3.5000], [ 3.5000, 3.5000, 3.5000, 3.5000, 3.5000, 3.5000], [ 3.5000, 3.5000, 3.5000, 3.5000, 3.5000, 3.5000]]]) >>> # using different paddings for different sides >>> m = nn.ConstantPad2d((3, 0, 2, 1), 3.5) >>> m(input) tensor([[[ 3.5000, 3.5000, 3.5000, 3.5000, 3.5000], [ 3.5000, 3.5000, 3.5000, 3.5000, 3.5000], [ 3.5000, 3.5000, 3.5000, 1.6585, 0.4320], [ 3.5000, 3.5000, 3.5000, 0.8701, 0.4649], [ 3.5000, 3.5000, 3.5000, 3.5000, 3.5000]]])
ConstantPad3d¶

class
torch.nn.
ConstantPad3d
(padding, value)[source]¶ Pads the input tensor boundaries with a constant value.
For Ndimensional padding, use
torch.nn.functional.pad()
. Parameters
padding (int, tuple) – the size of the padding. If is int, uses the same padding in all boundaries. If a 6tuple, uses (\(\text{padding\_left}\), \(\text{padding\_right}\), \(\text{padding\_top}\), \(\text{padding\_bottom}\), \(\text{padding\_front}\), \(\text{padding\_back}\))
 Shape:
Input: \((N, C, D_{in}, H_{in}, W_{in})\)
Output: \((N, C, D_{out}, H_{out}, W_{out})\) where
\(D_{out} = D_{in} + \text{padding\_front} + \text{padding\_back}\)
\(H_{out} = H_{in} + \text{padding\_top} + \text{padding\_bottom}\)
\(W_{out} = W_{in} + \text{padding\_left} + \text{padding\_right}\)
Examples:
>>> m = nn.ConstantPad3d(3, 3.5) >>> input = torch.randn(16, 3, 10, 20, 30) >>> output = m(input) >>> # using different paddings for different sides >>> m = nn.ConstantPad3d((3, 3, 6, 6, 0, 1), 3.5) >>> output = m(input)
Nonlinear activations (weighted sum, nonlinearity)¶
ELU¶

class
torch.nn.
ELU
(alpha=1.0, inplace=False)[source]¶ Applies the elementwise function:
\[\text{ELU}(x) = \max(0,x) + \min(0, \alpha * (\exp(x)  1)) \] Parameters
alpha – the \(\alpha\) value for the ELU formulation. Default: 1.0
inplace – can optionally do the operation inplace. Default:
False
 Shape:
Input: \((N, *)\) where * means, any number of additional dimensions
Output: \((N, *)\), same shape as the input
Examples:
>>> m = nn.ELU() >>> input = torch.randn(2) >>> output = m(input)
Hardshrink¶

class
torch.nn.
Hardshrink
(lambd=0.5)[source]¶ Applies the hard shrinkage function elementwise:
\[\text{HardShrink}(x) = \begin{cases} x, & \text{ if } x > \lambda \\ x, & \text{ if } x < \lambda \\ 0, & \text{ otherwise } \end{cases} \] Parameters
lambd – the \(\lambda\) value for the Hardshrink formulation. Default: 0.5
 Shape:
Input: \((N, *)\) where * means, any number of additional dimensions
Output: \((N, *)\), same shape as the input
Examples:
>>> m = nn.Hardshrink() >>> input = torch.randn(2) >>> output = m(input)
Hardtanh¶

class
torch.nn.
Hardtanh
(min_val=1.0, max_val=1.0, inplace=False, min_value=None, max_value=None)[source]¶ Applies the HardTanh function elementwise
HardTanh is defined as:
\[\text{HardTanh}(x) = \begin{cases} 1 & \text{ if } x > 1 \\ 1 & \text{ if } x < 1 \\ x & \text{ otherwise } \\ \end{cases} \]The range of the linear region \([1, 1]\) can be adjusted using
min_val
andmax_val
. Parameters
min_val – minimum value of the linear region range. Default: 1
max_val – maximum value of the linear region range. Default: 1
inplace – can optionally do the operation inplace. Default:
False
Keyword arguments
min_value
andmax_value
have been deprecated in favor ofmin_val
andmax_val
. Shape:
Input: \((N, *)\) where * means, any number of additional dimensions
Output: \((N, *)\), same shape as the input
Examples:
>>> m = nn.Hardtanh(2, 2) >>> input = torch.randn(2) >>> output = m(input)
LeakyReLU¶

class
torch.nn.
LeakyReLU
(negative_slope=0.01, inplace=False)[source]¶ Applies the elementwise function:
\[\text{LeakyReLU}(x) = \max(0, x) + \text{negative\_slope} * \min(0, x) \]or
\[\text{LeakyRELU}(x) = \begin{cases} x, & \text{ if } x \geq 0 \\ \text{negative\_slope} \times x, & \text{ otherwise } \end{cases} \] Parameters
negative_slope – Controls the angle of the negative slope. Default: 1e2
inplace – can optionally do the operation inplace. Default:
False
 Shape:
Input: \((N, *)\) where * means, any number of additional dimensions
Output: \((N, *)\), same shape as the input
Examples:
>>> m = nn.LeakyReLU(0.1) >>> input = torch.randn(2) >>> output = m(input)
LogSigmoid¶

class
torch.nn.
LogSigmoid
[source]¶ Applies the elementwise function:
\[\text{LogSigmoid}(x) = \log\left(\frac{ 1 }{ 1 + \exp(x)}\right) \] Shape:
Input: \((N, *)\) where * means, any number of additional dimensions
Output: \((N, *)\), same shape as the input
Examples:
>>> m = nn.LogSigmoid() >>> input = torch.randn(2) >>> output = m(input)
MultiheadAttention¶

class
torch.nn.
MultiheadAttention
(embed_dim, num_heads, dropout=0.0, bias=True, add_bias_kv=False, add_zero_attn=False)[source]¶ Allows the model to jointly attend to information from different representation subspaces. See reference: Attention Is All You Need
\[\text{MultiHead}(Q, K, V) = \text{Concat}(head_1,\dots,head_h)W^O \text{where} head_i = \text{Attention}(QW_i^Q, KW_i^K, VW_i^V) \] Parameters
embed_dim – total dimension of the model
num_heads – parallel attention layers, or heads
Examples:
>>> multihead_attn = nn.MultiheadAttention(embed_dim, num_heads) >>> attn_output, attn_output_weights = multihead_attn(query, key, value)

forward
(query, key, value, key_padding_mask=None, incremental_state=None, need_weights=True, static_kv=False, attn_mask=None)[source]¶  Inputs of forward function
query: [target length, batch size, embed dim] key: [sequence length, batch size, embed dim] value: [sequence length, batch size, embed dim] key_padding_mask: if True, mask padding based on batch size incremental_state: if provided, previous time steps are cashed need_weights: output attn_output_weights static_kv: key and value are static
 Outputs of forward function
attn_output: [target length, batch size, embed dim] attn_output_weights: [batch size, target length, sequence length]
PReLU¶

class
torch.nn.
PReLU
(num_parameters=1, init=0.25)[source]¶ Applies the elementwise function:
\[\text{PReLU}(x) = \max(0,x) + a * \min(0,x) \]or
\[\text{PReLU}(x) = \begin{cases} x, & \text{ if } x \geq 0 \\ ax, & \text{ otherwise } \end{cases} \]Here \(a\) is a learnable parameter. When called without arguments, nn.PReLU() uses a single parameter \(a\) across all input channels. If called with nn.PReLU(nChannels), a separate \(a\) is used for each input channel.
Note
weight decay should not be used when learning \(a\) for good performance.
Note
Channel dim is the 2nd dim of input. When input has dims < 2, then there is no channel dim and the number of channels = 1.
 Parameters
 Shape:
Input: \((N, *)\) where * means, any number of additional dimensions
Output: \((N, *)\), same shape as the input
 Variables
~PReLU.weight (Tensor) – the learnable weights of shape (
num_parameters
).
Examples:
>>> m = nn.PReLU() >>> input = torch.randn(2) >>> output = m(input)
ReLU¶

class
torch.nn.
ReLU
(inplace=False)[source]¶ Applies the rectified linear unit function elementwise:
\(\text{ReLU}(x)= \max(0, x)\)
 Parameters
inplace – can optionally do the operation inplace. Default:
False
 Shape:
Input: \((N, *)\) where * means, any number of additional dimensions
Output: \((N, *)\), same shape as the input
Examples:
>>> m = nn.ReLU() >>> input = torch.randn(2) >>> output = m(input) An implementation of CReLU  https://arxiv.org/abs/1603.05201 >>> m = nn.ReLU() >>> input = torch.randn(2).unsqueeze(0) >>> output = torch.cat((m(input),m(input)))
ReLU6¶

class
torch.nn.
ReLU6
(inplace=False)[source]¶ Applies the elementwise function:
\[\text{ReLU6}(x) = \min(\max(0,x), 6) \] Parameters
inplace – can optionally do the operation inplace. Default:
False
 Shape:
Input: \((N, *)\) where * means, any number of additional dimensions
Output: \((N, *)\), same shape as the input
Examples:
>>> m = nn.ReLU6() >>> input = torch.randn(2) >>> output = m(input)
RReLU¶

class
torch.nn.
RReLU
(lower=0.125, upper=0.3333333333333333, inplace=False)[source]¶ Applies the randomized leaky rectified liner unit function, elementwise, as described in the paper:
Empirical Evaluation of Rectified Activations in Convolutional Network.
The function is defined as:
\[\text{RReLU}(x) = \begin{cases} x & \text{if } x \geq 0 \\ ax & \text{ otherwise } \end{cases} \]where \(a\) is randomly sampled from uniform distribution \(\mathcal{U}(\text{lower}, \text{upper})\).
 Parameters
lower – lower bound of the uniform distribution. Default: \(\frac{1}{8}\)
upper – upper bound of the uniform distribution. Default: \(\frac{1}{3}\)
inplace – can optionally do the operation inplace. Default:
False
 Shape:
Input: \((N, *)\) where * means, any number of additional dimensions
Output: \((N, *)\), same shape as the input
Examples:
>>> m = nn.RReLU(0.1, 0.3) >>> input = torch.randn(2) >>> output = m(input)
SELU¶

class
torch.nn.
SELU
(inplace=False)[source]¶ Applied elementwise, as:
\[\text{SELU}(x) = \text{scale} * (\max(0,x) + \min(0, \alpha * (\exp(x)  1))) \]with \(\alpha = 1.6732632423543772848170429916717\) and \(\text{scale} = 1.0507009873554804934193349852946\).
More details can be found in the paper SelfNormalizing Neural Networks .
 Parameters
inplace (bool, optional) – can optionally do the operation inplace. Default:
False
 Shape:
Input: \((N, *)\) where * means, any number of additional dimensions
Output: \((N, *)\), same shape as the input
Examples:
>>> m = nn.SELU() >>> input = torch.randn(2) >>> output = m(input)
CELU¶

class
torch.nn.
CELU
(alpha=1.0, inplace=False)[source]¶ Applies the elementwise function:
\[\text{CELU}(x) = \max(0,x) + \min(0, \alpha * (\exp(x/\alpha)  1)) \]More details can be found in the paper Continuously Differentiable Exponential Linear Units .
 Parameters
alpha – the \(\alpha\) value for the CELU formulation. Default: 1.0
inplace – can optionally do the operation inplace. Default:
False
 Shape:
Input: \((N, *)\) where * means, any number of additional dimensions
Output: \((N, *)\), same shape as the input
Examples:
>>> m = nn.CELU() >>> input = torch.randn(2) >>> output = m(input)
Sigmoid¶

class
torch.nn.
Sigmoid
[source]¶ Applies the elementwise function:
\[\text{Sigmoid}(x) = \frac{1}{1 + \exp(x)} \] Shape:
Input: \((N, *)\) where * means, any number of additional dimensions
Output: \((N, *)\), same shape as the input
Examples:
>>> m = nn.Sigmoid() >>> input = torch.randn(2) >>> output = m(input)
Softplus¶

class
torch.nn.
Softplus
(beta=1, threshold=20)[source]¶ Applies the elementwise function:
\[\text{Softplus}(x) = \frac{1}{\beta} * \log(1 + \exp(\beta * x)) \]SoftPlus is a smooth approximation to the ReLU function and can be used to constrain the output of a machine to always be positive.
For numerical stability the implementation reverts to the linear function for inputs above a certain value.
 Parameters
beta – the \(\beta\) value for the Softplus formulation. Default: 1
threshold – values above this revert to a linear function. Default: 20
 Shape:
Input: \((N, *)\) where * means, any number of additional dimensions
Output: \((N, *)\), same shape as the input
Examples:
>>> m = nn.Softplus() >>> input = torch.randn(2) >>> output = m(input)
Softshrink¶

class
torch.nn.
Softshrink
(lambd=0.5)[source]¶ Applies the soft shrinkage function elementwise:
\[\text{SoftShrinkage}(x) = \begin{cases} x  \lambda, & \text{ if } x > \lambda \\ x + \lambda, & \text{ if } x < \lambda \\ 0, & \text{ otherwise } \end{cases} \] Parameters
lambd – the \(\lambda\) value for the Softshrink formulation. Default: 0.5
 Shape:
Input: \((N, *)\) where * means, any number of additional dimensions
Output: \((N, *)\), same shape as the input
Examples:
>>> m = nn.Softshrink() >>> input = torch.randn(2) >>> output = m(input)
Softsign¶

class
torch.nn.
Softsign
[source]¶ Applies the elementwise function:
\[\text{SoftSign}(x) = \frac{x}{ 1 + x} \] Shape:
Input: \((N, *)\) where * means, any number of additional dimensions
Output: \((N, *)\), same shape as the input
Examples:
>>> m = nn.Softsign() >>> input = torch.randn(2) >>> output = m(input)
Tanh¶

class
torch.nn.
Tanh
[source]¶ Applies the elementwise function:
\[\text{Tanh}(x) = \tanh(x) = \frac{e^x  e^{x}} {e^x + e^{x}} \] Shape:
Input: \((N, *)\) where * means, any number of additional dimensions
Output: \((N, *)\), same shape as the input
Examples:
>>> m = nn.Tanh() >>> input = torch.randn(2) >>> output = m(input)
Tanhshrink¶

class
torch.nn.
Tanhshrink
[source]¶ Applies the elementwise function:
\[\text{Tanhshrink}(x) = x  \text{Tanh}(x) \] Shape:
Input: \((N, *)\) where * means, any number of additional dimensions
Output: \((N, *)\), same shape as the input
Examples:
>>> m = nn.Tanhshrink() >>> input = torch.randn(2) >>> output = m(input)
Threshold¶

class
torch.nn.
Threshold
(threshold, value, inplace=False)[source]¶ Thresholds each element of the input Tensor.
Threshold is defined as:
\[y = \begin{cases} x, &\text{ if } x > \text{threshold} \\ \text{value}, &\text{ otherwise } \end{cases} \] Parameters
threshold – The value to threshold at
value – The value to replace with
inplace – can optionally do the operation inplace. Default:
False
 Shape:
Input: \((N, *)\) where * means, any number of additional dimensions
Output: \((N, *)\), same shape as the input
Examples:
>>> m = nn.Threshold(0.1, 20) >>> input = torch.randn(2) >>> output = m(input)
Nonlinear activations (other)¶
Softmin¶

class
torch.nn.
Softmin
(dim=None)[source]¶ Applies the Softmin function to an ndimensional input Tensor rescaling them so that the elements of the ndimensional output Tensor lie in the range [0, 1] and sum to 1.
Softmin is defined as:
\[\text{Softmin}(x_{i}) = \frac{\exp(x_i)}{\sum_j \exp(x_j)} \] Shape:
Input: \((*)\) where * means, any number of additional dimensions
Output: \((*)\), same shape as the input
 Parameters
dim (int) – A dimension along which Softmin will be computed (so every slice along dim will sum to 1).
 Returns
a Tensor of the same dimension and shape as the input, with values in the range [0, 1]
Examples:
>>> m = nn.Softmin() >>> input = torch.randn(2, 3) >>> output = m(input)
Softmax¶

class
torch.nn.
Softmax
(dim=None)[source]¶ Applies the Softmax function to an ndimensional input Tensor rescaling them so that the elements of the ndimensional output Tensor lie in the range [0,1] and sum to 1.
Softmax is defined as:
\[\text{Softmax}(x_{i}) = \frac{\exp(x_i)}{\sum_j \exp(x_j)} \] Shape:
Input: \((*)\) where * means, any number of additional dimensions
Output: \((*)\), same shape as the input
 Returns
a Tensor of the same dimension and shape as the input with values in the range [0, 1]
 Parameters
dim (int) – A dimension along which Softmax will be computed (so every slice along dim will sum to 1).
Note
This module doesn’t work directly with NLLLoss, which expects the Log to be computed between the Softmax and itself. Use LogSoftmax instead (it’s faster and has better numerical properties).
Examples:
>>> m = nn.Softmax() >>> input = torch.randn(2, 3) >>> output = m(input)
Softmax2d¶

class
torch.nn.
Softmax2d
[source]¶ Applies SoftMax over features to each spatial location.
When given an image of
Channels x Height x Width
, it will apply Softmax to each location \((Channels, h_i, w_j)\) Shape:
Input: \((N, C, H, W)\)
Output: \((N, C, H, W)\) (same shape as input)
 Returns
a Tensor of the same dimension and shape as the input with values in the range [0, 1]
Examples:
>>> m = nn.Softmax2d() >>> # you softmax over the 2nd dimension >>> input = torch.randn(2, 3, 12, 13) >>> output = m(input)
LogSoftmax¶

class
torch.nn.
LogSoftmax
(dim=None)[source]¶ Applies the \(\log(\text{Softmax}(x))\) function to an ndimensional input Tensor. The LogSoftmax formulation can be simplified as:
\[\text{LogSoftmax}(x_{i}) = \log\left(\frac{\exp(x_i) }{ \sum_j \exp(x_j)} \right) \] Shape:
Input: \((*)\) where * means, any number of additional dimensions
Output: \((*)\), same shape as the input
 Parameters
dim (int) – A dimension along which LogSoftmax will be computed.
 Returns
a Tensor of the same dimension and shape as the input with values in the range [inf, 0)
Examples:
>>> m = nn.LogSoftmax() >>> input = torch.randn(2, 3) >>> output = m(input)
AdaptiveLogSoftmaxWithLoss¶

class
torch.nn.
AdaptiveLogSoftmaxWithLoss
(in_features, n_classes, cutoffs, div_value=4.0, head_bias=False)[source]¶ Efficient softmax approximation as described in Efficient softmax approximation for GPUs by Edouard Grave, Armand Joulin, Moustapha Cissé, David Grangier, and Hervé Jégou.
Adaptive softmax is an approximate strategy for training models with large output spaces. It is most effective when the label distribution is highly imbalanced, for example in natural language modelling, where the word frequency distribution approximately follows the Zipf’s law.
Adaptive softmax partitions the labels into several clusters, according to their frequency. These clusters may contain different number of targets each. Additionally, clusters containing less frequent labels assign lower dimensional embeddings to those labels, which speeds up the computation. For each minibatch, only clusters for which at least one target is present are evaluated.
The idea is that the clusters which are accessed frequently (like the first one, containing most frequent labels), should also be cheap to compute – that is, contain a small number of assigned labels.
We highly recommend taking a look at the original paper for more details.
cutoffs
should be an ordered Sequence of integers sorted in the increasing order. It controls number of clusters and the partitioning of targets into clusters. For example settingcutoffs = [10, 100, 1000]
means that first 10 targets will be assigned to the ‘head’ of the adaptive softmax, targets 11, 12, …, 100 will be assigned to the first cluster, and targets 101, 102, …, 1000 will be assigned to the second cluster, while targets 1001, 1002, …, n_classes  1 will be assigned to the last, third cluster.div_value
is used to compute the size of each additional cluster, which is given as \(\left\lfloor\frac{in\_features}{div\_value^{idx}}\right\rfloor\), where \(idx\) is the cluster index (with clusters for less frequent words having larger indices, and indices starting from \(1\)).head_bias
if set to True, adds a bias term to the ‘head’ of the adaptive softmax. See paper for details. Set to False in the official implementation.
Warning
Labels passed as inputs to this module should be sorted accoridng to their frequency. This means that the most frequent label should be represented by the index 0, and the least frequent label should be represented by the index n_classes  1.
Note
This module returns a
NamedTuple
withoutput
andloss
fields. See further documentation for details.Note
To compute logprobabilities for all classes, the
log_prob
method can be used. Parameters
in_features (int) – Number of features in the input tensor
n_classes (int) – Number of classes in the dataset
cutoffs (Sequence) – Cutoffs used to assign targets to their buckets
div_value (float, optional) – value used as an exponent to compute sizes of the clusters. Default: 4.0
head_bias (bool, optional) – If
True
, adds a bias term to the ‘head’ of the adaptive softmax. Default:False
 Returns
output is a Tensor of size
N
containing computed target log probabilities for each exampleloss is a Scalar representing the computed negative log likelihood loss
 Return type
NamedTuple
withoutput
andloss
fields
 Shape:
input: \((N, in\_features)\)
target: \((N)\) where each value satisfies \(0 <= target[i] <= n\_classes\)
output1: \((N)\)
output2:
Scalar

log_prob
(input)[source]¶ Computes log probabilities for all \(n\_classes\)
 Parameters
input (Tensor) – a minibatch of examples
 Returns
logprobabilities of for each class \(c\) in range \(0 <= c <= n\_classes\), where \(n\_classes\) is a parameter passed to
AdaptiveLogSoftmaxWithLoss
constructor.
 Shape:
Input: \((N, in\_features)\)
Output: \((N, n\_classes)\)

predict
(input)[source]¶ This is equivalent to self.log_pob(input).argmax(dim=1), but is more efficient in some cases.
 Parameters
input (Tensor) – a minibatch of examples
 Returns
a class with the highest probability for each example
 Return type
output (Tensor)
 Shape:
Input: \((N, in\_features)\)
Output: \((N)\)
Normalization layers¶
BatchNorm1d¶

class
torch.nn.
BatchNorm1d
(num_features, eps=1e05, momentum=0.1, affine=True, track_running_stats=True)[source]¶ Applies Batch Normalization over a 2D or 3D input (a minibatch of 1D inputs with optional additional channel dimension) as described in the paper Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift .
\[y = \frac{x  \mathrm{E}[x]}{\sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta\]The mean and standarddeviation are calculated perdimension over the minibatches and \(\gamma\) and \(\beta\) are learnable parameter vectors of size C (where C is the input size). By default, the elements of \(\gamma\) are sampled from \(\mathcal{U}(0, 1)\) and the elements of \(\beta\) are set to 0.
Also by default, during training this layer keeps running estimates of its computed mean and variance, which are then used for normalization during evaluation. The running estimates are kept with a default
momentum
of 0.1.If
track_running_stats
is set toFalse
, this layer then does not keep running estimates, and batch statistics are instead used during evaluation time as well.Note
This
momentum
argument is different from one used in optimizer classes and the conventional notion of momentum. Mathematically, the update rule for running statistics here is \(\hat{x}_\text{new} = (1  \text{momentum}) \times \hat{x} + \text{momentum} \times x_t\), where \(\hat{x}\) is the estimated statistic and \(x_t\) is the new observed value.Because the Batch Normalization is done over the C dimension, computing statistics on (N, L) slices, it’s common terminology to call this Temporal Batch Normalization.
 Parameters
num_features – \(C\) from an expected input of size \((N, C, L)\) or \(L\) from input of size \((N, L)\)
eps – a value added to the denominator for numerical stability. Default: 1e5
momentum – the value used for the running_mean and running_var computation. Can be set to
None
for cumulative moving average (i.e. simple average). Default: 0.1affine – a boolean value that when set to
True
, this module has learnable affine parameters. Default:True
track_running_stats – a boolean value that when set to
True
, this module tracks the running mean and variance, and when set toFalse
, this module does not track such statistics and always uses batch statistics in both training and eval modes. Default:True
 Shape:
Input: \((N, C)\) or \((N, C, L)\)
Output: \((N, C)\) or \((N, C, L)\) (same shape as input)
Examples:
>>> # With Learnable Parameters >>> m = nn.BatchNorm1d(100) >>> # Without Learnable Parameters >>> m = nn.BatchNorm1d(100, affine=False) >>> input = torch.randn(20, 100) >>> output = m(input)
BatchNorm2d¶

class
torch.nn.
BatchNorm2d
(num_features, eps=1e05, momentum=0.1, affine=True, track_running_stats=True)[source]¶ Applies Batch Normalization over a 4D input (a minibatch of 2D inputs with additional channel dimension) as described in the paper Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift .
\[y = \frac{x  \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta\]The mean and standarddeviation are calculated perdimension over the minibatches and \(\gamma\) and \(\beta\) are learnable parameter vectors of size C (where C is the input size). By default, the elements of \(\gamma\) are sampled from \(\mathcal{U}(0, 1)\) and the elements of \(\beta\) are set to 0.
Also by default, during training this layer keeps running estimates of its computed mean and variance, which are then used for normalization during evaluation. The running estimates are kept with a default
momentum
of 0.1.If
track_running_stats
is set toFalse
, this layer then does not keep running estimates, and batch statistics are instead used during evaluation time as well.Note
This
momentum
argument is different from one used in optimizer classes and the conventional notion of momentum. Mathematically, the update rule for running statistics here is \(\hat{x}_\text{new} = (1  \text{momentum}) \times \hat{x} + \text{momentum} \times x_t\), where \(\hat{x}\) is the estimated statistic and \(x_t\) is the new observed value.Because the Batch Normalization is done over the C dimension, computing statistics on (N, H, W) slices, it’s common terminology to call this Spatial Batch Normalization.
 Parameters
num_features – \(C\) from an expected input of size \((N, C, H, W)\)
eps – a value added to the denominator for numerical stability. Default: 1e5
momentum – the value used for the running_mean and running_var computation. Can be set to
None
for cumulative moving average (i.e. simple average). Default: 0.1affine – a boolean value that when set to
True
, this module has learnable affine parameters. Default:True
track_running_stats – a boolean value that when set to
True
, this module tracks the running mean and variance, and when set toFalse
, this module does not track such statistics and always uses batch statistics in both training and eval modes. Default:True
 Shape:
Input: \((N, C, H, W)\)
Output: \((N, C, H, W)\) (same shape as input)
Examples:
>>> # With Learnable Parameters >>> m = nn.BatchNorm2d(100) >>> # Without Learnable Parameters >>> m = nn.BatchNorm2d(100, affine=False) >>> input = torch.randn(20, 100, 35, 45) >>> output = m(input)
BatchNorm3d¶

class
torch.nn.
BatchNorm3d
(num_features, eps=1e05, momentum=0.1, affine=True, track_running_stats=True)[source]¶ Applies Batch Normalization over a 5D input (a minibatch of 3D inputs with additional channel dimension) as described in the paper Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift .
\[y = \frac{x  \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta\]The mean and standarddeviation are calculated perdimension over the minibatches and \(\gamma\) and \(\beta\) are learnable parameter vectors of size C (where C is the input size). By default, the elements of \(\gamma\) are sampled from \(\mathcal{U}(0, 1)\) and the elements of \(\beta\) are set to 0.
Also by default, during training this layer keeps running estimates of its computed mean and variance, which are then used for normalization during evaluation. The running estimates are kept with a default
momentum
of 0.1.If
track_running_stats
is set toFalse
, this layer then does not keep running estimates, and batch statistics are instead used during evaluation time as well.Note
This
momentum
argument is different from one used in optimizer classes and the conventional notion of momentum. Mathematically, the update rule for running statistics here is \(\hat{x}_\text{new} = (1  \text{momentum}) \times \hat{x} + \text{momentum} \times x_t\), where \(\hat{x}\) is the estimated statistic and \(x_t\) is the new observed value.Because the Batch Normalization is done over the C dimension, computing statistics on (N, D, H, W) slices, it’s common terminology to call this Volumetric Batch Normalization or Spatiotemporal Batch Normalization.
 Parameters
num_features – \(C\) from an expected input of size \((N, C, D, H, W)\)
eps – a value added to the denominator for numerical stability. Default: 1e5
momentum – the value used for the running_mean and running_var computation. Can be set to
None
for cumulative moving average (i.e. simple average). Default: 0.1affine – a boolean value that when set to
True
, this module has learnable affine parameters. Default:True
track_running_stats – a boolean value that when set to
True
, this module tracks the running mean and variance, and when set toFalse
, this module does not track such statistics and always uses batch statistics in both training and eval modes. Default:True
 Shape:
Input: \((N, C, D, H, W)\)
Output: \((N, C, D, H, W)\) (same shape as input)
Examples:
>>> # With Learnable Parameters >>> m = nn.BatchNorm3d(100) >>> # Without Learnable Parameters >>> m = nn.BatchNorm3d(100, affine=False) >>> input = torch.randn(20, 100, 35, 45, 10) >>> output = m(input)
GroupNorm¶

class
torch.nn.
GroupNorm
(num_groups, num_channels, eps=1e05, affine=True)[source]¶ Applies Group Normalization over a minibatch of inputs as described in the paper Group Normalization .
\[y = \frac{x  \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta \]The input channels are separated into
num_groups
groups, each containingnum_channels / num_groups
channels. The mean and standarddeviation are calculated separately over the each group. \(\gamma\) and \(\beta\) are learnable perchannel affine transform parameter vectors of sizenum_channels
ifaffine
isTrue
.This layer uses statistics computed from input data in both training and evaluation modes.
 Parameters
num_groups (int) – number of groups to separate the channels into
num_channels (int) – number of channels expected in input
eps – a value added to the denominator for numerical stability. Default: 1e5
affine – a boolean value that when set to
True
, this module has learnable perchannel affine parameters initialized to ones (for weights) and zeros (for biases). Default:True
.
 Shape:
Input: \((N, C, *)\) where \(C=\text{num\_channels}\)
Output: \((N, C, *)\) (same shape as input)
Examples:
>>> input = torch.randn(20, 6, 10, 10) >>> # Separate 6 channels into 3 groups >>> m = nn.GroupNorm(3, 6) >>> # Separate 6 channels into 6 groups (equivalent with InstanceNorm) >>> m = nn.GroupNorm(6, 6) >>> # Put all 6 channels into a single group (equivalent with LayerNorm) >>> m = nn.GroupNorm(1, 6) >>> # Activating the module >>> output = m(input)
SyncBatchNorm¶

class
torch.nn.
SyncBatchNorm
(num_features, eps=1e05, momentum=0.1, affine=True, track_running_stats=True, process_group=None)[source]¶ Applies Batch Normalization over a NDimensional input (a minibatch of [N2]D inputs with additional channel dimension) as described in the paper Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift .
\[y = \frac{x  \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta\]The mean and standarddeviation are calculated perdimension over all minibatches of the same process groups. \(\gamma\) and \(\beta\) are learnable parameter vectors of size C (where C is the input size). By default, the elements of \(\gamma\) are sampled from \(\mathcal{U}(0, 1)\) and the elements of \(\beta\) are set to 0.
Also by default, during training this layer keeps running estimates of its computed mean and variance, which are then used for normalization during evaluation. The running estimates are kept with a default
momentum
of 0.1.If
track_running_stats
is set toFalse
, this layer then does not keep running estimates, and batch statistics are instead used during evaluation time as well.Note
This
momentum
argument is different from one used in optimizer classes and the conventional notion of momentum. Mathematically, the update rule for running statistics here is \(\hat{x}_\text{new} = (1  \text{momentum}) \times \hat{x} + \text{momemtum} \times x_t\), where \(\hat{x}\) is the estimated statistic and \(x_t\) is the new observed value.Because the Batch Normalization is done over the C dimension, computing statistics on (N, +) slices, it’s common terminology to call this Volumetric Batch Normalization or Spatiotemporal Batch Normalization.
Currently SyncBatchNorm only supports DistributedDataParallel with single GPU per process. Use torch.nn.SyncBatchNorm.convert_sync_batchnorm() to convert BatchNorm layer to SyncBatchNorm before wrapping Network with DDP.
 Parameters
num_features – \(C\) from an expected input of size \((N, C, +)\)
eps – a value added to the denominator for numerical stability. Default: 1e5
momentum – the value used for the running_mean and running_var computation. Can be set to
None
for cumulative moving average (i.e. simple average). Default: 0.1affine – a boolean value that when set to
True
, this module has learnable affine parameters. Default:True
track_running_stats – a boolean value that when set to
True
, this module tracks the running mean and variance, and when set toFalse
, this module does not track such statistics and always uses batch statistics in both training and eval modes. Default:True
process_group – synchronization of stats happen within each process group individually. Default behavior is synchronization across the whole world
 Shape:
Input: \((N, C, +)\)
Output: \((N, C, +)\) (same shape as input)
Examples:
>>> # With Learnable Parameters >>> m = nn.SyncBatchNorm(100) >>> # creating process group (optional) >>> # process_ids is a list of int identifying rank ids. >>> process_group = torch.distributed.new_group(process_ids) >>> # Without Learnable Parameters >>> m = nn.BatchNorm3d(100, affine=False, process_group=process_group) >>> input = torch.randn(20, 100, 35, 45, 10) >>> output = m(input) >>> # network is nn.BatchNorm layer >>> sync_bn_network = torch.nn.utils.convert_sync_batchnorm(network, process_group) >>> # only single gpu per process is currently supported >>> ddp_sync_bn_network = torch.nn.parallel.DistributedDataParallel( >>> sync_bn_network, >>> device_ids=[args.local_rank], >>> output_device=args.local_rank)

classmethod
convert_sync_batchnorm
(module, process_group=None)[source]¶ Helper function to convert torch.nn.BatchNormND layer in the model to torch.nn.SyncBatchNorm layer.
 Parameters
module (nn.Module) – containing module
process_group (optional) – process group to scope synchronization,
default is the whole world
 Returns
The original module with the converted torch.nn.SyncBatchNorm layer
Example:
>>> # Network with nn.BatchNorm layer >>> module = torch.nn.Sequential( >>> torch.nn.Linear(20, 100), >>> torch.nn.BatchNorm1d(100) >>> ).cuda() >>> # creating process group (optional) >>> # process_ids is a list of int identifying rank ids. >>> process_group = torch.distributed.new_group(process_ids) >>> sync_bn_module = convert_sync_batchnorm(module, process_group)
InstanceNorm1d¶

class
torch.nn.
InstanceNorm1d
(num_features, eps=1e05, momentum=0.1, affine=False, track_running_stats=False)[source]¶ Applies Instance Normalization over a 3D input (a minibatch of 1D inputs with optional additional channel dimension) as described in the paper Instance Normalization: The Missing Ingredient for Fast Stylization .
\[y = \frac{x  \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta\]The mean and standarddeviation are calculated perdimension separately for each object in a minibatch. \(\gamma\) and \(\beta\) are learnable parameter vectors of size C (where C is the input size) if
affine
isTrue
.By default, this layer uses instance statistics computed from input data in both training and evaluation modes.
If
track_running_stats
is set toTrue
, during training this layer keeps running estimates of its computed mean and variance, which are then used for normalization during evaluation. The running estimates are kept with a defaultmomentum
of 0.1.Note
This
momentum
argument is different from one used in optimizer classes and the conventional notion of momentum. Mathematically, the update rule for running statistics here is \(\hat{x}_\text{new} = (1  \text{momentum}) \times \hat{x} + \text{momemtum} \times x_t\), where \(\hat{x}\) is the estimated statistic and \(x_t\) is the new observed value.Note
InstanceNorm1d
andLayerNorm
are very similar, but have some subtle differences.InstanceNorm1d
is applied on each channel of channeled data like multidimensional time series, butLayerNorm
is usually applied on entire sample and often in NLP tasks. Additionaly,LayerNorm
applies elementwise affine transform, whileInstanceNorm1d
usually don’t apply affine transform. Parameters
num_features – \(C\) from an expected input of size \((N, C, L)\) or \(L\) from input of size \((N, L)\)
eps – a value added to the denominator for numerical stability. Default: 1e5
momentum – the value used for the running_mean and running_var computation. Default: 0.1
affine – a boolean value that when set to
True
, this module has learnable affine parameters, initialized the same way as done for batch normalization. Default:False
.track_running_stats – a boolean value that when set to
True
, this module tracks the running mean and variance, and when set toFalse
, this module does not track such statistics and always uses batch statistics in both training and eval modes. Default:False
 Shape:
Input: \((N, C, L)\)
Output: \((N, C, L)\) (same shape as input)
Examples:
>>> # Without Learnable Parameters >>> m = nn.InstanceNorm1d(100) >>> # With Learnable Parameters >>> m = nn.InstanceNorm1d(100, affine=True) >>> input = torch.randn(20, 100, 40) >>> output = m(input)
InstanceNorm2d¶

class
torch.nn.
InstanceNorm2d
(num_features, eps=1e05, momentum=0.1, affine=False, track_running_stats=False)[source]¶ Applies Instance Normalization over a 4D input (a minibatch of 2D inputs with additional channel dimension) as described in the paper Instance Normalization: The Missing Ingredient for Fast Stylization .
\[y = \frac{x  \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta\]The mean and standarddeviation are calculated perdimension separately for each object in a minibatch. \(\gamma\) and \(\beta\) are learnable parameter vectors of size C (where C is the input size) if
affine
isTrue
.By default, this layer uses instance statistics computed from input data in both training and evaluation modes.
If
track_running_stats
is set toTrue
, during training this layer keeps running estimates of its computed mean and variance, which are then used for normalization during evaluation. The running estimates are kept with a defaultmomentum
of 0.1.Note
This
momentum
argument is different from one used in optimizer classes and the conventional notion of momentum. Mathematically, the update rule for running statistics here is \(\hat{x}_\text{new} = (1  \text{momentum}) \times \hat{x} + \text{momemtum} \times x_t\), where \(\hat{x}\) is the estimated statistic and \(x_t\) is the new observed value.Note
InstanceNorm2d
andLayerNorm
are very similar, but have some subtle differences.InstanceNorm2d
is applied on each channel of channeled data like RGB images, butLayerNorm
is usually applied on entire sample and often in NLP tasks. Additionaly,LayerNorm
applies elementwise affine transform, whileInstanceNorm2d
usually don’t apply affine transform. Parameters
num_features – \(C\) from an expected input of size \((N, C, H, W)\)
eps – a value added to the denominator for numerical stability. Default: 1e5
momentum – the value used for the running_mean and running_var computation. Default: 0.1
affine – a boolean value that when set to
True
, this module has learnable affine parameters, initialized the same way as done for batch normalization. Default:False
.track_running_stats – a boolean value that when set to
True
, this module tracks the running mean and variance, and when set toFalse
, this module does not track such statistics and always uses batch statistics in both training and eval modes. Default:False
 Shape:
Input: \((N, C, H, W)\)
Output: \((N, C, H, W)\) (same shape as input)
Examples:
>>> # Without Learnable Parameters >>> m = nn.InstanceNorm2d(100) >>> # With Learnable Parameters >>> m = nn.InstanceNorm2d(100, affine=True) >>> input = torch.randn(20, 100, 35, 45) >>> output = m(input)
InstanceNorm3d¶

class
torch.nn.
InstanceNorm3d
(num_features, eps=1e05, momentum=0.1, affine=False, track_running_stats=False)[source]¶ Applies Instance Normalization over a 5D input (a minibatch of 3D inputs with additional channel dimension) as described in the paper Instance Normalization: The Missing Ingredient for Fast Stylization .
\[y = \frac{x  \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta\]The mean and standarddeviation are calculated perdimension separately for each object in a minibatch. \(\gamma\) and \(\beta\) are learnable parameter vectors of size C (where C is the input size) if
affine
isTrue
.By default, this layer uses instance statistics computed from input data in both training and evaluation modes.
If
track_running_stats
is set toTrue
, during training this layer keeps running estimates of its computed mean and variance, which are then used for normalization during evaluation. The running estimates are kept with a defaultmomentum
of 0.1.Note
This
momentum
argument is different from one used in optimizer classes and the conventional notion of momentum. Mathematically, the update rule for running statistics here is \(\hat{x}_\text{new} = (1  \text{momentum}) \times \hat{x} + \text{momemtum} \times x_t\), where \(\hat{x}\) is the estimated statistic and \(x_t\) is the new observed value.Note
InstanceNorm3d
andLayerNorm
are very similar, but have some subtle differences.InstanceNorm3d
is applied on each channel of channeled data like 3D models with RGB color, butLayerNorm
is usually applied on entire sample and often in NLP tasks. Additionaly,LayerNorm
applies elementwise affine transform, whileInstanceNorm3d
usually don’t apply affine transform. Parameters
num_features – \(C\) from an expected input of size \((N, C, D, H, W)\)
eps – a value added to the denominator for numerical stability. Default: 1e5
momentum – the value used for the running_mean and running_var computation. Default: 0.1
affine – a boolean value that when set to
True
, this module has learnable affine parameters, initialized the same way as done for batch normalization. Default:False
.track_running_stats – a boolean value that when set to
True
, this module tracks the running mean and variance, and when set toFalse
, this module does not track such statistics and always uses batch statistics in both training and eval modes. Default:False
 Shape:
Input: \((N, C, D, H, W)\)
Output: \((N, C, D, H, W)\) (same shape as input)
Examples:
>>> # Without Learnable Parameters >>> m = nn.InstanceNorm3d(100) >>> # With Learnable Parameters >>> m = nn.InstanceNorm3d(100, affine=True) >>> input = torch.randn(20, 100, 35, 45, 10) >>> output = m(input)
LayerNorm¶

class
torch.nn.
LayerNorm
(normalized_shape, eps=1e05, elementwise_affine=True)[source]¶ Applies Layer Normalization over a minibatch of inputs as described in the paper Layer Normalization .
\[y = \frac{x  \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta \]The mean and standarddeviation are calculated separately over the last certain number dimensions which have to be of the shape specified by
normalized_shape
. \(\gamma\) and \(\beta\) are learnable affine transform parameters ofnormalized_shape
ifelementwise_affine
isTrue
.Note
Unlike Batch Normalization and Instance Normalization, which applies scalar scale and bias for each entire channel/plane with the
affine
option, Layer Normalization applies perelement scale and bias withelementwise_affine
.This layer uses statistics computed from input data in both training and evaluation modes.
 Parameters
normalized_shape (int or list or torch.Size) –
input shape from an expected input of size
\[[* \times \text{normalized\_shape}[0] \times \text{normalized\_shape}[1] \times \ldots \times \text{normalized\_shape}[1]] \]If a single integer is used, it is treated as a singleton list, and this module will normalize over the last dimension which is expected to be of that specific size.
eps – a value added to the denominator for numerical stability. Default: 1e5
elementwise_affine – a boolean value that when set to
True
, this module has learnable perelement affine parameters initialized to ones (for weights) and zeros (for biases). Default:True
.
 Shape:
Input: \((N, *)\)
Output: \((N, *)\) (same shape as input)
Examples:
>>> input = torch.randn(20, 5, 10, 10) >>> # With Learnable Parameters >>> m = nn.LayerNorm(input.size()[1:]) >>> # Without Learnable Parameters >>> m = nn.LayerNorm(input.size()[1:], elementwise_affine=False) >>> # Normalize over last two dimensions >>> m = nn.LayerNorm([10, 10]) >>> # Normalize over last dimension of size 10 >>> m = nn.LayerNorm(10) >>> # Activating the module >>> output = m(input)
LocalResponseNorm¶

class
torch.nn.
LocalResponseNorm
(size, alpha=0.0001, beta=0.75, k=1.0)[source]¶ Applies local response normalization over an input signal composed of several input planes, where channels occupy the second dimension. Applies normalization across channels.
\[b_{c} = a_{c}\left(k + \frac{\alpha}{n} \sum_{c'=\max(0, cn/2)}^{\min(N1,c+n/2)}a_{c'}^2\right)^{\beta} \] Parameters
size – amount of neighbouring channels used for normalization
alpha – multiplicative factor. Default: 0.0001
beta – exponent. Default: 0.75
k – additive factor. Default: 1
 Shape:
Input: \((N, C, *)\)
Output: \((N, C, *)\) (same shape as input)
Examples:
>>> lrn = nn.LocalResponseNorm(2) >>> signal_2d = torch.randn(32, 5, 24, 24) >>> signal_4d = torch.randn(16, 5, 7, 7, 7, 7) >>> output_2d = lrn(signal_2d) >>> output_4d = lrn(signal_4d)
Recurrent layers¶
RNN¶

class
torch.nn.
RNN
(*args, **kwargs)[source]¶ Applies a multilayer Elman RNN with \(tanh\) or \(ReLU\) nonlinearity to an input sequence.
For each element in the input sequence, each layer computes the following function:
\[h_t = \text{tanh}(W_{ih} x_t + b_{ih} + W_{hh} h_{(t1)} + b_{hh}) \]where \(h_t\) is the hidden state at time t, \(x_t\) is the input at time t, and \(h_{(t1)}\) is the hidden state of the previous layer at time t1 or the initial hidden state at time 0. If
nonlinearity
is'relu'
, then ReLU is used instead of tanh. Parameters
input_size – The number of expected features in the input x
hidden_size – The number of features in the hidden state h
num_layers – Number of recurrent layers. E.g., setting
num_layers=2
would mean stacking two RNNs together to form a stacked RNN, with the second RNN taking in outputs of the first RNN and computing the final results. Default: 1nonlinearity – The nonlinearity to use. Can be either
'tanh'
or'relu'
. Default:'tanh'
bias – If
False
, then the layer does not use bias weights b_ih and b_hh. Default:True
batch_first – If
True
, then the input and output tensors are provided as (batch, seq, feature). Default:False
dropout – If nonzero, introduces a Dropout layer on the outputs of each RNN layer except the last layer, with dropout probability equal to
dropout
. Default: 0bidirectional – If
True
, becomes a bidirectional RNN. Default:False
 Inputs: input, h_0
input of shape (seq_len, batch, input_size): tensor containing the features of the input sequence. The input can also be a packed variable length sequence. See
torch.nn.utils.rnn.pack_padded_sequence()
ortorch.nn.utils.rnn.pack_sequence()
for details.h_0 of shape (num_layers * num_directions, batch, hidden_size): tensor containing the initial hidden state for each element in the batch. Defaults to zero if not provided. If the RNN is bidirectional, num_directions should be 2, else it should be 1.
 Outputs: output, h_n
output of shape (seq_len, batch, num_directions * hidden_size): tensor containing the output features (h_t) from the last layer of the RNN, for each t. If a
torch.nn.utils.rnn.PackedSequence
has been given as the input, the output will also be a packed sequence.For the unpacked case, the directions can be separated using
output.view(seq_len, batch, num_directions, hidden_size)
, with forward and backward being direction 0 and 1 respectively. Similarly, the directions can be separated in the packed case.h_n of shape (num_layers * num_directions, batch, hidden_size): tensor containing the hidden state for t = seq_len.
Like output, the layers can be separated using
h_n.view(num_layers, num_directions, batch, hidden_size)
.
 Shape:
Input1: \((L, N, H_{in})\) tensor containing input features where \(H_{in}=\text{input\_size}\) and L represents a sequence length.
Input2: \((S, N, H_{out})\) tensor containing the initial hidden state for each element in the batch. \(H_{out}=\text{hidden\_size}\) Defaults to zero if not provided. where \(S=\text{num\_layers} * \text{num\_directions}\) If the RNN is bidirectional, num_directions should be 2, else it should be 1.
Output1: \((L, N, H_{all})\) where \(H_all=\text{num\_directions} * \text{hidden\_size}\)
Output2: \((S, N, H_{out})\) tensor containing the next hidden state for each element in the batch
 Variables
~RNN.weight_ih_l[k] – the learnable inputhidden weights of the kth layer, of shape (hidden_size, input_size) for k = 0. Otherwise, the shape is (hidden_size, num_directions * hidden_size)
~RNN.weight_hh_l[k] – the learnable hiddenhidden weights of the kth layer, of shape (hidden_size, hidden_size)
~RNN.bias_ih_l[k] – the learnable inputhidden bias of the kth layer, of shape (hidden_size)
~RNN.bias_hh_l[k] – the learnable hiddenhidden bias of the kth layer, of shape (hidden_size)
Note
All the weights and biases are initialized from \(\mathcal{U}(\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{\text{hidden\_size}}\)
Note
If the following conditions are satisfied: 1) cudnn is enabled, 2) input data is on the GPU 3) input data has dtype
torch.float16
4) V100 GPU is used, 5) input data is not inPackedSequence
format persistent algorithm can be selected to improve performance.Examples:
>>> rnn = nn.RNN(10, 20, 2) >>> input = torch.randn(5, 3, 10) >>> h0 = torch.randn(2, 3, 20) >>> output, hn = rnn(input, h0)
LSTM¶

class
torch.nn.
LSTM
(*args, **kwargs)[source]¶ Applies a multilayer long shortterm memory (LSTM) RNN to an input sequence.
For each element in the input sequence, each layer computes the following function:
\[\begin{array}{ll} \\ i_t = \sigma(W_{ii} x_t + b_{ii} + W_{hi} h_{(t1)} + b_{hi}) \\ f_t = \sigma(W_{if} x_t + b_{if} + W_{hf} h_{(t1)} + b_{hf}) \\ g_t = \tanh(W_{ig} x_t + b_{ig} + W_{hg} h_{(t1)} + b_{hg}) \\ o_t = \sigma(W_{io} x_t + b_{io} + W_{ho} h_{(t1)} + b_{ho}) \\ c_t = f_t * c_{(t1)} + i_t * g_t \\ h_t = o_t * \tanh(c_t) \\ \end{array} \]where \(h_t\) is the hidden state at time t, \(c_t\) is the cell state at time t, \(x_t\) is the input at time t, \(h_{(t1)}\) is the hidden state of the layer at time t1 or the initial hidden state at time 0, and \(i_t\), \(f_t\), \(g_t\), \(o_t\) are the input, forget, cell, and output gates, respectively. \(\sigma\) is the sigmoid function, and \(*\) is the Hadamard product.
In a multilayer LSTM, the input \(x^{(l)}_t\) of the \(l\) th layer (\(l >= 2\)) is the hidden state \(h^{(l1)}_t\) of the previous layer multiplied by dropout \(\delta^{(l1)}_t\) where each \(\delta^{(l1)}_t\) is a Bernoulli random variable which is \(0\) with probability
dropout
. Parameters
input_size – The number of expected features in the input x
hidden_size – The number of features in the hidden state h
num_layers – Number of recurrent layers. E.g., setting
num_layers=2
would mean stacking two LSTMs together to form a stacked LSTM, with the second LSTM taking in outputs of the first LSTM and computing the final results. Default: 1bias – If
False
, then the layer does not use bias weights b_ih and b_hh. Default:True
batch_first – If
True
, then the input and output tensors are provided as (batch, seq, feature). Default:False
dropout – If nonzero, introduces a Dropout layer on the outputs of each LSTM layer except the last layer, with dropout probability equal to
dropout
. Default: 0bidirectional – If
True
, becomes a bidirectional LSTM. Default:False
 Inputs: input, (h_0, c_0)
input of shape (seq_len, batch, input_size): tensor containing the features of the input sequence. The input can also be a packed variable length sequence. See
torch.nn.utils.rnn.pack_padded_sequence()
ortorch.nn.utils.rnn.pack_sequence()
for details.h_0 of shape (num_layers * num_directions, batch, hidden_size): tensor containing the initial hidden state for each element in the batch. If the LSTM is bidirectional, num_directions should be 2, else it should be 1.
c_0 of shape (num_layers * num_directions, batch, hidden_size): tensor containing the initial cell state for each element in the batch.
If (h_0, c_0) is not provided, both h_0 and c_0 default to zero.
 Outputs: output, (h_n, c_n)
output of shape (seq_len, batch, num_directions * hidden_size): tensor containing the output features (h_t) from the last layer of the LSTM, for each t. If a
torch.nn.utils.rnn.PackedSequence
has been given as the input, the output will also be a packed sequence.For the unpacked case, the directions can be separated using
output.view(seq_len, batch, num_directions, hidden_size)
, with forward and backward being direction 0 and 1 respectively. Similarly, the directions can be separated in the packed case.h_n of shape (num_layers * num_directions, batch, hidden_size): tensor containing the hidden state for t = seq_len.
Like output, the layers can be separated using
h_n.view(num_layers, num_directions, batch, hidden_size)
and similarly for c_n.c_n of shape (num_layers * num_directions, batch, hidden_size): tensor containing the cell state for t = seq_len.
 Variables
~LSTM.weight_ih_l[k] – the learnable inputhidden weights of the \(\text{k}^{th}\) layer (W_iiW_ifW_igW_io), of shape (4*hidden_size, input_size) for k = 0. Otherwise, the shape is (4*hidden_size, num_directions * hidden_size)
~LSTM.weight_hh_l[k] – the learnable hiddenhidden weights of the \(\text{k}^{th}\) layer (W_hiW_hfW_hgW_ho), of shape (4*hidden_size, hidden_size)
~LSTM.bias_ih_l[k] – the learnable inputhidden bias of the \(\text{k}^{th}\) layer (b_iib_ifb_igb_io), of shape (4*hidden_size)
~LSTM.bias_hh_l[k] – the learnable hiddenhidden bias of the \(\text{k}^{th}\) layer (b_hib_hfb_hgb_ho), of shape (4*hidden_size)
Note
All the weights and biases are initialized from \(\mathcal{U}(\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{\text{hidden\_size}}\)
Note
If the following conditions are satisfied: 1) cudnn is enabled, 2) input data is on the GPU 3) input data has dtype
torch.float16
4) V100 GPU is used, 5) input data is not inPackedSequence
format persistent algorithm can be selected to improve performance.Examples:
>>> rnn = nn.LSTM(10, 20, 2) >>> input = torch.randn(5, 3, 10) >>> h0 = torch.randn(2, 3, 20) >>> c0 = torch.randn(2, 3, 20) >>> output, (hn, cn) = rnn(input, (h0, c0))
GRU¶

class
torch.nn.
GRU
(*args, **kwargs)[source]¶ Applies a multilayer gated recurrent unit (GRU) RNN to an input sequence.
For each element in the input sequence, each layer computes the following function:
\[\begin{array}{ll} r_t = \sigma(W_{ir} x_t + b_{ir} + W_{hr} h_{(t1)} + b_{hr}) \\ z_t = \sigma(W_{iz} x_t + b_{iz} + W_{hz} h_{(t1)} + b_{hz}) \\ n_t = \tanh(W_{in} x_t + b_{in} + r_t * (W_{hn} h_{(t1)}+ b_{hn})) \\ h_t = (1  z_t) * n_t + z_t * h_{(t1)} \end{array} \]where \(h_t\) is the hidden state at time t, \(x_t\) is the input at time t, \(h_{(t1)}\) is the hidden state of the layer at time t1 or the initial hidden state at time 0, and \(r_t\), \(z_t\), \(n_t\) are the reset, update, and new gates, respectively. \(\sigma\) is the sigmoid function, and \(*\) is the Hadamard product.
In a multilayer GRU, the input \(x^{(l)}_t\) of the \(l\) th layer (\(l >= 2\)) is the hidden state \(h^{(l1)}_t\) of the previous layer multiplied by dropout \(\delta^{(l1)}_t\) where each \(\delta^{(l1)}_t\) is a Bernoulli random variable which is \(0\) with probability
dropout
. Parameters
input_size – The number of expected features in the input x
hidden_size – The number of features in the hidden state h
num_layers – Number of recurrent layers. E.g., setting
num_layers=2
would mean stacking two GRUs together to form a stacked GRU, with the second GRU taking in outputs of the first GRU and computing the final results. Default: 1bias – If
False
, then the layer does not use bias weights b_ih and b_hh. Default:True
batch_first – If
True
, then the input and output tensors are provided as (batch, seq, feature). Default:False
dropout – If nonzero, introduces a Dropout layer on the outputs of each GRU layer except the last layer, with dropout probability equal to
dropout
. Default: 0bidirectional – If
True
, becomes a bidirectional GRU. Default:False
 Inputs: input, h_0
input of shape (seq_len, batch, input_size): tensor containing the features of the input sequence. The input can also be a packed variable length sequence. See
torch.nn.utils.rnn.pack_padded_sequence()
for details.h_0 of shape (num_layers * num_directions, batch, hidden_size): tensor containing the initial hidden state for each element in the batch. Defaults to zero if not provided. If the RNN is bidirectional, num_directions should be 2, else it should be 1.
 Outputs: output, h_n
output of shape (seq_len, batch, num_directions * hidden_size): tensor containing the output features h_t from the last layer of the GRU, for each t. If a
torch.nn.utils.rnn.PackedSequence
has been given as the input, the output will also be a packed sequence. For the unpacked case, the directions can be separated usingoutput.view(seq_len, batch, num_directions, hidden_size)
, with forward and backward being direction 0 and 1 respectively.Similarly, the directions can be separated in the packed case.
h_n of shape (num_layers * num_directions, batch, hidden_size): tensor containing the hidden state for t = seq_len
Like output, the layers can be separated using
h_n.view(num_layers, num_directions, batch, hidden_size)
.
 Shape:
Input1: \((L, N, H_{in})\) tensor containing input features where \(H_{in}=\text{input\_size}\) and L represents a sequence length.
Input2: \((S, N, H_{out})\) tensor containing the initial hidden state for each element in the batch. \(H_{out}=\text{hidden\_size}\) Defaults to zero if not provided. where \(S=\text{num\_layers} * \text{num\_directions}\) If the RNN is bidirectional, num_directions should be 2, else it should be 1.
Output1: \((L, N, H_{all})\) where \(H_all=\text{num\_directions} * \text{hidden\_size}\)
Output2: \((S, N, H_{out})\) tensor containing the next hidden state for each element in the batch
 Variables
~GRU.weight_ih_l[k] – the learnable inputhidden weights of the \(\text{k}^{th}\) layer (W_irW_izW_in), of shape (3*hidden_size, input_size) for k = 0. Otherwise, the shape is (3*hidden_size, num_directions * hidden_size)
~GRU.weight_hh_l[k] – the learnable hiddenhidden weights of the \(\text{k}^{th}\) layer (W_hrW_hzW_hn), of shape (3*hidden_size, hidden_size)
~GRU.bias_ih_l[k] – the learnable inputhidden bias of the \(\text{k}^{th}\) layer (b_irb_izb_in), of shape (3*hidden_size)
~GRU.bias_hh_l[k] – the learnable hiddenhidden bias of the \(\text{k}^{th}\) layer (b_hrb_hzb_hn), of shape (3*hidden_size)
Note
All the weights and biases are initialized from \(\mathcal{U}(\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{\text{hidden\_size}}\)
Note
If the following conditions are satisfied: 1) cudnn is enabled, 2) input data is on the GPU 3) input data has dtype
torch.float16
4) V100 GPU is used, 5) input data is not inPackedSequence
format persistent algorithm can be selected to improve performance.Examples:
>>> rnn = nn.GRU(10, 20, 2) >>> input = torch.randn(5, 3, 10) >>> h0 = torch.randn(2, 3, 20) >>> output, hn = rnn(input, h0)
RNNCell¶

class
torch.nn.
RNNCell
(input_size, hidden_size, bias=True, nonlinearity='tanh')[source]¶ An Elman RNN cell with tanh or ReLU nonlinearity.
\[h' = \tanh(W_{ih} x + b_{ih} + W_{hh} h + b_{hh})\]If
nonlinearity
is ‘relu’, then ReLU is used in place of tanh. Parameters
input_size – The number of expected features in the input x
hidden_size – The number of features in the hidden state h
bias – If
False
, then the layer does not use bias weights b_ih and b_hh. Default:True
nonlinearity – The nonlinearity to use. Can be either
'tanh'
or'relu'
. Default:'tanh'
 Inputs: input, hidden
input of shape (batch, input_size): tensor containing input features
hidden of shape (batch, hidden_size): tensor containing the initial hidden state for each element in the batch. Defaults to zero if not provided.
 Outputs: h’
h’ of shape (batch, hidden_size): tensor containing the next hidden state for each element in the batch
 Shape:
Input1: \((N, H_{in})\) tensor containing input features where \(H_{in}\) = input_size
Input2: \((N, H_{out})\) tensor containing the initial hidden state for each element in the batch where \(H_{out}\) = hidden_size Defaults to zero if not provided.
Output: \((N, H_{out})\) tensor containing the next hidden state for each element in the batch
 Variables
~RNNCell.weight_ih – the learnable inputhidden weights, of shape (hidden_size, input_size)
~RNNCell.weight_hh – the learnable hiddenhidden weights, of shape (hidden_size, hidden_size)
~RNNCell.bias_ih – the learnable inputhidden bias, of shape (hidden_size)
~RNNCell.bias_hh – the learnable hiddenhidden bias, of shape (hidden_size)
Note
All the weights and biases are initialized from \(\mathcal{U}(\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{\text{hidden\_size}}\)
Examples:
>>> rnn = nn.RNNCell(10, 20) >>> input = torch.randn(6, 3, 10) >>> hx = torch.randn(3, 20) >>> output = [] >>> for i in range(6): hx = rnn(input[i], hx) output.append(hx)
LSTMCell¶

class
torch.nn.
LSTMCell
(input_size, hidden_size, bias=True)[source]¶ A long shortterm memory (LSTM) cell.
\[\begin{array}{ll} i = \sigma(W_{ii} x + b_{ii} + W_{hi} h + b_{hi}) \\ f = \sigma(W_{if} x + b_{if} + W_{hf} h + b_{hf}) \\ g = \tanh(W_{ig} x + b_{ig} + W_{hg} h + b_{hg}) \\ o = \sigma(W_{io} x + b_{io} + W_{ho} h + b_{ho}) \\ c' = f * c + i * g \\ h' = o * \tanh(c') \\ \end{array}\]where \(\sigma\) is the sigmoid function, and \(*\) is the Hadamard product.
 Parameters
input_size – The number of expected features in the input x
hidden_size – The number of features in the hidden state h
bias – If
False
, then the layer does not use bias weights b_ih and b_hh. Default:True
 Inputs: input, (h_0, c_0)
input of shape (batch, input_size): tensor containing input features
h_0 of shape (batch, hidden_size): tensor containing the initial hidden state for each element in the batch.
c_0 of shape (batch, hidden_size): tensor containing the initial cell state for each element in the batch.
If (h_0, c_0) is not provided, both h_0 and c_0 default to zero.
 Outputs: (h_1, c_1)
h_1 of shape (batch, hidden_size): tensor containing the next hidden state for each element in the batch
c_1 of shape (batch, hidden_size): tensor containing the next cell state for each element in the batch
 Variables
~LSTMCell.weight_ih – the learnable inputhidden weights, of shape (4*hidden_size, input_size)
~LSTMCell.weight_hh – the learnable hiddenhidden weights, of shape (4*hidden_size, hidden_size)
~LSTMCell.bias_ih – the learnable inputhidden bias, of shape (4*hidden_size)
~LSTMCell.bias_hh – the learnable hiddenhidden bias, of shape (4*hidden_size)
Note
All the weights and biases are initialized from \(\mathcal{U}(\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{\text{hidden\_size}}\)
Examples:
>>> rnn = nn.LSTMCell(10, 20) >>> input = torch.randn(6, 3, 10) >>> hx = torch.randn(3, 20) >>> cx = torch.randn(3, 20) >>> output = [] >>> for i in range(6): hx, cx = rnn(input[i], (hx, cx)) output.append(hx)
GRUCell¶

class
torch.nn.
GRUCell
(input_size, hidden_size, bias=True)[source]¶ A gated recurrent unit (GRU) cell
\[\begin{array}{ll} r = \sigma(W_{ir} x + b_{ir} + W_{hr} h + b_{hr}) \\ z = \sigma(W_{iz} x + b_{iz} + W_{hz} h + b_{hz}) \\ n = \tanh(W_{in} x + b_{in} + r * (W_{hn} h + b_{hn})) \\ h' = (1  z) * n + z * h \end{array}\]where \(\sigma\) is the sigmoid function, and \(*\) is the Hadamard product.
 Parameters
input_size – The number of expected features in the input x
hidden_size – The number of features in the hidden state h
bias – If
False
, then the layer does not use bias weights b_ih and b_hh. Default:True
 Inputs: input, hidden
input of shape (batch, input_size): tensor containing input features
hidden of shape (batch, hidden_size): tensor containing the initial hidden state for each element in the batch. Defaults to zero if not provided.
 Outputs: h’
h’ of shape (batch, hidden_size): tensor containing the next hidden state for each element in the batch
 Shape:
Input1: \((N, H_{in})\) tensor containing input features where \(H_{in}\) = input_size
Input2: \((N, H_{out})\) tensor containing the initial hidden state for each element in the batch where \(H_{out}\) = hidden_size Defaults to zero if not provided.
Output: \((N, H_{out})\) tensor containing the next hidden state for each element in the batch
 Variables
~GRUCell.weight_ih – the learnable inputhidden weights, of shape (3*hidden_size, input_size)
~GRUCell.weight_hh – the learnable hiddenhidden weights, of shape (3*hidden_size, hidden_size)
~GRUCell.bias_ih – the learnable inputhidden bias, of shape (3*hidden_size)
~GRUCell.bias_hh – the learnable hiddenhidden bias, of shape (3*hidden_size)
Note
All the weights and biases are initialized from \(\mathcal{U}(\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{\text{hidden\_size}}\)
Examples:
>>> rnn = nn.GRUCell(10, 20) >>> input = torch.randn(6, 3, 10) >>> hx = torch.randn(3, 20) >>> output = [] >>> for i in range(6): hx = rnn(input[i], hx) output.append(hx)
Linear layers¶
Identity¶

class
torch.nn.
Identity
(*args, **kwargs)[source]¶ A placeholder identity operator that is argumentinsensitive.
 Parameters
args – any argument (unused)
kwargs – any keyword argument (unused)
Examples:
>>> m = nn.Identity(54, unused_argument1=0.1, unused_argument2=False) >>> input = torch.randn(128, 20) >>> output = m(input) >>> print(output.size()) torch.Size([128, 20])
Linear¶

class
torch.nn.
Linear
(in_features, out_features, bias=True)[source]¶ Applies a linear transformation to the incoming data: \(y = xA^T + b\)
 Parameters
in_features – size of each input sample
out_features – size of each output sample
bias – If set to
False
, the layer will not learn an additive bias. Default:True
 Shape:
Input: \((N, *, H_{in})\) where \(*\) means any number of additional dimensions and \(H_{in} = \text{in\_features}\)
Output: \((N, *, H_{out})\) where all but the last dimension are the same shape as the input and \(H_{out} = \text{out\_features}\).
 Variables
~Linear.weight – the learnable weights of the module of shape \((\text{out\_features}, \text{in\_features})\). The values are initialized from \(\mathcal{U}(\sqrt{k}, \sqrt{k})\), where \(k = \frac{1}{\text{in\_features}}\)
~Linear.bias – the learnable bias of the module of shape \((\text{out\_features})\). If
bias
isTrue
, the values are initialized from \(\mathcal{U}(\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{\text{in\_features}}\)
Examples:
>>> m = nn.Linear(20, 30) >>> input = torch.randn(128, 20) >>> output = m(input) >>> print(output.size()) torch.Size([128, 30])
Bilinear¶

class
torch.nn.
Bilinear
(in1_features, in2_features, out_features, bias=True)[source]¶ Applies a bilinear transformation to the incoming data: \(y = x_1 A x_2 + b\)
 Parameters
in1_features – size of each first input sample
in2_features – size of each second input sample
out_features – size of each output sample
bias – If set to False, the layer will not learn an additive bias. Default:
True
 Shape:
Input1: \((N, *, H_{in1})\) where \(H_{in1}=\text{in1\_features}\) and \(*\) means any number of additional dimensions. All but the last dimension of the inputs should be the same.
Input2: \((N, *, H_{in2})\) where \(H_{in2}=\text{in2\_features}\).
Output: \((N, *, H_{out})\) where \(H_{out}=\text{out\_features}\) and all but the last dimension are the same shape as the input.
 Variables
~Bilinear.weight – the learnable weights of the module of shape \((\text{out\_features}, \text{in1\_features}, \text{in2\_features})\). The values are initialized from \(\mathcal{U}(\sqrt{k}, \sqrt{k})\), where \(k = \frac{1}{\text{in1\_features}}\)
~Bilinear.bias – the learnable bias of the module of shape \((\text{out\_features})\). If
bias
isTrue
, the values are initialized from \(\mathcal{U}(\sqrt{k}, \sqrt{k})\), where \(k = \frac{1}{\text{in1\_features}}\)
Examples:
>>> m = nn.Bilinear(20, 30, 40) >>> input1 = torch.randn(128, 20) >>> input2 = torch.randn(128, 30) >>> output = m(input1, input2) >>> print(output.size()) torch.Size([128, 40])
Dropout layers¶
Dropout¶

class
torch.nn.
Dropout
(p=0.5, inplace=False)[source]¶ During training, randomly zeroes some of the elements of the input tensor with probability
p
using samples from a Bernoulli distribution. Each channel will be zeroed out independently on every forward call.This has proven to be an effective technique for regularization and preventing the coadaptation of neurons as described in the paper Improving neural networks by preventing coadaptation of feature detectors .
Furthermore, the outputs are scaled by a factor of \(\frac{1}{1p}\) during training. This means that during evaluation the module simply computes an identity function.
 Parameters
p – probability of an element to be zeroed. Default: 0.5
inplace – If set to
True
, will do this operation inplace. Default:False
 Shape:
Input: \((*)\). Input can be of any shape
Output: \((*)\). Output is of the same shape as input
Examples:
>>> m = nn.Dropout(p=0.2) >>> input = torch.randn(20, 16) >>> output = m(input)
Dropout2d¶

class
torch.nn.
Dropout2d
(p=0.5, inplace=False)[source]¶ Randomly zero out entire channels (a channel is a 2D feature map, e.g., the \(j\)th channel of the \(i\)th sample in the batched input is a 2D tensor \(\text{input}[i, j]\)). Each channel will be zeroed out independently on every forward call with probability
p
using samples from a Bernoulli distribution.Usually the input comes from
nn.Conv2d
modules.As described in the paper Efficient Object Localization Using Convolutional Networks , if adjacent pixels within feature maps are strongly correlated (as is normally the case in early convolution layers) then i.i.d. dropout will not regularize the activations and will otherwise just result in an effective learning rate decrease.
In this case,
nn.Dropout2d()
will help promote independence between feature maps and should be used instead. Parameters
 Shape:
Input: \((N, C, H, W)\)
Output: \((N, C, H, W)\) (same shape as input)
Examples:
>>> m = nn.Dropout2d(p=0.2) >>> input = torch.randn(20, 16, 32, 32) >>> output = m(input)
Dropout3d¶

class
torch.nn.
Dropout3d
(p=0.5, inplace=False)[source]¶ Randomly zero out entire channels (a channel is a 3D feature map, e.g., the \(j\)th channel of the \(i\)th sample in the batched input is a 3D tensor \(\text{input}[i, j]\)). Each channel will be zeroed out independently on every forward call with probability
p
using samples from a Bernoulli distribution.Usually the input comes from
nn.Conv3d
modules.As described in the paper Efficient Object Localization Using Convolutional Networks , if adjacent pixels within feature maps are strongly correlated (as is normally the case in early convolution layers) then i.i.d. dropout will not regularize the activations and will otherwise just result in an effective learning rate decrease.
In this case,
nn.Dropout3d()
will help promote independence between feature maps and should be used instead. Parameters
 Shape:
Input: \((N, C, D, H, W)\)
Output: \((N, C, D, H, W)\) (same shape as input)
Examples:
>>> m = nn.Dropout3d(p=0.2) >>> input = torch.randn(20, 16, 4, 32, 32) >>> output = m(input)
AlphaDropout¶

class
torch.nn.
AlphaDropout
(p=0.5, inplace=False)[source]¶ Applies Alpha Dropout over the input.
Alpha Dropout is a type of Dropout that maintains the selfnormalizing property. For an input with zero mean and unit standard deviation, the output of Alpha Dropout maintains the original mean and standard deviation of the input. Alpha Dropout goes handinhand with SELU activation function, which ensures that the outputs have zero mean and unit standard deviation.
During training, it randomly masks some of the elements of the input tensor with probability p using samples from a bernoulli distribution. The elements to masked are randomized on every forward call, and scaled and shifted to maintain zero mean and unit standard deviation.
During evaluation the module simply computes an identity function.
More details can be found in the paper SelfNormalizing Neural Networks .
 Parameters
 Shape:
Input: \((*)\). Input can be of any shape
Output: \((*)\). Output is of the same shape as input
Examples:
>>> m = nn.AlphaDropout(p=0.2) >>> input = torch.randn(20, 16) >>> output = m(input)
Sparse layers¶
Embedding¶

class
torch.nn.
Embedding
(num_embeddings, embedding_dim, padding_idx=None, max_norm=None, norm_type=2.0, scale_grad_by_freq=False, sparse=False, _weight=None)[source]¶ A simple lookup table that stores embeddings of a fixed dictionary and size.
This module is often used to store word embeddings and retrieve them using indices. The input to the module is a list of indices, and the output is the corresponding word embeddings.
 Parameters
num_embeddings (int) – size of the dictionary of embeddings
embedding_dim (int) – the size of each embedding vector
padding_idx (int, optional) – If given, pads the output with the embedding vector at
padding_idx
(initialized to zeros) whenever it encounters the index.max_norm (float, optional) – If given, each embedding vector with norm larger than
max_norm
is renormalized to have normmax_norm
.norm_type (float, optional) – The p of the pnorm to compute for the
max_norm
option. Default2
.scale_grad_by_freq (boolean, optional) – If given, this will scale gradients by the inverse of frequency of the words in the minibatch. Default
False
.sparse (bool, optional) – If
True
, gradient w.r.t.weight
matrix will be a sparse tensor. See Notes for more details regarding sparse gradients.
 Variables
~Embedding.weight (Tensor) – the learnable weights of the module of shape (num_embeddings, embedding_dim) initialized from \(\mathcal{N}(0, 1)\)
 Shape:
Input: \((*)\), LongTensor of arbitrary shape containing the indices to extract
Output: \((*, H)\), where * is the input shape and \(H=\text{embedding\_dim}\)
Note
Keep in mind that only a limited number of optimizers support sparse gradients: currently it’s
optim.SGD
(CUDA and CPU),optim.SparseAdam
(CUDA and CPU) andoptim.Adagrad
(CPU)Note
With
padding_idx
set, the embedding vector atpadding_idx
is initialized to all zeros. However, note that this vector can be modified afterwards, e.g., using a customized initialization method, and thus changing the vector used to pad the output. The gradient for this vector fromEmbedding
is always zero.Examples:
>>> # an Embedding module containing 10 tensors of size 3 >>> embedding = nn.Embedding(10, 3) >>> # a batch of 2 samples of 4 indices each >>> input = torch.LongTensor([[1,2,4,5],[4,3,2,9]]) >>> embedding(input) tensor([[[0.0251, 1.6902, 0.7172], [0.6431, 0.0748, 0.6969], [ 1.4970, 1.3448, 0.9685], [0.3677, 2.7265, 0.1685]], [[ 1.4970, 1.3448, 0.9685], [ 0.4362, 0.4004, 0.9400], [0.6431, 0.0748, 0.6969], [ 0.9124, 2.3616, 1.1151]]]) >>> # example with padding_idx >>> embedding = nn.Embedding(10, 3, padding_idx=0) >>> input = torch.LongTensor([[0,2,0,5]]) >>> embedding(input) tensor([[[ 0.0000, 0.0000, 0.0000], [ 0.1535, 2.0309, 0.9315], [ 0.0000, 0.0000, 0.0000], [0.1655, 0.9897, 0.0635]]])

classmethod
from_pretrained
(embeddings, freeze=True, padding_idx=None, max_norm=None, norm_type=2.0, scale_grad_by_freq=False, sparse=False)[source]¶ Creates Embedding instance from given 2dimensional FloatTensor.
 Parameters
embeddings (Tensor) – FloatTensor containing weights for the Embedding. First dimension is being passed to Embedding as
num_embeddings
, second asembedding_dim
.freeze (boolean, optional) – If
True
, the tensor does not get updated in the learning process. Equivalent toembedding.weight.requires_grad = False
. Default:True
padding_idx (int, optional) – See module initialization documentation.
max_norm (float, optional) – See module initialization documentation.
norm_type (float, optional) – See module initialization documentation. Default
2
.scale_grad_by_freq (boolean, optional) – See module initialization documentation. Default
False
.sparse (bool, optional) – See module initialization documentation.
Examples:
>>> # FloatTensor containing pretrained weights >>> weight = torch.FloatTensor([[1, 2.3, 3], [4, 5.1, 6.3]]) >>> embedding = nn.Embedding.from_pretrained(weight) >>> # Get embeddings for index 1 >>> input = torch.LongTensor([1]) >>> embedding(input) tensor([[ 4.0000, 5.1000, 6.3000]])
EmbeddingBag¶

class
torch.nn.
EmbeddingBag
(num_embeddings, embedding_dim, max_norm=None, norm_type=2.0, scale_grad_by_freq=False, mode='mean', sparse=False, _weight=None)[source]¶ Computes sums or means of ‘bags’ of embeddings, without instantiating the intermediate embeddings.
For bags of constant length and no
per_sample_weights
, this classHowever,
EmbeddingBag
is much more time and memory efficient than using a chain of these operations.EmbeddingBag also supports persample weights as an argument to the forward pass. This scales the output of the Embedding before performing a weighted reduction as specified by
mode
. Ifper_sample_weights`
is passed, the only supportedmode
is"sum"
, which computes a weighted sum according toper_sample_weights
. Parameters
num_embeddings (int) – size of the dictionary of embeddings
embedding_dim (int) – the size of each embedding vector
max_norm (float, optional) – If given, each embedding vector with norm larger than
max_norm
is renormalized to have normmax_norm
.norm_type (float, optional) – The p of the pnorm to compute for the
max_norm
option. Default2
.scale_grad_by_freq (boolean, optional) – if given, this will scale gradients by the inverse of frequency of the words in the minibatch. Default
False
. Note: this option is not supported whenmode="max"
.mode (string, optional) –
"sum"
,"mean"
or"max"
. Specifies the way to reduce the bag."sum"
computes the weighted sum, takingper_sample_weights
into consideration."mean"
computes the average of the values in the bag,"max"
computes the max value over each bag. Default:"mean"
sparse (bool, optional) – if
True
, gradient w.r.t.weight
matrix will be a sparse tensor. See Notes for more details regarding sparse gradients. Note: this option is not supported whenmode="max"
.
 Variables
~EmbeddingBag.weight (Tensor) – the learnable weights of the module of shape (num_embeddings, embedding_dim) initialized from \(\mathcal{N}(0, 1)\).
 Inputs:
input
(LongTensor),offsets
(LongTensor, optional), and per_index_weights
(Tensor, optional)If
input
is 2D of shape (B, N),it will be treated as
B
bags (sequences) each of fixed lengthN
, and this will returnB
values aggregated in a way depending on themode
.offsets
is ignored and required to beNone
in this case.If
input
is 1D of shape (N),it will be treated as a concatenation of multiple bags (sequences).
offsets
is required to be a 1D tensor containing the starting index positions of each bag ininput
. Therefore, foroffsets
of shape (B),input
will be viewed as havingB
bags. Empty bags (i.e., having 0length) will have returned vectors filled by zeros.
 per_sample_weights (Tensor, optional): a tensor of float / double weights, or None
to indicate all weights should be taken to be
1
. If specified,per_sample_weights
must have exactly the same shape as input and is treated as having the sameoffsets
, if those are notNone
. Only supported formode='sum'
.
Output shape: (B, embedding_dim)
Examples:
>>> # an Embedding module containing 10 tensors of size 3 >>> embedding_sum = nn.EmbeddingBag(10, 3, mode='sum') >>> # a batch of 2 samples of 4 indices each >>> input = torch.LongTensor([1,2,4,5,4,3,2,9]) >>> offsets = torch.LongTensor([0,4]) >>> embedding_sum(input, offsets) tensor([[0.8861, 5.4350, 0.0523], [ 1.1306, 2.5798, 1.0044]])

classmethod
from_pretrained
(embeddings, freeze=True, max_norm=None, norm_type=2.0, scale_grad_by_freq=False, mode='mean', sparse=False)[source]¶ Creates EmbeddingBag instance from given 2dimensional FloatTensor.
 Parameters
embeddings (Tensor) – FloatTensor containing weights for the EmbeddingBag. First dimension is being passed to EmbeddingBag as ‘num_embeddings’, second as ‘embedding_dim’.
freeze (boolean, optional) – If
True
, the tensor does not get updated in the learning process. Equivalent toembeddingbag.weight.requires_grad = False
. Default:True
max_norm (float, optional) – See module initialization documentation. Default:
None
norm_type (float, optional) – See module initialization documentation. Default
2
.scale_grad_by_freq (boolean, optional) – See module initialization documentation. Default
False
.mode (string, optional) – See module initialization documentation. Default:
"mean"
sparse (bool, optional) – See module initialization documentation. Default:
False
.
Examples:
>>> # FloatTensor containing pretrained weights >>> weight = torch.FloatTensor([[1, 2.3, 3], [4, 5.1, 6.3]]) >>> embeddingbag = nn.EmbeddingBag.from_pretrained(weight) >>> # Get embeddings for index 1 >>> input = torch.LongTensor([[1, 0]]) >>> embeddingbag(input) tensor([[ 2.5000, 3.7000, 4.6500]])
Distance functions¶
CosineSimilarity¶

class
torch.nn.
CosineSimilarity
(dim=1, eps=1e08)[source]¶ Returns cosine similarity between \(x_1\) and \(x_2\), computed along dim.
\[\text{similarity} = \dfrac{x_1 \cdot x_2}{\max(\Vert x_1 \Vert _2 \cdot \Vert x_2 \Vert _2, \epsilon)}. \] Parameters
 Shape:
Input1: \((\ast_1, D, \ast_2)\) where D is at position dim
Input2: \((\ast_1, D, \ast_2)\), same shape as the Input1
Output: \((\ast_1, \ast_2)\)
 Examples::
>>> input1 = torch.randn(100, 128) >>> input2 = torch.randn(100, 128) >>> cos = nn.CosineSimilarity(dim=1, eps=1e6) >>> output = cos(input1, input2)
PairwiseDistance¶

class
torch.nn.
PairwiseDistance
(p=2.0, eps=1e06, keepdim=False)[source]¶ Computes the batchwise pairwise distance between vectors \(v_1\), \(v_2\) using the pnorm:
\[\Vert x \Vert _p = \left( \sum_{i=1}^n \vert x_i \vert ^ p \right) ^ {1/p}. \] Parameters
 Shape:
Input1: \((N, D)\) where D = vector dimension
Input2: \((N, D)\), same shape as the Input1
Output: \((N)\). If
keepdim
isTrue
, then \((N, 1)\).
 Examples::
>>> pdist = nn.PairwiseDistance(p=2) >>> input1 = torch.randn(100, 128) >>> input2 = torch.randn(100, 128) >>> output = pdist(input1, input2)
Loss functions¶
L1Loss¶

class
torch.nn.
L1Loss
(size_average=None, reduce=None, reduction='mean')[source]¶ Creates a criterion that measures the mean absolute error (MAE) between each element in the input \(x\) and target \(y\).
The unreduced (i.e. with
reduction
set to'none'
) loss can be described as:\[\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = \left x_n  y_n \right, \]where \(N\) is the batch size. If
reduction
is not'none'
(default'mean'
), then:\[\ell(x, y) = \begin{cases} \operatorname{mean}(L), & \text{if reduction} = \text{'mean';}\\ \operatorname{sum}(L), & \text{if reduction} = \text{'sum'.} \end{cases} \]\(x\) and \(y\) are tensors of arbitrary shapes with a total of \(n\) elements each.
The sum operation still operates over all the elements, and divides by \(n\).
The division by \(n\) can be avoided if one sets
reduction = 'sum'
. Parameters
size_average (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there are multiple elements per sample. If the fieldsize_average
is set toFalse
, the losses are instead summed for each minibatch. Ignored when reduce isFalse
. Default:True
reduce (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged or summed over observations for each minibatch depending onsize_average
. Whenreduce
isFalse
, returns a loss per batch element instead and ignoressize_average
. Default:True
reduction (string, optional) – Specifies the reduction to apply to the output:
'none'
'mean'
'sum'
.'none'
: no reduction will be applied,'mean'
: the sum of the output will be divided by the number of elements in the output,'sum'
: the output will be summed. Note:size_average
andreduce
are in the process of being deprecated, and in the meantime, specifying either of those two args will overridereduction
. Default:'mean'
 Shape:
Input: \((N, *)\) where \(*\) means, any number of additional dimensions
Target: \((N, *)\), same shape as the input
Output: scalar. If
reduction
is'none'
, then \((N, *)\), same shape as the input
Examples:
>>> loss = nn.L1Loss() >>> input = torch.randn(3, 5, requires_grad=True) >>> target = torch.randn(3, 5) >>> output = loss(input, target) >>> output.backward()
MSELoss¶

class
torch.nn.
MSELoss
(size_average=None, reduce=None, reduction='mean')[source]¶ Creates a criterion that measures the mean squared error (squared L2 norm) between each element in the input \(x\) and target \(y\).
The unreduced (i.e. with
reduction
set to'none'
) loss can be described as:\[\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = \left( x_n  y_n \right)^2, \]where \(N\) is the batch size. If
reduction
is not'none'
(default'mean'
), then:\[\ell(x, y) = \begin{cases} \operatorname{mean}(L), & \text{if reduction} = \text{'mean';}\\ \operatorname{sum}(L), & \text{if reduction} = \text{'sum'.} \end{cases} \]\(x\) and \(y\) are tensors of arbitrary shapes with a total of \(n\) elements each.
The sum operation still operates over all the elements, and divides by \(n\).
The division by \(n\) can be avoided if one sets
reduction = 'sum'
. Parameters
size_average (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there are multiple elements per sample. If the fieldsize_average
is set toFalse
, the losses are instead summed for each minibatch. Ignored when reduce isFalse
. Default:True
reduce (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged or summed over observations for each minibatch depending onsize_average
. Whenreduce
isFalse
, returns a loss per batch element instead and ignoressize_average
. Default:True
reduction (string, optional) – Specifies the reduction to apply to the output:
'none'
'mean'
'sum'
.'none'
: no reduction will be applied,'mean'
: the sum of the output will be divided by the number of elements in the output,'sum'
: the output will be summed. Note:size_average
andreduce
are in the process of being deprecated, and in the meantime, specifying either of those two args will overridereduction
. Default:'mean'
 Shape:
Input: \((N, *)\) where \(*\) means, any number of additional dimensions
Target: \((N, *)\), same shape as the input
Examples:
>>> loss = nn.MSELoss() >>> input = torch.randn(3, 5, requires_grad=True) >>> target = torch.randn(3, 5) >>> output = loss(input, target) >>> output.backward()
CrossEntropyLoss¶

class
torch.nn.
CrossEntropyLoss
(weight=None, size_average=None, ignore_index=100, reduce=None, reduction='mean')[source]¶ This criterion combines
nn.LogSoftmax()
andnn.NLLLoss()
in one single class.It is useful when training a classification problem with C classes. If provided, the optional argument
weight
should be a 1D Tensor assigning weight to each of the classes. This is particularly useful when you have an unbalanced training set.The input is expected to contain raw, unnormalized scores for each class.
input has to be a Tensor of size either \((minibatch, C)\) or \((minibatch, C, d_1, d_2, ..., d_K)\) with \(K \geq 1\) for the Kdimensional case (described later).
This criterion expects a class index in the range \([0, C1]\) as the target for each value of a 1D tensor of size minibatch; if ignore_index is specified, this criterion also accepts this class index (this index may not necessarily be in the class range).
The loss can be described as:
\[\text{loss}(x, class) = \log\left(\frac{\exp(x[class])}{\sum_j \exp(x[j])}\right) = x[class] + \log\left(\sum_j \exp(x[j])\right) \]or in the case of the
weight
argument being specified:\[\text{loss}(x, class) = weight[class] \left(x[class] + \log\left(\sum_j \exp(x[j])\right)\right) \]The losses are averaged across observations for each minibatch.
Can also be used for higher dimension inputs, such as 2D images, by providing an input of size \((minibatch, C, d_1, d_2, ..., d_K)\) with \(K \geq 1\), where \(K\) is the number of dimensions, and a target of appropriate shape (see below).
 Parameters
weight (Tensor, optional) – a manual rescaling weight given to each class. If given, has to be a Tensor of size C
size_average (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there are multiple elements per sample. If the fieldsize_average
is set toFalse
, the losses are instead summed for each minibatch. Ignored when reduce isFalse
. Default:True
ignore_index (int, optional) – Specifies a target value that is ignored and does not contribute to the input gradient. When
size_average
isTrue
, the loss is averaged over nonignored targets.reduce (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged or summed over observations for each minibatch depending onsize_average
. Whenreduce
isFalse
, returns a loss per batch element instead and ignoressize_average
. Default:True
reduction (string, optional) – Specifies the reduction to apply to the output:
'none'
'mean'
'sum'
.'none'
: no reduction will be applied,'mean'
: the sum of the output will be divided by the number of elements in the output,'sum'
: the output will be summed. Note:size_average
andreduce
are in the process of being deprecated, and in the meantime, specifying either of those two args will overridereduction
. Default:'mean'
 Shape:
Input: \((N, C)\) where C = number of classes, or \((N, C, d_1, d_2, ..., d_K)\) with \(K \geq 1\) in the case of Kdimensional loss.
Target: \((N)\) where each value is \(0 \leq \text{targets}[i] \leq C1\), or \((N, d_1, d_2, ..., d_K)\) with \(K \geq 1\) in the case of Kdimensional loss.
Output: scalar. If
reduction
is'none'
, then the same size as the target: \((N)\), or \((N, d_1, d_2, ..., d_K)\) with \(K \geq 1\) in the case of Kdimensional loss.
Examples:
>>> loss = nn.CrossEntropyLoss() >>> input = torch.randn(3, 5, requires_grad=True) >>> target = torch.empty(3, dtype=torch.long).random_(5) >>> output = loss(input, target) >>> output.backward()
CTCLoss¶

class
torch.nn.
CTCLoss
(blank=0, reduction='mean', zero_infinity=False)[source]¶ The Connectionist Temporal Classification loss.
Calculates loss between a continuous (unsegmented) time series and a target sequence. CTCLoss sums over the probability of possible alignments of input to target, producing a loss value which is differentiable with respect to each input node. The alignment of input to target is assumed to be “manytoone”, which limits the length of the target sequence such that it must be \(\leq\) the input length.
 Args:
blank (int, optional): blank label. Default \(0\). reduction (string, optional): Specifies the reduction to apply to the output:
'none'
'mean'
'sum'
.'none'
: no reduction will be applied,'mean'
: the output losses will be divided by the target lengths and then the mean over the batch is taken. Default:'mean'
 zero_infinity (bool, optional):
Whether to zero infinite losses and the associated gradients. Default:
False
Infinite losses mainly occur when the inputs are too short to be aligned to the targets.
 Inputs:
 log_probs: Tensor of size \((T, N, C)\)
 \(T = \text{input length}\)\(N = \text{batch size}\)\(C = \text{number of classes (including blank)}\)
The logarithmized probabilities of the outputs (e.g. obtained with
torch.nn.functional.log_softmax()
).  targets: Tensor of size \((N, S)\) or \((\text{sum(target_lengths)})\)
 \(N = \text{batch size}\)\(S = \text{max target length, if shape is } (N, S)\).Target sequences. Each element in the target sequence is a class index. Target index cannot be blank (default=0).In the \((N, S)\) form, targets are padded to the length of the longest sequence, and stacked.In the \((\text{sum(target_lengths)})\) form, the targets are assumed to be unpadded and concatenated within 1 dimension.
 input_lengths: Tuple or tensor of size \((N)\).
Lengths of the inputs (must each be \(\leq T\)). Lengths are specified for each sequence to achieve masking under the assumption that sequences are padded to equal lengths.
 target_lengths: Tuple or tensor of size \((N)\).
 Lengths of the targets. Lengths are specified for each sequence to achieve masking under the assumption that sequences are padded to equal lengths.If target shape is \((N,S)\), target_lengths are effectively the stop index \(s_n\) for each target sequence, such that
target_n = targets[n,0:s_n]
for each target in a batch. Lengths must each be \(\leq S\)If the targets are given as a 1d tensor that is the concatenation of individual targets, the target_lengths must add up to the total length of the tensor.
Example:
>>> T = 50 # Input sequence length >>> C = 20 # Number of classes (excluding blank) >>> N = 16 # Batch size >>> S = 30 # Target sequence length of longest target in batch >>> S_min = 10 # Minimum target length, for demonstration purposes >>> >>> # Initialize random batch of input vectors, for *size = (T,N,C) >>> input = torch.randn(T, N, C).log_softmax(2).detach().requires_grad_() >>> >>> # Initialize random batch of targets (0 = blank, 1:C+1 = classes) >>> target = torch.randint(low=1, high=C+1, size=(N, S), dtype=torch.long) >>> >>> input_lengths = torch.full(size=(N,), fill_value=T, dtype=torch.long) >>> target_lengths = torch.randint(low=S_min, high=S, size=(N,), dtype=torch.long) >>> ctc_loss = nn.CTCLoss() >>> loss = ctc_loss(input, target, input_lengths, target_lengths) >>> loss.backward()
 Reference:
A. Graves et al.: Connectionist Temporal Classification: Labelling Unsegmented Sequence Data with Recurrent Neural Networks: https://www.cs.toronto.edu/~graves/icml_2006.pdf
Note
In order to use CuDNN, the following must be satisfied:
targets
must be in concatenated format, allinput_lengths
must be T. \(blank=0\),target_lengths
\(\leq 256\), the integer arguments must be of dtypetorch.int32
.The regular implementation uses the (more common in PyTorch) torch.long dtype.
Note
In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting
torch.backends.cudnn.deterministic = True
. Please see the notes on Reproducibility for background.
NLLLoss¶

class
torch.nn.
NLLLoss
(weight=None, size_average=None, ignore_index=100, reduce=None, reduction='mean')[source]¶ The negative log likelihood loss. It is useful to train a classification problem with C classes.
If provided, the optional argument
weight
should be a 1D Tensor assigning weight to each of the classes. This is particularly useful when you have an unbalanced training set.The input given through a forward call is expected to contain logprobabilities of each class. input has to be a Tensor of size either \((minibatch, C)\) or \((minibatch, C, d_1, d_2, ..., d_K)\) with \(K \geq 1\) for the Kdimensional case (described later).
Obtaining logprobabilities in a neural network is easily achieved by adding a LogSoftmax layer in the last layer of your network. You may use CrossEntropyLoss instead, if you prefer not to add an extra layer.
The target that this loss expects should be a class index in the range \([0, C1]\) where C = number of classes; if ignore_index is specified, this loss also accepts this class index (this index may not necessarily be in the class range).
The unreduced (i.e. with
reduction
set to'none'
) loss can be described as:\[\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n =  w_{y_n} x_{n,y_n}, \quad w_{c} = \text{weight}[c] \cdot \mathbb{1}\{c \not= \text{ignore\_index}\}, \]where \(N\) is the batch size. If
reduction
is not'none'
(default'mean'
), then\[\ell(x, y) = \begin{cases} \sum_{n=1}^N \frac{1}{\sum_{n=1}^N w_{y_n}} l_n, & \text{if reduction} = \text{'mean';}\\ \sum_{n=1}^N l_n, & \text{if reduction} = \text{'sum'.} \end{cases} \]Can also be used for higher dimension inputs, such as 2D images, by providing an input of size \((minibatch, C, d_1, d_2, ..., d_K)\) with \(K \geq 1\), where \(K\) is the number of dimensions, and a target of appropriate shape (see below). In the case of images, it computes NLL loss perpixel.
 Parameters
weight (Tensor, optional) – a manual rescaling weight given to each class. If given, it has to be a Tensor of size C. Otherwise, it is treated as if having all ones.
size_average (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there are multiple elements per sample. If the fieldsize_average
is set toFalse
, the losses are instead summed for each minibatch. Ignored when reduce isFalse
. Default:True
ignore_index (int, optional) – Specifies a target value that is ignored and does not contribute to the input gradient. When
size_average
isTrue
, the loss is averaged over nonignored targets.reduce (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged or summed over observations for each minibatch depending onsize_average
. Whenreduce
isFalse
, returns a loss per batch element instead and ignoressize_average
. Default:True
reduction (string, optional) – Specifies the reduction to apply to the output:
'none'
'mean'
'sum'
.'none'
: no reduction will be applied,'mean'
: the sum of the output will be divided by the number of elements in the output,'sum'
: the output will be summed. Note:size_average
andreduce
are in the process of being deprecated, and in the meantime, specifying either of those two args will overridereduction
. Default:'mean'
 Shape:
Input: \((N, C)\) where C = number of classes, or \((N, C, d_1, d_2, ..., d_K)\) with \(K \geq 1\) in the case of Kdimensional loss.
Target: \((N)\) where each value is \(0 \leq \text{targets}[i] \leq C1\), or \((N, d_1, d_2, ..., d_K)\) with \(K \geq 1\) in the case of Kdimensional loss.
Output: scalar. If
reduction
is'none'
, then the same size as the target: \((N)\), or \((N, d_1, d_2, ..., d_K)\) with \(K \geq 1\) in the case of Kdimensional loss.
Examples:
>>> m = nn.LogSoftmax(dim=1) >>> loss = nn.NLLLoss() >>> # input is of size N x C = 3 x 5 >>> input = torch.randn(3, 5, requires_grad=True) >>> # each element in target has to have 0 <= value < C >>> target = torch.tensor([1, 0, 4]) >>> output = loss(m(input), target) >>> output.backward() >>> >>> >>> # 2D loss example (used, for example, with image inputs) >>> N, C = 5, 4 >>> loss = nn.NLLLoss() >>> # input is of size N x C x height x width >>> data = torch.randn(N, 16, 10, 10) >>> conv = nn.Conv2d(16, C, (3, 3)) >>> m = nn.LogSoftmax(dim=1) >>> # each element in target has to have 0 <= value < C >>> target = torch.empty(N, 8, 8, dtype=torch.long).random_(0, C) >>> output = loss(m(conv(data)), target) >>> output.backward()
PoissonNLLLoss¶

class
torch.nn.
PoissonNLLLoss
(log_input=True, full=False, size_average=None, eps=1e08, reduce=None, reduction='mean')[source]¶ Negative log likelihood loss with Poisson distribution of target.
The loss can be described as:
\[\text{target} \sim \mathrm{Poisson}(\text{input}) \text{loss}(\text{input}, \text{target}) = \text{input}  \text{target} * \log(\text{input}) + \log(\text{target!})\]The last term can be omitted or approximated with Stirling formula. The approximation is used for target values more than 1. For targets less or equal to 1 zeros are added to the loss.
 Parameters
log_input (bool, optional) – if
True
the loss is computed as \(\exp(\text{input})  \text{target}*\text{input}\), ifFalse
the loss is \(\text{input}  \text{target}*\log(\text{input}+\text{eps})\).full (bool, optional) –
whether to compute full loss, i. e. to add the Stirling approximation term
\[\text{target}*\log(\text{target})  \text{target} + 0.5 * \log(2\pi\text{target}). \]size_average (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there are multiple elements per sample. If the fieldsize_average
is set toFalse
, the losses are instead summed for each minibatch. Ignored when reduce isFalse
. Default:True
eps (float, optional) – Small value to avoid evaluation of \(\log(0)\) when
log_input = False
. Default: 1e8reduce (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged or summed over observations for each minibatch depending onsize_average
. Whenreduce
isFalse
, returns a loss per batch element instead and ignoressize_average
. Default:True
reduction (string, optional) – Specifies the reduction to apply to the output:
'none'
'mean'
'sum'
.'none'
: no reduction will be applied,'mean'
: the sum of the output will be divided by the number of elements in the output,'sum'
: the output will be summed. Note:size_average
andreduce
are in the process of being deprecated, and in the meantime, specifying either of those two args will overridereduction
. Default:'mean'
Examples:
>>> loss = nn.PoissonNLLLoss() >>> log_input = torch.randn(5, 2, requires_grad=True) >>> target = torch.randn(5, 2) >>> output = loss(log_input, target) >>> output.backward()
 Shape:
Input: \((N, *)\) where \(*\) means, any number of additional dimensions
Target: \((N, *)\), same shape as the input
Output: scalar by default. If
reduction
is'none'
, then \((N, *)\), the same shape as the input
KLDivLoss¶

class
torch.nn.
KLDivLoss
(size_average=None, reduce=None, reduction='mean')[source]¶ The KullbackLeibler divergence Loss
KL divergence is a useful distance measure for continuous distributions and is often useful when performing direct regression over the space of (discretely sampled) continuous output distributions.
As with
NLLLoss
, the input given is expected to contain logprobabilities and is not restricted to a 2D Tensor. The targets are given as probabilities (i.e. without taking the logarithm).This criterion expects a target Tensor of the same size as the input Tensor.
The unreduced (i.e. with
reduction
set to'none'
) loss can be described as:\[l(x,y) = L = \{ l_1,\dots,l_N \}, \quad l_n = y_n \cdot \left( \log y_n  x_n \right) \]where the index \(N\) spans all dimensions of
input
and \(L\) has the same shape asinput
. Ifreduction
is not'none'
(default'mean'
), then:\[\ell(x, y) = \begin{cases} \operatorname{mean}(L), & \text{if reduction} = \text{'mean';} \\ \operatorname{sum}(L), & \text{if reduction} = \text{'sum'.} \end{cases} \]In default
reduction
mode'mean'
, the losses are averaged for each minibatch over observations as well as over dimensions.'batchmean'
mode gives the correct KL divergence where losses are averaged over batch dimension only.'mean'
mode’s behavior will be changed to the same as'batchmean'
in the next major release. Parameters
size_average (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there are multiple elements per sample. If the fieldsize_average
is set toFalse
, the losses are instead summed for each minibatch. Ignored when reduce isFalse
. Default:True
reduce (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged or summed over observations for each minibatch depending onsize_average
. Whenreduce
isFalse
, returns a loss per batch element instead and ignoressize_average
. Default:True
reduction (string, optional) – Specifies the reduction to apply to the output:
'none'
'batchmean'
'sum'
'mean'
.'none'
: no reduction will be applied.'batchmean'
: the sum of the output will be divided by batchsize.'sum'
: the output will be summed.'mean'
: the output will be divided by the number of elements in the output. Default:'mean'
Note
size_average
andreduce
are in the process of being deprecated, and in the meantime, specifying either of those two args will overridereduction
.Note
reduction
='mean'
doesn’t return the true kl divergence value, please usereduction
='batchmean'
which aligns with KL math definition. In the next major release,'mean'
will be changed to be the same as'batchmean'
. Shape:
Input: \((N, *)\) where \(*\) means, any number of additional dimensions
Target: \((N, *)\), same shape as the input
Output: scalar by default. If :attr:
reduction
is'none'
, then \((N, *)\), the same shape as the input
BCELoss¶

class
torch.nn.
BCELoss
(weight=None, size_average=None, reduce=None, reduction='mean')[source]¶ Creates a criterion that measures the Binary Cross Entropy between the target and the output:
The unreduced (i.e. with
reduction
set to'none'
) loss can be described as:\[\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n =  w_n \left[ y_n \cdot \log x_n + (1  y_n) \cdot \log (1  x_n) \right], \]where \(N\) is the batch size. If
reduction
is not'none'
(default'mean'
), then\[\ell(x, y) = \begin{cases} \operatorname{mean}(L), & \text{if reduction} = \text{'mean';}\\ \operatorname{sum}(L), & \text{if reduction} = \text{'sum'.} \end{cases} \]This is used for measuring the error of a reconstruction in for example an autoencoder. Note that the targets \(y\) should be numbers between 0 and 1.
 Parameters
weight (Tensor, optional) – a manual rescaling weight given to the loss of each batch element. If given, has to be a Tensor of size nbatch.
size_average (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there are multiple elements per sample. If the fieldsize_average
is set toFalse
, the losses are instead summed for each minibatch. Ignored when reduce isFalse
. Default:True
reduce (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged or summed over observations for each minibatch depending onsize_average
. Whenreduce
isFalse
, returns a loss per batch element instead and ignoressize_average
. Default:True
reduction (string, optional) – Specifies the reduction to apply to the output:
'none'
'mean'
'sum'
.'none'
: no reduction will be applied,'mean'
: the sum of the output will be divided by the number of elements in the output,'sum'
: the output will be summed. Note:size_average
andreduce
are in the process of being deprecated, and in the meantime, specifying either of those two args will overridereduction
. Default:'mean'
 Shape:
Input: \((N, *)\) where \(*\) means, any number of additional dimensions
Target: \((N, *)\), same shape as the input
Output: scalar. If
reduction
is'none'
, then \((N, *)\), same shape as input.
Examples:
>>> m = nn.Sigmoid() >>> loss = nn.BCELoss() >>> input = torch.randn(3, requires_grad=True) >>> target = torch.empty(3).random_(2) >>> output = loss(m(input), target) >>> output.backward()
BCEWithLogitsLoss¶

class
torch.nn.
BCEWithLogitsLoss
(weight=None, size_average=None, reduce=None, reduction='mean', pos_weight=None)[source]¶ This loss combines a Sigmoid layer and the BCELoss in one single class. This version is more numerically stable than using a plain Sigmoid followed by a BCELoss as, by combining the operations into one layer, we take advantage of the logsumexp trick for numerical stability.
The unreduced (i.e. with
reduction
set to'none'
) loss can be described as:\[\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n =  w_n \left[ y_n \cdot \log \sigma(x_n) + (1  y_n) \cdot \log (1  \sigma(x_n)) \right], \]where \(N\) is the batch size. If
reduction
is not'none'
(default'mean'
), then\[\ell(x, y) = \begin{cases} \operatorname{mean}(L), & \text{if reduction} = \text{'mean';}\\ \operatorname{sum}(L), & \text{if reduction} = \text{'sum'.} \end{cases} \]This is used for measuring the error of a reconstruction in for example an autoencoder. Note that the targets t[i] should be numbers between 0 and 1.
It’s possible to trade off recall and precision by adding weights to positive examples. In the case of multilabel classification the loss can be described as:
\[\ell_c(x, y) = L_c = \{l_{1,c},\dots,l_{N,c}\}^\top, \quad l_{n,c} =  w_{n,c} \left[ p_c y_{n,c} \cdot \log \sigma(x_{n,c}) + (1  y_{n,c}) \cdot \log (1  \sigma(x_{n,c})) \right], \]where \(c\) is the class number (\(c > 1\) for multilabel binary classification, \(c = 1\) for singlelabel binary classification), \(n\) is the number of the sample in the batch and \(p_c\) is the weight of the positive answer for the class \(c\).
\(p_c > 1\) increases the recall, \(p_c < 1\) increases the precision.
For example, if a dataset contains 100 positive and 300 negative examples of a single class, then pos_weight for the class should be equal to \(\frac{300}{100}=3\). The loss would act as if the dataset contains \(3\times 100=300\) positive examples.
Examples:
>>> target = torch.ones([10, 64], dtype=torch.float32) # 64 classes, batch size = 10 >>> output = torch.full([10, 64], 0.999) # A prediction (logit) >>> pos_weight = torch.ones([64]) # All weights are equal to 1 >>> criterion = torch.nn.BCEWithLogitsLoss(pos_weight=pos_weight) >>> criterion(output, target) # log(sigmoid(0.999)) tensor(0.3135)
 Parameters
weight (Tensor, optional) – a manual rescaling weight given to the loss of each batch element. If given, has to be a Tensor of size nbatch.
size_average (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there are multiple elements per sample. If the fieldsize_average
is set toFalse
, the losses are instead summed for each minibatch. Ignored when reduce isFalse
. Default:True
reduce (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged or summed over observations for each minibatch depending onsize_average
. Whenreduce
isFalse
, returns a loss per batch element instead and ignoressize_average
. Default:True
reduction (string, optional) – Specifies the reduction to apply to the output:
'none'
'mean'
'sum'
.'none'
: no reduction will be applied,'mean'
: the sum of the output will be divided by the number of elements in the output,'sum'
: the output will be summed. Note:size_average
andreduce
are in the process of being deprecated, and in the meantime, specifying either of those two args will overridereduction
. Default:'mean'
pos_weight (Tensor, optional) – a weight of positive examples. Must be a vector with length equal to the number of classes.
 Shape:
Input: \((N, *)\) where \(*\) means, any number of additional dimensions
Target: \((N, *)\), same shape as the input
Output: scalar. If
reduction
is'none'
, then \((N, *)\), same shape as input.
Examples:
>>> loss = nn.BCEWithLogitsLoss() >>> input = torch.randn(3, requires_grad=True) >>> target = torch.empty(3).random_(2) >>> output = loss(input, target) >>> output.backward()
MarginRankingLoss¶

class
torch.nn.
MarginRankingLoss
(margin=0.0, size_average=None, reduce=None, reduction='mean')[source]¶ Creates a criterion that measures the loss given inputs \(x1\), \(x2\), two 1D minibatch Tensors, and a label 1D minibatch tensor \(y\) (containing 1 or 1).
If \(y = 1\) then it assumed the first input should be ranked higher (have a larger value) than the second input, and viceversa for \(y = 1\).
The loss function for each sample in the minibatch is:
\[\text{loss}(x, y) = \max(0, y * (x1  x2) + \text{margin}) \] Parameters
margin (float, optional) – Has a default value of \(0\).
size_average (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there are multiple elements per sample. If the fieldsize_average
is set toFalse
, the losses are instead summed for each minibatch. Ignored when reduce isFalse
. Default:True
reduce (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged or summed over observations for each minibatch depending onsize_average
. Whenreduce
isFalse
, returns a loss per batch element instead and ignoressize_average
. Default:True
reduction (string, optional) – Specifies the reduction to apply to the output:
'none'
'mean'
'sum'
.'none'
: no reduction will be applied,'mean'
: the sum of the output will be divided by the number of elements in the output,'sum'
: the output will be summed. Note:size_average
andreduce
are in the process of being deprecated, and in the meantime, specifying either of those two args will overridereduction
. Default:'mean'
 Shape:
Input: \((N, D)\) where N is the batch size and D is the size of a sample.
Target: \((N)\)
Output: scalar. If
reduction
is'none'
, then \((N)\).
HingeEmbeddingLoss¶

class
torch.nn.
HingeEmbeddingLoss
(margin=1.0, size_average=None, reduce=None, reduction='mean')[source]¶ Measures the loss given an input tensor \(x\) and a labels tensor \(y\) (containing 1 or 1). This is usually used for measuring whether two inputs are similar or dissimilar, e.g. using the L1 pairwise distance as \(x\), and is typically used for learning nonlinear embeddings or semisupervised learning.
The loss function for \(n\)th sample in the minibatch is
\[l_n = \begin{cases} x_n, & \text{if}\; y_n = 1,\\ \max \{0, \Delta  x_n\}, & \text{if}\; y_n = 1, \end{cases} \]and the total loss functions is
\[\ell(x, y) = \begin{cases} \operatorname{mean}(L), & \text{if reduction} = \text{'mean';}\\ \operatorname{sum}(L), & \text{if reduction} = \text{'sum'.} \end{cases} \]where \(L = \{l_1,\dots,l_N\}^\top\).
 Parameters
margin (float, optional) – Has a default value of 1.
size_average (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there are multiple elements per sample. If the fieldsize_average
is set toFalse
, the losses are instead summed for each minibatch. Ignored when reduce isFalse
. Default:True
reduce (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged or summed over observations for each minibatch depending onsize_average
. Whenreduce
isFalse
, returns a loss per batch element instead and ignoressize_average
. Default:True
reduction (string, optional) – Specifies the reduction to apply to the output:
'none'
'mean'
'sum'
.'none'
: no reduction will be applied,'mean'
: the sum of the output will be divided by the number of elements in the output,'sum'
: the output will be summed. Note:size_average
andreduce
are in the process of being deprecated, and in the meantime, specifying either of those two args will overridereduction
. Default:'mean'
 Shape:
Input: \((*)\) where \(*\) means, any number of dimensions. The sum operation operates over all the elements.
Target: \((*)\), same shape as the input
Output: scalar. If
reduction
is'none'
, then same shape as the input
MultiLabelMarginLoss¶

class
torch.nn.
MultiLabelMarginLoss
(size_average=None, reduce=None, reduction='mean')[source]¶ Creates a criterion that optimizes a multiclass multiclassification hinge loss (marginbased loss) between input \(x\) (a 2D minibatch Tensor) and output \(y\) (which is a 2D Tensor of target class indices). For each sample in the minibatch:
\[\text{loss}(x, y) = \sum_{ij}\frac{\max(0, 1  (x[y[j]]  x[i]))}{\text{x.size}(0)} \]where \(x \in \left\{0, \; \cdots , \; \text{x.size}(0)  1\right\}\), \(y \in \left\{0, \; \cdots , \; \text{y.size}(0)  1\right\}\), \(0 \leq y[j] \leq \text{x.size}(0)1\), and \(i \neq y[j]\) for all \(i\) and \(j\).
\(y\) and \(x\) must have the same size.
The criterion only considers a contiguous block of nonnegative targets that starts at the front.
This allows for different samples to have variable amounts of target classes.
 Parameters
size_average (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there are multiple elements per sample. If the fieldsize_average
is set toFalse
, the losses are instead summed for each minibatch. Ignored when reduce isFalse
. Default:True
reduce (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged or summed over observations for each minibatch depending onsize_average
. Whenreduce
isFalse
, returns a loss per batch element instead and ignoressize_average
. Default:True
reduction (string, optional) – Specifies the reduction to apply to the output:
'none'
'mean'
'sum'
.'none'
: no reduction will be applied,'mean'
: the sum of the output will be divided by the number of elements in the output,'sum'
: the output will be summed. Note:size_average
andreduce
are in the process of being deprecated, and in the meantime, specifying either of those two args will overridereduction
. Default:'mean'
 Shape:
Input: \((C)\) or \((N, C)\) where N is the batch size and C is the number of classes.
Target: \((C)\) or \((N, C)\), label targets padded by 1 ensuring same shape as the input.
Output: scalar. If
reduction
is'none'
, then \((N)\).
Examples:
>>> loss = nn.MultiLabelMarginLoss() >>> x = torch.FloatTensor([[0.1, 0.2, 0.4, 0.8]]) >>> # for target y, only consider labels 3 and 0, not after label 1 >>> y = torch.LongTensor([[3, 0, 1, 1]]) >>> loss(x, y) >>> # 0.25 * ((1(0.10.2)) + (1(0.10.4)) + (1(0.80.2)) + (1(0.80.4))) tensor(0.8500)
SmoothL1Loss¶

class
torch.nn.
SmoothL1Loss
(size_average=None, reduce=None, reduction='mean')[source]¶ Creates a criterion that uses a squared term if the absolute elementwise error falls below 1 and an L1 term otherwise. It is less sensitive to outliers than the MSELoss and in some cases prevents exploding gradients (e.g. see Fast RCNN paper by Ross Girshick). Also known as the Huber loss:
\[\text{loss}(x, y) = \frac{1}{n} \sum_{i} z_{i} \]where \(z_{i}\) is given by:
\[z_{i} = \begin{cases} 0.5 (x_i  y_i)^2, & \text{if } x_i  y_i < 1 \\ x_i  y_i  0.5, & \text{otherwise } \end{cases} \]\(x\) and \(y\) arbitrary shapes with a total of \(n\) elements each the sum operation still operates over all the elements, and divides by \(n\).
The division by \(n\) can be avoided if sets
reduction = 'sum'
. Parameters
size_average (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there are multiple elements per sample. If the fieldsize_average
is set toFalse
, the losses are instead summed for each minibatch. Ignored when reduce isFalse
. Default:True
reduce (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged or summed over observations for each minibatch depending onsize_average
. Whenreduce
isFalse
, returns a loss per batch element instead and ignoressize_average
. Default:True
reduction (string, optional) – Specifies the reduction to apply to the output:
'none'
'mean'
'sum'
.'none'
: no reduction will be applied,'mean'
: the sum of the output will be divided by the number of elements in the output,'sum'
: the output will be summed. Note:size_average
andreduce
are in the process of being deprecated, and in the meantime, specifying either of those two args will overridereduction
. Default:'mean'
 Shape:
Input: \((N, *)\) where \(*\) means, any number of additional dimensions
Target: \((N, *)\), same shape as the input
Output: scalar. If
reduction
is'none'
, then \((N, *)\), same shape as the input
SoftMarginLoss¶

class
torch.nn.
SoftMarginLoss
(size_average=None, reduce=None, reduction='mean')[source]¶ Creates a criterion that optimizes a twoclass classification logistic loss between input tensor \(x\) and target tensor \(y\) (containing 1 or 1).
\[\text{loss}(x, y) = \sum_i \frac{\log(1 + \exp(y[i]*x[i]))}{\text{x.nelement}()} \] Parameters
size_average (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there are multiple elements per sample. If the fieldsize_average
is set toFalse
, the losses are instead summed for each minibatch. Ignored when reduce isFalse
. Default:True
reduce (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged or summed over observations for each minibatch depending onsize_average
. Whenreduce
isFalse
, returns a loss per batch element instead and ignoressize_average
. Default:True
reduction (string, optional) – Specifies the reduction to apply to the output:
'none'
'mean'
'sum'
.'none'
: no reduction will be applied,'mean'
: the sum of the output will be divided by the number of elements in the output,'sum'
: the output will be summed. Note:size_average
andreduce
are in the process of being deprecated, and in the meantime, specifying either of those two args will overridereduction
. Default:'mean'
 Shape:
Input: \((*)\) where \(*\) means, any number of additional dimensions
Target: \((*)\), same shape as the input
Output: scalar. If
reduction
is'none'
, then same shape as the input
MultiLabelSoftMarginLoss¶

class
torch.nn.
MultiLabelSoftMarginLoss
(weight=None, size_average=None, reduce=None, reduction='mean')[source]¶ Creates a criterion that optimizes a multilabel oneversusall loss based on maxentropy, between input \(x\) and target \(y\) of size \((N, C)\). For each sample in the minibatch:
\[loss(x, y) =  \frac{1}{C} * \sum_i y[i] * \log((1 + \exp(x[i]))^{1}) + (1y[i]) * \log\left(\frac{\exp(x[i])}{(1 + \exp(x[i]))}\right) \]where \(i \in \left\{0, \; \cdots , \; \text{x.nElement}()  1\right\}\), \(y[i] \in \left\{0, \; 1\right\}\).
 Parameters
weight (Tensor, optional) – a manual rescaling weight given to each class. If given, it has to be a Tensor of size C. Otherwise, it is treated as if having all ones.
size_average (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there are multiple elements per sample. If the fieldsize_average
is set toFalse
, the losses are instead summed for each minibatch. Ignored when reduce isFalse
. Default:True
reduce (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged or summed over observations for each minibatch depending onsize_average
. Whenreduce
isFalse
, returns a loss per batch element instead and ignoressize_average
. Default:True
reduction (string, optional) – Specifies the reduction to apply to the output:
'none'
'mean'
'sum'
.'none'
: no reduction will be applied,'mean'
: the sum of the output will be divided by the number of elements in the output,'sum'
: the output will be summed. Note:size_average
andreduce
are in the process of being deprecated, and in the meantime, specifying either of those two args will overridereduction
. Default:'mean'
 Shape:
Input: \((N, C)\) where N is the batch size and C is the number of classes.
Target: \((N, C)\), label targets padded by 1 ensuring same shape as the input.
Output: scalar. If
reduction
is'none'
, then \((N)\).
CosineEmbeddingLoss¶

class
torch.nn.
CosineEmbeddingLoss
(margin=0.0, size_average=None, reduce=None, reduction='mean')[source]¶ Creates a criterion that measures the loss given input tensors \(x_1\), \(x_2\) and a Tensor label \(y\) with values 1 or 1. This is used for measuring whether two inputs are similar or dissimilar, using the cosine distance, and is typically used for learning nonlinear embeddings or semisupervised learning.
The loss function for each sample is:
\[\text{loss}(x, y) = \begin{cases} 1  \cos(x_1, x_2), & \text{if } y = 1 \\ \max(0, \cos(x_1, x_2)  \text{margin}), & \text{if } y = 1 \end{cases} \] Parameters
margin (float, optional) – Should be a number from \(1\) to \(1\), \(0\) to \(0.5\) is suggested. If
margin
is missing, the default value is \(0\).size_average (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there are multiple elements per sample. If the fieldsize_average
is set toFalse
, the losses are instead summed for each minibatch. Ignored when reduce isFalse
. Default:True
reduce (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged or summed over observations for each minibatch depending onsize_average
. Whenreduce
isFalse
, returns a loss per batch element instead and ignoressize_average
. Default:True
reduction (string, optional) – Specifies the reduction to apply to the output:
'none'
'mean'
'sum'
.'none'
: no reduction will be applied,'mean'
: the sum of the output will be divided by the number of elements in the output,'sum'
: the output will be summed. Note:size_average
andreduce
are in the process of being deprecated, and in the meantime, specifying either of those two args will overridereduction
. Default:'mean'
MultiMarginLoss¶

class
torch.nn.
MultiMarginLoss
(p=1, margin=1.0, weight=None, size_average=None, reduce=None, reduction='mean')[source]¶ Creates a criterion that optimizes a multiclass classification hinge loss (marginbased loss) between input \(x\) (a 2D minibatch Tensor) and output \(y\) (which is a 1D tensor of target class indices, \(0 \leq y \leq \text{x.size}(1)1\)):
For each minibatch sample, the loss in terms of the 1D input \(x\) and scalar output \(y\) is:
\[\text{loss}(x, y) = \frac{\sum_i \max(0, \text{margin}  x[y] + x[i]))^p}{\text{x.size}(0)} \]where \(x \in \left\{0, \; \cdots , \; \text{x.size}(0)  1\right\}\) and \(i \neq y\).
Optionally, you can give nonequal weighting on the classes by passing a 1D
weight
tensor into the constructor.The loss function then becomes:
\[\text{loss}(x, y) = \frac{\sum_i \max(0, w[y] * (\text{margin}  x[y] + x[i]))^p)}{\text{x.size}(0)} \] Parameters
p (int, optional) – Has a default value of \(1\). \(1\) and \(2\) are the only supported values.
margin (float, optional) – Has a default value of \(1\).
weight (Tensor, optional) – a manual rescaling weight given to each class. If given, it has to be a Tensor of size C. Otherwise, it is treated as if having all ones.
size_average (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there are multiple elements per sample. If the fieldsize_average
is set toFalse
, the losses are instead summed for each minibatch. Ignored when reduce isFalse
. Default:True
reduce (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged or summed over observations for each minibatch depending onsize_average
. Whenreduce
isFalse
, returns a loss per batch element instead and ignoressize_average
. Default:True
reduction (string, optional) – Specifies the reduction to apply to the output:
'none'
'mean'
'sum'
.'none'
: no reduction will be applied,'mean'
: the sum of the output will be divided by the number of elements in the output,'sum'
: the output will be summed. Note:size_average
andreduce
are in the process of being deprecated, and in the meantime, specifying either of those two args will overridereduction
. Default:'mean'
TripletMarginLoss¶

class
torch.nn.
TripletMarginLoss
(margin=1.0, p=2.0, eps=1e06, swap=False, size_average=None, reduce=None, reduction='mean')[source]¶ Creates a criterion that measures the triplet loss given an input tensors \(x1\), \(x2\), \(x3\) and a margin with a value greater than \(0\). This is used for measuring a relative similarity between samples. A triplet is composed by a, p and n (i.e., anchor, positive examples and negative examples respectively). The shapes of all input tensors should be \((N, D)\).
The distance swap is described in detail in the paper Learning shallow convolutional feature descriptors with triplet losses by V. Balntas, E. Riba et al.
The loss function for each sample in the minibatch is:
\[L(a, p, n) = \max \{d(a_i, p_i)  d(a_i, n_i) + {\rm margin}, 0\} \]where
\[d(x_i, y_i) = \left\lVert {\bf x}_i  {\bf y}_i \right\rVert_p \] Parameters
margin (float, optional) – Default: \(1\).
p (int, optional) – The norm degree for pairwise distance. Default: \(2\).
swap (bool, optional) – The distance swap is described in detail in the paper Learning shallow convolutional feature descriptors with triplet losses by V. Balntas, E. Riba et al. Default:
False
.size_average (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there are multiple elements per sample. If the fieldsize_average
is set toFalse
, the losses are instead summed for each minibatch. Ignored when reduce isFalse
. Default:True
reduce (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged or summed over observations for each minibatch depending onsize_average
. Whenreduce
isFalse
, returns a loss per batch element instead and ignoressize_average
. Default:True
reduction (string, optional) – Specifies the reduction to apply to the output:
'none'
'mean'
'sum'
.'none'
: no reduction will be applied,'mean'
: the sum of the output will be divided by the number of elements in the output,'sum'
: the output will be summed. Note:size_average
andreduce
are in the process of being deprecated, and in the meantime, specifying either of those two args will overridereduction
. Default:'mean'
 Shape:
Input: \((N, D)\) where \(D\) is the vector dimension.
Output: scalar. If
reduction
is'none'
, then \((N)\).
>>> triplet_loss = nn.TripletMarginLoss(margin=1.0, p=2) >>> input1 = torch.randn(100, 128, requires_grad=True) >>> input2 = torch.randn(100, 128, requires_grad=True) >>> input3 = torch.randn(100, 128, requires_grad=True) >>> output = triplet_loss(input1, input2, input3) >>> output.backward()
Vision layers¶
PixelShuffle¶

class
torch.nn.
PixelShuffle
(upscale_factor)[source]¶ Rearranges elements in a tensor of shape \((*, C \times r^2, H, W)\) to a tensor of shape \((*, C, H \times r, W \times r)\).
This is useful for implementing efficient subpixel convolution with a stride of \(1/r\).
Look at the paper: RealTime Single Image and Video SuperResolution Using an Efficient SubPixel Convolutional Neural Network by Shi et. al (2016) for more details.
 Parameters
upscale_factor (int) – factor to increase spatial resolution by
 Shape:
Input: \((N, L, H_{in}, W_{in})\) where \(L=C \times \text{upscale\_factor}^2\)
Output: \((N, C, H_{out}, W_{out})\) where \(H_{out} = H_{in} \times \text{upscale\_factor}\) and \(W_{out} = W_{in} \times \text{upscale\_factor}\)
Examples:
>>> pixel_shuffle = nn.PixelShuffle(3) >>> input = torch.randn(1, 9, 4, 4) >>> output = pixel_shuffle(input) >>> print(output.size()) torch.Size([1, 1, 12, 12])
Upsample¶

class
torch.nn.
Upsample
(size=None, scale_factor=None, mode='nearest', align_corners=None)[source]¶ Upsamples a given multichannel 1D (temporal), 2D (spatial) or 3D (volumetric) data.
The input data is assumed to be of the form minibatch x channels x [optional depth] x [optional height] x width. Hence, for spatial inputs, we expect a 4D Tensor and for volumetric inputs, we expect a 5D Tensor.
The algorithms available for upsampling are nearest neighbor and linear, bilinear, bicubic and trilinear for 3D, 4D and 5D input Tensor, respectively.
One can either give a
scale_factor
or the target outputsize
to calculate the output size. (You cannot give both, as it is ambiguous) Parameters
size (int or Tuple[int] or Tuple[int, int] or Tuple[int, int, int], optional) – output spatial sizes
scale_factor (float or Tuple[float] or Tuple[float, float] or Tuple[float, float, float], optional) – multiplier for spatial size. Has to match input size if it is a tuple.
mode (str, optional) – the upsampling algorithm: one of
'nearest'
,'linear'
,'bilinear'
,'bicubic'
and'trilinear'
. Default:'nearest'
align_corners (bool, optional) – if
True
, the corner pixels of the input and output tensors are aligned, and thus preserving the values at those pixels. This only has effect whenmode
is'linear'
,'bilinear'
, or'trilinear'
. Default:False
 Shape:
Input: \((N, C, W_{in})\), \((N, C, H_{in}, W_{in})\) or \((N, C, D_{in}, H_{in}, W_{in})\)
Output: \((N, C, W_{out})\), \((N, C, H_{out}, W_{out})\) or \((N, C, D_{out}, H_{out}, W_{out})\), where
\[D_{out} = \left\lfloor D_{in} \times \text{scale\_factor} \right\rfloor \]\[H_{out} = \left\lfloor H_{in} \times \text{scale\_factor} \right\rfloor \]\[W_{out} = \left\lfloor W_{in} \times \text{scale\_factor} \right\rfloor \]Warning
With
align_corners = True
, the linearly interpolating modes (linear, bilinear, bicubic, and trilinear) don’t proportionally align the output and input pixels, and thus the output values can depend on the input size. This was the default behavior for these modes up to version 0.3.1. Since then, the default behavior isalign_corners = False
. See below for concrete examples on how this affects the outputs.Note
If you want downsampling/general resizing, you should use
interpolate()
.Examples:
>>> input = torch.arange(1, 5, dtype=torch.float32).view(1, 1, 2, 2) >>> input tensor([[[[ 1., 2.], [ 3., 4.]]]]) >>> m = nn.Upsample(scale_factor=2, mode='nearest') >>> m(input) tensor([[[[ 1., 1., 2., 2.], [ 1., 1., 2., 2.], [ 3., 3., 4., 4.], [ 3., 3., 4., 4.]]]]) >>> m = nn.Upsample(scale_factor=2, mode='bilinear') # align_corners=False >>> m(input) tensor([[[[ 1.0000, 1.2500, 1.7500, 2.0000], [ 1.5000, 1.7500, 2.2500, 2.5000], [ 2.5000, 2.7500, 3.2500, 3.5000], [ 3.0000, 3.2500, 3.7500, 4.0000]]]]) >>> m = nn.Upsample(scale_factor=2, mode='bilinear', align_corners=True) >>> m(input) tensor([[[[ 1.0000, 1.3333, 1.6667, 2.0000], [ 1.6667, 2.0000, 2.3333, 2.6667], [ 2.3333, 2.6667, 3.0000, 3.3333], [ 3.0000, 3.3333, 3.6667, 4.0000]]]]) >>> # Try scaling the same data in a larger tensor >>> >>> input_3x3 = torch.zeros(3, 3).view(1, 1, 3, 3) >>> input_3x3[:, :, :2, :2].copy_(input) tensor([[[[ 1., 2.], [ 3., 4.]]]]) >>> input_3x3 tensor([[[[ 1., 2., 0.], [ 3., 4., 0.], [ 0., 0., 0.]]]]) >>> m = nn.Upsample(scale_factor=2, mode='bilinear') # align_corners=False >>> # Notice that values in top left corner are the same with the small input (except at boundary) >>> m(input_3x3) tensor([[[[ 1.0000, 1.2500, 1.7500, 1.5000, 0.5000, 0.0000], [ 1.5000, 1.7500, 2.2500, 1.8750, 0.6250, 0.0000], [ 2.5000, 2.7500, 3.2500, 2.6250, 0.8750, 0.0000], [ 2.2500, 2.4375, 2.8125, 2.2500, 0.7500, 0.0000], [ 0.7500, 0.8125, 0.9375, 0.7500, 0.2500, 0.0000], [ 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000]]]]) >>> m = nn.Upsample(scale_factor=2, mode='bilinear', align_corners=True) >>> # Notice that values in top left corner are now changed >>> m(input_3x3) tensor([[[[ 1.0000, 1.4000, 1.8000, 1.6000, 0.8000, 0.0000], [ 1.8000, 2.2000, 2.6000, 2.2400, 1.1200, 0.0000], [ 2.6000, 3.0000, 3.4000, 2.8800, 1.4400, 0.0000], [ 2.4000, 2.7200, 3.0400, 2.5600, 1.2800, 0.0000], [ 1.2000, 1.3600, 1.5200, 1.2800, 0.6400, 0.0000], [ 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000]]]])
UpsamplingNearest2d¶

class
torch.nn.
UpsamplingNearest2d
(size=None, scale_factor=None)[source]¶ Applies a 2D nearest neighbor upsampling to an input signal composed of several input channels.
To specify the scale, it takes either the
size
or thescale_factor
as it’s constructor argument.When
size
is given, it is the output size of the image (h, w). Parameters
Warning
This class is deprecated in favor of
interpolate()
. Shape:
Input: \((N, C, H_{in}, W_{in})\)
Output: \((N, C, H_{out}, W_{out})\) where
\[H_{out} = \left\lfloor H_{in} \times \text{scale\_factor} \right\rfloor \]\[W_{out} = \left\lfloor W_{in} \times \text{scale\_factor} \right\rfloor \]Examples:
>>> input = torch.arange(1, 5, dtype=torch.float32).view(1, 1, 2, 2) >>> input tensor([[[[ 1., 2.], [ 3., 4.]]]]) >>> m = nn.UpsamplingNearest2d(scale_factor=2) >>> m(input) tensor([[[[ 1., 1., 2., 2.], [ 1., 1., 2., 2.], [ 3., 3., 4., 4.], [ 3., 3., 4., 4.]]]])
UpsamplingBilinear2d¶

class
torch.nn.
UpsamplingBilinear2d
(size=None, scale_factor=None)[source]¶ Applies a 2D bilinear upsampling to an input signal composed of several input channels.
To specify the scale, it takes either the
size
or thescale_factor
as it’s constructor argument.When
size
is given, it is the output size of the image (h, w). Parameters
Warning
This class is deprecated in favor of
interpolate()
. It is equivalent tonn.functional.interpolate(..., mode='bilinear', align_corners=True)
. Shape:
Input: \((N, C, H_{in}, W_{in})\)
Output: \((N, C, H_{out}, W_{out})\) where
\[H_{out} = \left\lfloor H_{in} \times \text{scale\_factor} \right\rfloor \]\[W_{out} = \left\lfloor W_{in} \times \text{scale\_factor} \right\rfloor \]Examples:
>>> input = torch.arange(1, 5, dtype=torch.float32).view(1, 1, 2, 2) >>> input tensor([[[[ 1., 2.], [ 3., 4.]]]]) >>> m = nn.UpsamplingBilinear2d(scale_factor=2) >>> m(input) tensor([[[[ 1.0000, 1.3333, 1.6667, 2.0000], [ 1.6667, 2.0000, 2.3333, 2.6667], [ 2.3333, 2.6667, 3.0000, 3.3333], [ 3.0000, 3.3333, 3.6667, 4.0000]]]])
DataParallel layers (multiGPU, distributed)¶
DataParallel¶

class
torch.nn.
DataParallel
(module, device_ids=None, output_device=None, dim=0)[source]¶ Implements data parallelism at the module level.
This container parallelizes the application of the given
module
by splitting the input across the specified devices by chunking in the batch dimension (other objects will be copied once per device). In the forward pass, the module is replicated on each device, and each replica handles a portion of the input. During the backwards pass, gradients from each replica are summed into the original module.The batch size should be larger than the number of GPUs used.
See also: Use nn.DataParallel instead of multiprocessing
Arbitrary positional and keyword inputs are allowed to be passed into DataParallel but some types are specially handled. tensors will be scattered on dim specified (default 0). tuple, list and dict types will be shallow copied. The other types will be shared among different threads and can be corrupted if written to in the model’s forward pass.
The parallelized
module
must have its parameters and buffers ondevice_ids[0]
before running thisDataParallel
module.Warning
In each forward,
module
is replicated on each device, so any updates to the running module inforward
will be lost. For example, ifmodule
has a counter attribute that is incremented in eachforward
, it will always stay at the initial value because the update is done on the replicas which are destroyed afterforward
. However,DataParallel
guarantees that the replica ondevice[0]
will have its parameters and buffers sharing storage with the base parallelizedmodule
. So inplace updates to the parameters or buffers ondevice[0]
will be recorded. E.g.,BatchNorm2d
andspectral_norm()
rely on this behavior to update the buffers.Warning
Forward and backward hooks defined on
module
and its submodules will be invokedlen(device_ids)
times, each with inputs located on a particular device. Particularly, the hooks are only guaranteed to be executed in correct order with respect to operations on corresponding devices. For example, it is not guaranteed that hooks set viaregister_forward_pre_hook()
be executed before alllen(device_ids)
forward()
calls, but that each such hook be executed before the correspondingforward()
call of that device.Warning
When
module
returns a scalar (i.e., 0dimensional tensor) inforward()
, this wrapper will return a vector of length equal to number of devices used in data parallelism, containing the result from each device.Note
There is a subtlety in using the
pack sequence > recurrent network > unpack sequence
pattern in aModule
wrapped inDataParallel
. See My recurrent network doesn’t work with data parallelism section in FAQ for details. Parameters
module (Module) – module to be parallelized
device_ids (list of python:int or torch.device) – CUDA devices (default: all devices)
output_device (int or torch.device) – device location of output (default: device_ids[0])
 Variables
~DataParallel.module (Module) – the module to be parallelized
Example:
>>> net = torch.nn.DataParallel(model, device_ids=[0, 1, 2]) >>> output = net(input_var) # input_var can be on any device, including CPU
DistributedDataParallel¶

class
torch.nn.parallel.
DistributedDataParallel
(module, device_ids=None, output_device=None, dim=0, broadcast_buffers=True, process_group=None, bucket_cap_mb=25, find_unused_parameters=False, check_reduction=False)[source]¶ Implements distributed data parallelism that is based on
torch.distributed
package at the module level.This container parallelizes the application of the given module by splitting the input across the specified devices by chunking in the batch dimension. The module is replicated on each machine and each device, and each such replica handles a portion of the input. During the backwards pass, gradients from each node are averaged.
The batch size should be larger than the number of GPUs used locally.
See also: Basics and Use nn.DataParallel instead of multiprocessing. The same constraints on input as in
torch.nn.DataParallel
apply.Creation of this class requires that
torch.distributed
to be already initialized, by callingtorch.distributed.init_process_group()
.DistributedDataParallel
can be used in the following two ways:SingleProcess MultiGPU
In this case, a single process will be spawned on each host/node and each process will operate on all the GPUs of the node where it’s running. To use
DistributedDataParallel
in this way, you can simply construct the model as the following:>>> torch.distributed.init_process_group(backend="nccl") >>> model = DistributedDataParallel(model) # device_ids will include all GPU devices by default
MultiProcess SingleGPU
This is the highly recommended way to use
DistributedDataParallel
, with multiple processes, each of which operates on a single GPU. This is currently the fastest approach to do data parallel training using PyTorch and applies to both singlenode(multiGPU) and multinode data parallel training. It is proven to be significantly faster thantorch.nn.DataParallel
for singlenode multiGPU data parallel training.Here is how to use it: on each host with N GPUs, you should spawn up N processes, while ensuring that each process individually works on a single GPU from 0 to N1. Therefore, it is your job to ensure that your training script operates on a single given GPU by calling:
>>> torch.cuda.set_device(i)
where i is from 0 to N1. In each process, you should refer the following to construct this module:
>>> torch.distributed.init_process_group(backend='nccl', world_size=4, init_method='...') >>> model = DistributedDataParallel(model, device_ids=[i], output_device=i)
In order to spawn up multiple processes per node, you can use either
torch.distributed.launch
ortorch.multiprocessing.spawn
Note
nccl
backend is currently the fastest and highly recommended backend to be used with MultiProcess SingleGPU distributed training and this applies to both singlenode and multinode distributed trainingNote
This module also supports mixedprecision distributed training. This means that your model can have different types of parameters such as mixed types of fp16 and fp32, the gradient reduction on these mixed types of parameters will just work fine. Also note that
nccl
backend is currently the fastest and highly recommended backend for fp16/fp32 mixedprecision training.Note
If you use
torch.save
on one process to checkpoint the module, andtorch.load
on some other processes to recover it, make sure thatmap_location
is configured properly for every process. Withoutmap_location
,torch.load
would recover the module to devices where the module was saved from.Warning
This module works only with the
gloo
andnccl
backends.Warning
Constructor, forward method, and differentiation of the output (or a function of the output of this module) is a distributed synchronization point. Take that into account in case different processes might be executing different code.
Warning
This module assumes all parameters are registered in the model by the time it is created. No parameters should be added nor removed later. Same applies to buffers.
Warning
This module assumes all parameters are registered in the model of each distributed processes are in the same order. The module itself will conduct gradient allreduction following the reverse order of the registered parameters of the model. In other words, it is users’ responsibility to ensure that each distributed process has the exact same model and thus the exact same parameter registration order.
Warning
This module assumes all buffers and gradients are dense.
Warning
This module doesn’t work with
torch.autograd.grad()
(i.e. it will only work if gradients are to be accumulated in.grad
attributes of parameters).Warning
If you plan on using this module with a
nccl
backend or agloo
backend (that uses Infiniband), together with a DataLoader that uses multiple workers, please change the multiprocessing start method toforkserver
(Python 3 only) orspawn
. Unfortunately Gloo (that uses Infiniband) and NCCL2 are not fork safe, and you will likely experience deadlocks if you don’t change this setting.Warning
Forward and backward hooks defined on
module
and its submodules won’t be invoked anymore, unless the hooks are initialized in theforward()
method.Warning
You should never try to change your model’s parameters after wrapping up your model with DistributedDataParallel. In other words, when wrapping up your model with DistributedDataParallel, the constructor of DistributedDataParallel will register the additional gradient reduction functions on all the parameters of the model itself at the time of construction. If you change the model’s parameters after the DistributedDataParallel construction, this is not supported and unexpected behaviors can happen, since some parameters’ gradient reduction functions might not get called.
Note
Parameters are never broadcast between processes. The module performs an allreduce step on gradients and assumes that they will be modified by the optimizer in all processes in the same way. Buffers (e.g. BatchNorm stats) are broadcast from the module in process of rank 0, to all other replicas in the system in every iteration.
 Parameters
module (Module) – module to be parallelized
device_ids (list of python:int or torch.device) – CUDA devices. This should only be provided when the input module resides on a single CUDA device. For singledevice modules, the
i``th :attr:`module` replica is placed on ``device_ids[i]
. For multidevice modules and CPU modules, device_ids must be None or an empty list, and input data for the forward pass must be placed on the correct device. (default: all devices for singledevice modules)output_device (int or torch.device) – device location of output for singledevice CUDA modules. For multidevice modules and CPU modules, it must be None, and the module itself dictates the output location. (default: device_ids[0] for singledevice modules)
broadcast_buffers (bool) – flag that enables syncing (broadcasting) buffers of the module at beginning of the forward function. (default:
True
)process_group – the process group to be used for distributed data allreduction. If
None
, the default process group, which is created by`torch.distributed.init_process_group`
, will be used. (default:None
)bucket_cap_mb – DistributedDataParallel will bucket parameters into multiple buckets so that gradient reduction of each bucket can potentially overlap with backward computation.
bucket_cap_mb
controls the bucket size in MegaBytes (MB) (default: 25)find_unused_parameters (bool) – Traverse the autograd graph of all tensors contained in the return value of the wrapped module’s
forward
function. Parameters that don’t receive gradients as part of this graph are preemptively marked as being ready to be reduced. (default:False
)check_reduction – when setting to
True
, it enables DistributedDataParallel to automatically check if the previous iteration’s backward reductions were successfully issued at the beginning of every iteration’s forward function. You normally don’t need this option enabled unless you are observing weird behaviors such as different ranks are getting different gradients, which should not happen if DistributedDataParallel is correctly used. (default:False
)
 Variables
~DistributedDataParallel.module (Module) – the module to be parallelized
Example:
>>> torch.distributed.init_process_group(backend='nccl', world_size=4, init_method='...') >>> net = torch.nn.DistributedDataParallel(model, pg)
DistributedDataParallelCPU¶

class
torch.nn.parallel.
DistributedDataParallelCPU
(module)[source]¶ Implements distributed data parallelism for CPU at the module level.
This module supports the
mpi
andgloo
backends.This container parallelizes the application of the given module by splitting the input across the specified devices by chunking in the batch dimension. The module is replicated on each machine, and each such replica handles a portion of the input. During the backwards pass, gradients from each node are averaged.
This module could be used in conjunction with the DistributedSampler, (see
DistributedSampler
) which will load a subset of the original dataset for each node with the same batch size. So strong scaling should be configured like this:n = 1, batch size = 12
n = 2, batch size = 64
n = 4, batch size = 32
n = 8, batch size = 16
Creation of this class requires the distributed package to be already initialized in the process group mode (see
torch.distributed.init_process_group()
).Warning
Constructor, forward method, and differentiation of the output (or a function of the output of this module) is a distributed synchronization point. Take that into account in case different node might be executing different code.
Warning
This module assumes all parameters are registered in the model by the time it is created. No parameters should be added nor removed later.
Warning
This module assumes all gradients are dense.
Warning
This module doesn’t work with
torch.autograd.grad()
(i.e. it will only work if gradients are to be accumulated in.grad
attributes of parameters).Warning
Forward and backward hooks defined on
module
and its submodules won’t be invoked anymore, unless the hooks are initialized in theforward()
method.Note
Parameters are broadcast between nodes in the __init__() function. The module performs an allreduce step on gradients and assumes that they will be modified by the optimizer in all nodes in the same way.
 Parameters
module – module to be parallelized
Example:
>>> torch.distributed.init_process_group(world_size=4, init_method='...') >>> net = torch.nn.DistributedDataParallelCPU(model)
Utilities¶
clip_grad_norm_¶

torch.nn.utils.
clip_grad_norm_
(parameters, max_norm, norm_type=2)[source]¶ Clips gradient norm of an iterable of parameters.
The norm is computed over all gradients together, as if they were concatenated into a single vector. Gradients are modified inplace.
 Parameters
 Returns
Total norm of the parameters (viewed as a single vector).
clip_grad_value_¶
parameters_to_vector¶
vector_to_parameters¶
weight_norm¶

torch.nn.utils.
weight_norm
(module, name='weight', dim=0)[source]¶ Applies weight normalization to a parameter in the given module.
\[\mathbf{w} = g \dfrac{\mathbf{v}}{\\mathbf{v}\} \]Weight normalization is a reparameterization that decouples the magnitude of a weight tensor from its direction. This replaces the parameter specified by
name
(e.g.'weight'
) with two parameters: one specifying the magnitude (e.g.'weight_g'
) and one specifying the direction (e.g.'weight_v'
). Weight normalization is implemented via a hook that recomputes the weight tensor from the magnitude and direction before everyforward()
call.By default, with
dim=0
, the norm is computed independently per output channel/plane. To compute a norm over the entire weight tensor, usedim=None
.See https://arxiv.org/abs/1602.07868
 Parameters
 Returns
The original module with the weight norm hook
Example:
>>> m = weight_norm(nn.Linear(20, 40), name='weight') >>> m Linear(in_features=20, out_features=40, bias=True) >>> m.weight_g.size() torch.Size([40, 1]) >>> m.weight_v.size() torch.Size([40, 20])
remove_weight_norm¶
spectral_norm¶

torch.nn.utils.
spectral_norm
(module, name='weight', n_power_iterations=1, eps=1e12, dim=None)[source]¶ Applies spectral normalization to a parameter in the given module.
\[\mathbf{W}_{SN} = \dfrac{\mathbf{W}}{\sigma(\mathbf{W})}, \sigma(\mathbf{W}) = \max_{\mathbf{h}: \mathbf{h} \ne 0} \dfrac{\\mathbf{W} \mathbf{h}\_2}{\\mathbf{h}\_2} \]Spectral normalization stabilizes the training of discriminators (critics) in Generative Adversarial Networks (GANs) by rescaling the weight tensor with spectral norm \(\sigma\) of the weight matrix calculated using power iteration method. If the dimension of the weight tensor is greater than 2, it is reshaped to 2D in power iteration method to get spectral norm. This is implemented via a hook that calculates spectral norm and rescales weight before every
forward()
call.See Spectral Normalization for Generative Adversarial Networks .
 Parameters
module (nn.Module) – containing module
name (str, optional) – name of weight parameter
n_power_iterations (int, optional) – number of power iterations to calculate spectral norm
eps (float, optional) – epsilon for numerical stability in calculating norms
dim (int, optional) – dimension corresponding to number of outputs, the default is
0
, except for modules that are instances of ConvTranspose{1,2,3}d, when it is1
 Returns
The original module with the spectral norm hook
Example:
>>> m = spectral_norm(nn.Linear(20, 40)) >>> m Linear(in_features=20, out_features=40, bias=True) >>> m.weight_u.size() torch.Size([40])
remove_spectral_norm¶
PackedSequence¶

torch.nn.utils.rnn.
PackedSequence
(data, batch_sizes=None, sorted_indices=None, unsorted_indices=None)[source]¶ Holds the data and list of
batch_sizes
of a packed sequence.All RNN modules accept packed sequences as inputs.
Note
Instances of this class should never be created manually. They are meant to be instantiated by functions like
pack_padded_sequence()
.Batch sizes represent the number elements at each sequence step in the batch, not the varying sequence lengths passed to
pack_padded_sequence()
. For instance, given dataabc
andx
thePackedSequence
would contain dataaxbc
withbatch_sizes=[2,1,1]
. Variables
~PackedSequence.data (Tensor) – Tensor containing packed sequence
~PackedSequence.batch_sizes (Tensor) – Tensor of integers holding information about the batch size at each sequence step
~PackedSequence.sorted_indices (Tensor, optional) – Tensor of integers holding how this
PackedSequence
is constructed from sequences.~PackedSequence.unsorted_indices (Tensor, optional) – Tensor of integers holding how this to recover the original sequences with correct order.
Note
data
can be on arbitrary device and of arbitrary dtype.sorted_indices
andunsorted_indices
must betorch.int64
tensors on the same device asdata
.However,
batch_sizes
should always be a CPUtorch.int64
tensor.This invariant is maintained throughout
PackedSequence
class, and all functions that construct a :class:PackedSequence in PyTorch (i.e., they only pass in tensors conforming to this constraint).
pack_padded_sequence¶

torch.nn.utils.rnn.
pack_padded_sequence
(input, lengths, batch_first=False, enforce_sorted=True)[source]¶ Packs a Tensor containing padded sequences of variable length.
input
can be of sizeT x B x *
where T is the length of the longest sequence (equal tolengths[0]
),B
is the batch size, and*
is any number of dimensions (including 0). Ifbatch_first
isTrue
,B x T x *
input
is expected.For unsorted sequences, use enforce_sorted = False. If
enforce_sorted
isTrue
, the sequences should be sorted by length in a decreasing order, i.e.input[:,0]
should be the longest sequence, andinput[:,B1]
the shortest one. enforce_sorted = True is only necessary for ONNX export.Note
This function accepts any input that has at least two dimensions. You can apply it to pack the labels, and use the output of the RNN with them to compute the loss directly. A Tensor can be retrieved from a
PackedSequence
object by accessing its.data
attribute. Parameters
input (Tensor) – padded batch of variable length sequences.
lengths (Tensor) – list of sequences lengths of each batch element.
batch_first (bool, optional) – if
True
, the input is expected inB x T x *
format.enforce_sorted (bool, optional) – if
True
, the input is expected to contain sequences sorted by length in a decreasing order. IfFalse
, this condition is not checked. Default:True
.
 Returns
a
PackedSequence
object
pad_packed_sequence¶

torch.nn.utils.rnn.
pad_packed_sequence
(sequence, batch_first=False, padding_value=0.0, total_length=None)[source]¶ Pads a packed batch of variable length sequences.
It is an inverse operation to
pack_padded_sequence()
.The returned Tensor’s data will be of size
T x B x *
, where T is the length of the longest sequence and B is the batch size. Ifbatch_first
is True, the data will be transposed intoB x T x *
format.Batch elements will be ordered decreasingly by their length.
Note
total_length
is useful to implement thepack sequence > recurrent network > unpack sequence
pattern in aModule
wrapped inDataParallel
. See this FAQ section for details. Parameters
sequence (PackedSequence) – batch to pad
batch_first (bool, optional) – if
True
, the output will be inB x T x *
format.padding_value (float, optional) – values for padded elements.
total_length (int, optional) – if not
None
, the output will be padded to have lengthtotal_length
. This method will throwValueError
iftotal_length
is less than the max sequence length insequence
.
 Returns
Tuple of Tensor containing the padded sequence, and a Tensor containing the list of lengths of each sequence in the batch.
pad_sequence¶

torch.nn.utils.rnn.
pad_sequence
(sequences, batch_first=False, padding_value=0)[source]¶ Pad a list of variable length Tensors with
padding_value
pad_sequence
stacks a list of Tensors along a new dimension, and pads them to equal length. For example, if the input is list of sequences with sizeL x *
and if batch_first is False, andT x B x *
otherwise.B is batch size. It is equal to the number of elements in
sequences
. T is length of the longest sequence. L is length of the sequence. * is any number of trailing dimensions, including none.Example
>>> from torch.nn.utils.rnn import pad_sequence >>> a = torch.ones(25, 300) >>> b = torch.ones(22, 300) >>> c = torch.ones(15, 300) >>> pad_sequence([a, b, c]).size() torch.Size([25, 3, 300])
Note
This function returns a Tensor of size
T x B x *
orB x T x *
where T is the length of the longest sequence. This function assumes trailing dimensions and type of all the Tensors in sequences are same. Parameters
 Returns
Tensor of size
T x B x *
ifbatch_first
isFalse
. Tensor of sizeB x T x *
otherwise
pack_sequence¶

torch.nn.utils.rnn.
pack_sequence
(sequences, enforce_sorted=True)[source]¶ Packs a list of variable length Tensors
sequences
should be a list of Tensors of sizeL x *
, where L is the length of a sequence and * is any number of trailing dimensions, including zero.For unsorted sequences, use enforce_sorted = False. If
enforce_sorted
isTrue
, the sequences should be sorted in the order of decreasing length.enforce_sorted = True
is only necessary for ONNX export.Example
>>> from torch.nn.utils.rnn import pack_sequence >>> a = torch.tensor([1,2,3]) >>> b = torch.tensor([4,5]) >>> c = torch.tensor([6]) >>> pack_sequence([a, b, c]) PackedSequence(data=tensor([ 1, 4, 6, 2, 5, 3]), batch_sizes=tensor([ 3, 2, 1]))
 Parameters
 Returns
a
PackedSequence
object
torch.nn.functional¶
Convolution functions¶
conv1d¶

torch.nn.functional.
conv1d
(input, weight, bias=None, stride=1, padding=0, dilation=1, groups=1, padding_mode='zeros') → Tensor¶ Applies a 1D convolution over an input signal composed of several input planes.
See
Conv1d
for details and output shape.Note
In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting
torch.backends.cudnn.deterministic = True
. Please see the notes on Reproducibility for background. Parameters
input – input tensor of shape \((\text{minibatch} , \text{in\_channels} , iW)\)
weight – filters of shape \((\text{out\_channels} , \frac{\text{in\_channels}}{\text{groups}} , kW)\)
bias – optional bias of shape \((\text{out\_channels})\). Default:
None
stride – the stride of the convolving kernel. Can be a single number or a oneelement tuple (sW,). Default: 1
padding – implicit paddings on both sides of the input. Can be a single number or a oneelement tuple (padW,). Default: 0
dilation – the spacing between kernel elements. Can be a single number or a oneelement tuple (dW,). Default: 1
groups – split input into groups, \(\text{in\_channels}\) should be divisible by the number of groups. Default: 1
padding_mode – the type of paddings applied to both sided can be: zeros or circular. Default: zeros
Examples:
>>> filters = torch.randn(33, 16, 3) >>> inputs = torch.randn(20, 16, 50) >>> F.conv1d(inputs, filters)
conv2d¶

torch.nn.functional.
conv2d
(input, weight, bias=None, stride=1, padding=0, dilation=1, groups=1, padding_mode='zeros') → Tensor¶ Applies a 2D convolution over an input image composed of several input planes.
See
Conv2d
for details and output shape.Note
In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting
torch.backends.cudnn.deterministic = True
. Please see the notes on Reproducibility for background. Parameters
input – input tensor of shape \((\text{minibatch} , \text{in\_channels} , iH , iW)\)
weight – filters of shape \((\text{out\_channels} , \frac{\text{in\_channels}}{\text{groups}} , kH , kW)\)
bias – optional bias tensor of shape \((\text{out\_channels})\). Default:
None
stride – the stride of the convolving kernel. Can be a single number or a tuple (sH, sW). Default: 1
padding – implicit paddings on both sides of the input. Can be a single number or a tuple (padH, padW). Default: 0
dilation – the spacing between kernel elements. Can be a single number or a tuple (dH, dW). Default: 1
groups – split input into groups, \(\text{in\_channels}\) should be divisible by the number of groups. Default: 1
padding_mode – the type of paddings applied to both sided can be: zeros or circular. Default: zeros
Examples:
>>> # With square kernels and equal stride >>> filters = torch.randn(8,4,3,3) >>> inputs = torch.randn(1,4,5,5) >>> F.conv2d(inputs, filters, padding=1)
conv3d¶

torch.nn.functional.
conv3d
(input, weight, bias=None, stride=1, padding=0, dilation=1, groups=1, padding_mode='zeros') → Tensor¶ Applies a 3D convolution over an input image composed of several input planes.
See
Conv3d
for details and output shape.Note
In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting
torch.backends.cudnn.deterministic = True
. Please see the notes on Reproducibility for background. Parameters
input – input tensor of shape \((\text{minibatch} , \text{in\_channels} , iT , iH , iW)\)
weight – filters of shape \((\text{out\_channels} , \frac{\text{in\_channels}}{\text{groups}} , kT , kH , kW)\)
bias – optional bias tensor of shape \((\text{out\_channels})\). Default: None
stride – the stride of the convolving kernel. Can be a single number or a tuple (sT, sH, sW). Default: 1
padding – implicit paddings on both sides of the input. Can be a single number or a tuple (padT, padH, padW). Default: 0
dilation – the spacing between kernel elements. Can be a single number or a tuple (dT, dH, dW). Default: 1
groups – split input into groups, \(\text{in\_channels}\) should be divisible by the number of groups. Default: 1
padding_mode – the type of paddings applied to both sided can be: zeros or circular. Default: zeros
Examples:
>>> filters = torch.randn(33, 16, 3, 3, 3) >>> inputs = torch.randn(20, 16, 50, 10, 20) >>> F.conv3d(inputs, filters)
conv_transpose1d¶

torch.nn.functional.
conv_transpose1d
(input, weight, bias=None, stride=1, padding=0, output_padding=0, groups=1, dilation=1) → Tensor¶ Applies a 1D transposed convolution operator over an input signal composed of several input planes, sometimes also called “deconvolution”.
See
ConvTranspose1d
for details and output shape.Note
In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting
torch.backends.cudnn.deterministic = True
. Please see the notes on Reproducibility for background. Parameters
input – input tensor of shape \((\text{minibatch} , \text{in\_channels} , iW)\)
weight – filters of shape \((\text{in\_channels} , \frac{\text{out\_channels}}{\text{groups}} , kW)\)
bias – optional bias of shape \((\text{out\_channels})\). Default: None
stride – the stride of the convolving kernel. Can be a single number or a tuple
(sW,)
. Default: 1padding –
dilation * (kernel_size  1)  padding
zeropadding will be added to both sides of each dimension in the input. Can be a single number or a tuple(padW,)
. Default: 0output_padding – additional size added to one side of each dimension in the output shape. Can be a single number or a tuple
(out_padW)
. Default: 0groups – split input into groups, \(\text{in\_channels}\) should be divisible by the number of groups. Default: 1
dilation – the spacing between kernel elements. Can be a single number or a tuple
(dW,)
. Default: 1
Examples:
>>> inputs = torch.randn(20, 16, 50) >>> weights = torch.randn(16, 33, 5) >>> F.conv_transpose1d(inputs, weights)
conv_transpose2d¶

torch.nn.functional.
conv_transpose2d
(input, weight, bias=None, stride=1, padding=0, output_padding=0, groups=1, dilation=1) → Tensor¶ Applies a 2D transposed convolution operator over an input image composed of several input planes, sometimes also called “deconvolution”.
See
ConvTranspose2d
for details and output shape.Note
In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting
torch.backends.cudnn.deterministic = True
. Please see the notes on Reproducibility for background. Parameters
input – input tensor of shape \((\text{minibatch} , \text{in\_channels} , iH , iW)\)
weight – filters of shape \((\text{in\_channels} , \frac{\text{out\_channels}}{\text{groups}} , kH , kW)\)
bias – optional bias of shape \((\text{out\_channels})\). Default: None
stride – the stride of the convolving kernel. Can be a single number or a tuple
(sH, sW)
. Default: 1padding –
dilation * (kernel_size  1)  padding
zeropadding will be added to both sides of each dimension in the input. Can be a single number or a tuple(padH, padW)
. Default: 0output_padding – additional size added to one side of each dimension in the output shape. Can be a single number or a tuple
(out_padH, out_padW)
. Default: 0groups – split input into groups, \(\text{in\_channels}\) should be divisible by the number of groups. Default: 1
dilation – the spacing between kernel elements. Can be a single number or a tuple
(dH, dW)
. Default: 1
Examples:
>>> # With square kernels and equal stride >>> inputs = torch.randn(1, 4, 5, 5) >>> weights = torch.randn(4, 8, 3, 3) >>> F.conv_transpose2d(inputs, weights, padding=1)
conv_transpose3d¶

torch.nn.functional.
conv_transpose3d
(input, weight, bias=None, stride=1, padding=0, output_padding=0, groups=1, dilation=1) → Tensor¶ Applies a 3D transposed convolution operator over an input image composed of several input planes, sometimes also called “deconvolution”
See
ConvTranspose3d
for details and output shape.Note
In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting
torch.backends.cudnn.deterministic = True
. Please see the notes on Reproducibility for background. Parameters
input – input tensor of shape \((\text{minibatch} , \text{in\_channels} , iT , iH , iW)\)
weight – filters of shape \((\text{in\_channels} , \frac{\text{out\_channels}}{\text{groups}} , kT , kH , kW)\)
bias – optional bias of shape \((\text{out\_channels})\). Default: None
stride – the stride of the convolving kernel. Can be a single number or a tuple
(sT, sH, sW)
. Default: 1padding –
dilation * (kernel_size  1)  padding
zeropadding will be added to both sides of each dimension in the input. Can be a single number or a tuple(padT, padH, padW)
. Default: 0output_padding – additional size added to one side of each dimension in the output shape. Can be a single number or a tuple
(out_padT, out_padH, out_padW)
. Default: 0groups – split input into groups, \(\text{in\_channels}\) should be divisible by the number of groups. Default: 1
dilation – the spacing between kernel elements. Can be a single number or a tuple (dT, dH, dW). Default: 1
Examples:
>>> inputs = torch.randn(20, 16, 50, 10, 20) >>> weights = torch.randn(16, 33, 3, 3, 3) >>> F.conv_transpose3d(inputs, weights)
unfold¶

torch.nn.functional.
unfold
(input, kernel_size, dilation=1, padding=0, stride=1)[source]¶ Extracts sliding local blocks from an batched input tensor.
Warning
Currently, only 4D input tensors (batched imagelike tensors) are supported.
Warning
More than one element of the unfolded tensor may refer to a single memory location. As a result, inplace operations (especially ones that are vectorized) may result in incorrect behavior. If you need to write to the tensor, please clone it first.
See
torch.nn.Unfold
for details
fold¶

torch.nn.functional.
fold
(input, output_size, kernel_size, dilation=1, padding=0, stride=1)[source]¶ Combines an array of sliding local blocks into a large containing tensor.
Warning
Currently, only 4D output tensors (batched imagelike tensors) are supported.
See
torch.nn.Fold
for details
Pooling functions¶
avg_pool1d¶

torch.nn.functional.
avg_pool1d
(input, kernel_size, stride=None, padding=0, ceil_mode=False, count_include_pad=True) → Tensor¶ Applies a 1D average pooling over an input signal composed of several input planes.
See
AvgPool1d
for details and output shape. Parameters
input – input tensor of shape \((\text{minibatch} , \text{in\_channels} , iW)\)
kernel_size – the size of the window. Can be a single number or a tuple (kW,)
stride – the stride of the window. Can be a single number or a tuple (sW,). Default:
kernel_size
padding – implicit zero paddings on both sides of the input. Can be a single number or a tuple (padW,). Default: 0
ceil_mode – when True, will use ceil instead of floor to compute the output shape. Default:
False
count_include_pad – when True, will include the zeropadding in the averaging calculation. Default:
True
Examples:
>>> # pool of square window of size=3, stride=2 >>> input = torch.tensor([[[1, 2, 3, 4, 5, 6, 7]]], dtype=torch.float32) >>> F.avg_pool1d(input, kernel_size=3, stride=2) tensor([[[ 2., 4., 6.]]])
avg_pool2d¶

torch.nn.functional.
avg_pool2d
(input, kernel_size, stride=None, padding=0, ceil_mode=False, count_include_pad=True) → Tensor¶ Applies 2D averagepooling operation in \(kH \times kW\) regions by step size \(sH \times sW\) steps. The number of output features is equal to the number of input planes.
See
AvgPool2d
for details and output shape. Parameters
input – input tensor \((\text{minibatch} , \text{in\_channels} , iH , iW)\)
kernel_size – size of the pooling region. Can be a single number or a tuple (kH, kW)
stride – stride of the pooling operation. Can be a single number or a tuple (sH, sW). Default:
kernel_size
padding – implicit zero paddings on both sides of the input. Can be a single number or a tuple (padH, padW). Default: 0
ceil_mode – when True, will use ceil instead of floor in the formula to compute the output shape. Default:
False
count_include_pad – when True, will include the zeropadding in the averaging calculation. Default:
True
avg_pool3d¶

torch.nn.functional.
avg_pool3d
(input, kernel_size, stride=None, padding=0, ceil_mode=False, count_include_pad=True) → Tensor¶ Applies 3D averagepooling operation in \(kT \times kH \times kW\) regions by step size \(sT \times sH \times sW\) steps. The number of output features is equal to \(\lfloor\frac{\text{input planes}}{sT}\rfloor\).
See
AvgPool3d
for details and output shape. Parameters
input – input tensor \((\text{minibatch} , \text{in\_channels} , iT \times iH , iW)\)
kernel_size – size of the pooling region. Can be a single number or a tuple (kT, kH, kW)
stride – stride of the pooling operation. Can be a single number or a tuple (sT, sH, sW). Default:
kernel_size
padding – implicit zero paddings on both sides of the input. Can be a single number or a tuple (padT, padH, padW), Default: 0
ceil_mode – when True, will use ceil instead of floor in the formula to compute the output shape
count_include_pad – when True, will include the zeropadding in the averaging calculation
max_pool1d¶
max_pool2d¶
max_pool3d¶
max_unpool1d¶

torch.nn.functional.
max_unpool1d
(input, indices, kernel_size, stride=None, padding=0, output_size=None)[source]¶ Computes a partial inverse of
MaxPool1d
.See
MaxUnpool1d
for details.
max_unpool2d¶

torch.nn.functional.
max_unpool2d
(input, indices, kernel_size, stride=None, padding=0, output_size=None)[source]¶ Computes a partial inverse of
MaxPool2d
.See
MaxUnpool2d
for details.
max_unpool3d¶

torch.nn.functional.
max_unpool3d
(input, indices, kernel_size, stride=None, padding=0, output_size=None)[source]¶ Computes a partial inverse of
MaxPool3d
.See
MaxUnpool3d
for details.
lp_pool1d¶

torch.nn.functional.
lp_pool1d
(input, norm_type, kernel_size, stride=None, ceil_mode=False)[source]¶ Applies a 1D poweraverage pooling over an input signal composed of several input planes. If the sum of all inputs to the power of p is zero, the gradient is set to zero as well.
See
LPPool1d
for details.
lp_pool2d¶

torch.nn.functional.
lp_pool2d
(input, norm_type, kernel_size, stride=None, ceil_mode=False)[source]¶ Applies a 2D poweraverage pooling over an input signal composed of several input planes. If the sum of all inputs to the power of p is zero, the gradient is set to zero as well.
See
LPPool2d
for details.
adaptive_max_pool1d¶

torch.nn.functional.
adaptive_max_pool1d
(*args, **kwargs)¶ Applies a 1D adaptive max pooling over an input signal composed of several input planes.
See
AdaptiveMaxPool1d
for details and output shape. Parameters
output_size – the target output size (single integer)
return_indices – whether to return pooling indices. Default:
False
adaptive_max_pool2d¶

torch.nn.functional.
adaptive_max_pool2d
(*args, **kwargs)¶ Applies a 2D adaptive max pooling over an input signal composed of several input planes.
See
AdaptiveMaxPool2d
for details and output shape. Parameters
output_size – the target output size (single integer or doubleinteger tuple)
return_indices – whether to return pooling indices. Default:
False
adaptive_max_pool3d¶

torch.nn.functional.
adaptive_max_pool3d
(*args, **kwargs)¶ Applies a 3D adaptive max pooling over an input signal composed of several input planes.
See
AdaptiveMaxPool3d
for details and output shape. Parameters
output_size – the target output size (single integer or tripleinteger tuple)
return_indices – whether to return pooling indices. Default:
False
adaptive_avg_pool1d¶

torch.nn.functional.
adaptive_avg_pool1d
(input, output_size) → Tensor¶ Applies a 1D adaptive average pooling over an input signal composed of several input planes.
See
AdaptiveAvgPool1d
for details and output shape. Parameters
output_size – the target output size (single integer)
adaptive_avg_pool2d¶

torch.nn.functional.
adaptive_avg_pool2d
(input, output_size)[source]¶ Applies a 2D adaptive average pooling over an input signal composed of several input planes.
See
AdaptiveAvgPool2d
for details and output shape. Parameters
output_size – the target output size (single integer or doubleinteger tuple)
adaptive_avg_pool3d¶

torch.nn.functional.
adaptive_avg_pool3d
(input, output_size)[source]¶ Applies a 3D adaptive average pooling over an input signal composed of several input planes.
See
AdaptiveAvgPool3d
for details and output shape. Parameters
output_size – the target output size (single integer or tripleinteger tuple)
Nonlinear activation functions¶
threshold¶

torch.nn.functional.
threshold
(input, threshold, value, inplace=False)[source]¶ Thresholds each element of the input Tensor.
See
Threshold
for more details.

torch.nn.functional.
threshold_
(input, threshold, value) → Tensor¶ Inplace version of
threshold()
.
relu¶
hardtanh¶

torch.nn.functional.
hardtanh
(input, min_val=1., max_val=1., inplace=False) → Tensor[source]¶ Applies the HardTanh function elementwise. See
Hardtanh
for more details.

torch.nn.functional.
hardtanh_
(input, min_val=1., max_val=1.) → Tensor¶ Inplace version of
hardtanh()
.
relu6¶
elu¶
selu¶
celu¶
leaky_relu¶

torch.nn.functional.
leaky_relu
(input, negative_slope=0.01, inplace=False) → Tensor[source]¶ Applies elementwise, \(\text{LeakyReLU}(x) = \max(0, x) + \text{negative\_slope} * \min(0, x)\)
See
LeakyReLU
for more details.

torch.nn.functional.
leaky_relu_
(input, negative_slope=0.01) → Tensor¶ Inplace version of
leaky_relu()
.
prelu¶
rrelu¶
glu¶
logsigmoid¶

torch.nn.functional.
logsigmoid
(input) → Tensor¶ Applies elementwise \(\text{LogSigmoid}(x_i) = \log \left(\frac{1}{1 + \exp(x_i)}\right)\)
See
LogSigmoid
for more details.
hardshrink¶

torch.nn.functional.
hardshrink
(input, lambd=0.5) → Tensor[source]¶ Applies the hard shrinkage function elementwise
See
Hardshrink
for more details.
tanhshrink¶

torch.nn.functional.
tanhshrink
(input) → Tensor[source]¶ Applies elementwise, \(\text{Tanhshrink}(x) = x  \text{Tanh}(x)\)
See
Tanhshrink
for more details.
softsign¶
softmin¶

torch.nn.functional.
softmin
(input, dim=None, _stacklevel=3, dtype=None)[source]¶ Applies a softmin function.
Note that \(\text{Softmin}(x) = \text{Softmax}(x)\). See softmax definition for mathematical formula.
See
Softmin
for more details. Parameters
input (Tensor) – input
dim (int) – A dimension along which softmin will be computed (so every slice along dim will sum to 1).
dtype (
torch.dtype
, optional) – the desired data type of returned tensor. If specified, the input tensor is casted todtype
before the operation is performed. This is useful for preventing data type overflows. Default: None.
softmax¶

torch.nn.functional.
softmax
(input, dim=None, _stacklevel=3, dtype=None)[source]¶ Applies a softmax function.
Softmax is defined as:
\(\text{Softmax}(x_{i}) = \frac{exp(x_i)}{\sum_j exp(x_j)}\)
It is applied to all slices along dim, and will rescale them so that the elements lie in the range [0, 1] and sum to 1.
See
Softmax
for more details. Parameters
input (Tensor) – input
dim (int) – A dimension along which softmax will be computed.
dtype (
torch.dtype
, optional) – the desired data type of returned tensor. If specified, the input tensor is casted todtype
before the operation is performed. This is useful for preventing data type overflows. Default: None.
Note
This function doesn’t work directly with NLLLoss, which expects the Log to be computed between the Softmax and itself. Use log_softmax instead (it’s faster and has better numerical properties).
softshrink¶

torch.nn.functional.
softshrink
(input, lambd=0.5) → Tensor¶ Applies the soft shrinkage function elementwise
See
Softshrink
for more details.
gumbel_softmax¶

torch.nn.functional.
gumbel_softmax
(logits, tau=1, hard=False, eps=1e10, dim=1)[source]¶ Samples from the GumbelSoftmax distribution and optionally discretizes.
 Parameters
logits – […, num_features] unnormalized log probabilities
tau – nonnegative scalar temperature
hard – if
True
, the returned samples will be discretized as onehot vectors, but will be differentiated as if it is the soft sample in autograddim (int) – A dimension along which softmax will be computed. Default: 1.
 Returns
Sampled tensor of same shape as logits from the GumbelSoftmax distribution. If
hard=True
, the returned samples will be onehot, otherwise they will be probability distributions that sum to 1 across dim.
Note
This function is here for legacy reasons, may be removed from nn.Functional in the future.
Note
The main trick for hard is to do y_hard  y_soft.detach() + y_soft
It achieves two things:  makes the output value exactly onehot (since we add then subtract y_soft value)  makes the gradient equal to y_soft gradient (since we strip all other gradients)
 Examples::
>>> logits = torch.randn(20, 32) >>> # Sample soft categorical using reparametrization trick: >>> F.gumbel_softmax(logits, tau=1, hard=False) >>> # Sample hard categorical using "Straightthrough" trick: >>> F.gumbel_softmax(logits, tau=1, hard=True)
log_softmax¶

torch.nn.functional.
log_softmax
(input, dim=None, _stacklevel=3, dtype=None)[source]¶ Applies a softmax followed by a logarithm.
While mathematically equivalent to log(softmax(x)), doing these two operations separately is slower, and numerically unstable. This function uses an alternative formulation to compute the output and gradient correctly.
See
LogSoftmax
for more details. Parameters
input (Tensor) – input
dim (int) – A dimension along which log_softmax will be computed.
dtype (
torch.dtype
, optional) – the desired data type of returned tensor. If specified, the input tensor is casted todtype
before the operation is performed. This is useful for preventing data type overflows. Default: None.
tanh¶
Normalization functions¶
batch_norm¶

torch.nn.functional.
batch_norm
(input, running_mean, running_var, weight=None, bias=None, training=False, momentum=0.1, eps=1e05)[source]¶ Applies Batch Normalization for each channel across a batch of data.
See
BatchNorm1d
,BatchNorm2d
,BatchNorm3d
for details.
instance_norm¶

torch.nn.functional.
instance_norm
(input, running_mean=None, running_var=None, weight=None, bias=None, use_input_stats=True, momentum=0.1, eps=1e05)[source]¶ Applies Instance Normalization for each channel in each data sample in a batch.
See
InstanceNorm1d
,InstanceNorm2d
,InstanceNorm3d
for details.
layer_norm¶
local_response_norm¶

torch.nn.functional.
local_response_norm
(input, size, alpha=0.0001, beta=0.75, k=1.0)[source]¶ Applies local response normalization over an input signal composed of several input planes, where channels occupy the second dimension. Applies normalization across channels.
See
LocalResponseNorm
for details.
normalize¶

torch.nn.functional.
normalize
(input, p=2, dim=1, eps=1e12, out=None)[source]¶ Performs \(L_p\) normalization of inputs over specified dimension.
For a tensor
input
of sizes \((n_0, ..., n_{dim}, ..., n_k)\), each \(n_{dim}\) element vector \(v\) along dimensiondim
is transformed as\[v = \frac{v}{\max(\lVert v \rVert_p, \epsilon)}. \]With the default arguments it uses the Euclidean norm over vectors along dimension \(1\) for normalization.
 Parameters
input – input tensor of any shape
p (float) – the exponent value in the norm formulation. Default: 2
dim (int) – the dimension to reduce. Default: 1
eps (float) – small value to avoid division by zero. Default: 1e12
out (Tensor, optional) – the output tensor. If
out
is used, this operation won’t be differentiable.
Linear functions¶
linear¶

torch.nn.functional.
linear
(input, weight, bias=None)[source]¶ Applies a linear transformation to the incoming data: \(y = xA^T + b\).
Shape:
Input: \((N, *, in\_features)\) where * means any number of additional dimensions
Weight: \((out\_features, in\_features)\)
Bias: \((out\_features)\)
Output: \((N, *, out\_features)\)
Dropout functions¶
dropout¶

torch.nn.functional.
dropout
(input, p=0.5, training=True, inplace=False)[source]¶ During training, randomly zeroes some of the elements of the input tensor with probability
p
using samples from a Bernoulli distribution.See
Dropout
for details. Parameters
p – probability of an element to be zeroed. Default: 0.5
training – apply dropout if is
True
. Default:True
inplace – If set to
True
, will do this operation inplace. Default:False
alpha_dropout¶

torch.nn.functional.
alpha_dropout
(input, p=0.5, training=False, inplace=False)[source]¶ Applies alpha dropout to the input.
See
AlphaDropout
for details.
dropout2d¶

torch.nn.functional.
dropout2d
(input, p=0.5, training=True, inplace=False)[source]¶ Randomly zero out entire channels (a channel is a 2D feature map, e.g., the \(j\)th channel of the \(i\)th sample in the batched input is a 2D tensor \(\text{input}[i, j]\)) of the input tensor). Each channel will be zeroed out independently on every forward call with probability
p
using samples from a Bernoulli distribution.See
Dropout2d
for details. Parameters
p – probability of a channel to be zeroed. Default: 0.5
training – apply dropout if is
True
. Default:True
inplace – If set to
True
, will do this operation inplace. Default:False
dropout3d¶

torch.nn.functional.
dropout3d
(input, p=0.5, training=True, inplace=False)[source]¶ Randomly zero out entire channels (a channel is a 3D feature map, e.g., the \(j\)th channel of the \(i\)th sample in the batched input is a 3D tensor \(\text{input}[i, j]\)) of the input tensor). Each channel will be zeroed out independently on every forward call with probability
p
using samples from a Bernoulli distribution.See
Dropout3d
for details. Parameters
p – probability of a channel to be zeroed. Default: 0.5
training – apply dropout if is
True
. Default:True
inplace – If set to
True
, will do this operation inplace. Default:False
Sparse functions¶
embedding¶

torch.nn.functional.
embedding
(input, weight, padding_idx=None, max_norm=None, norm_type=2.0, scale_grad_by_freq=False, sparse=False)[source]¶ A simple lookup table that looks up embeddings in a fixed dictionary and size.
This module is often used to retrieve word embeddings using indices. The input to the module is a list of indices, and the embedding matrix, and the output is the corresponding word embeddings.
See
torch.nn.Embedding
for more details. Parameters
input (LongTensor) – Tensor containing indices into the embedding matrix
weight (Tensor) – The embedding matrix with number of rows equal to the maximum possible index + 1, and number of columns equal to the embedding size
padding_idx (int, optional) – If given, pads the output with the embedding vector at
padding_idx
(initialized to zeros) whenever it encounters the index.max_norm (float, optional) – If given, each embedding vector with norm larger than
max_norm
is renormalized to have normmax_norm
. Note: this will modifyweight
inplace.norm_type (float, optional) – The p of the pnorm to compute for the
max_norm
option. Default2
.scale_grad_by_freq (boolean, optional) – If given, this will scale gradients by the inverse of frequency of the words in the minibatch. Default
False
.sparse (bool, optional) – If
True
, gradient w.r.t.weight
will be a sparse tensor. See Notes undertorch.nn.Embedding
for more details regarding sparse gradients.
 Shape:
Input: LongTensor of arbitrary shape containing the indices to extract
 Weight: Embedding matrix of floating point type with shape (V, embedding_dim),
where V = maximum index + 1 and embedding_dim = the embedding size
Output: (*, embedding_dim), where * is the input shape
Examples:
>>> # a batch of 2 samples of 4 indices each >>> input = torch.tensor([[1,2,4,5],[4,3,2,9]]) >>> # an embedding matrix containing 10 tensors of size 3 >>> embedding_matrix = torch.rand(10, 3) >>> F.embedding(input, embedding_matrix) tensor([[[ 0.8490, 0.9625, 0.6753], [ 0.9666, 0.7761, 0.6108], [ 0.6246, 0.9751, 0.3618], [ 0.4161, 0.2419, 0.7383]], [[ 0.6246, 0.9751, 0.3618], [ 0.0237, 0.7794, 0.0528], [ 0.9666, 0.7761, 0.6108], [ 0.3385, 0.8612, 0.1867]]]) >>> # example with padding_idx >>> weights = torch.rand(10, 3) >>> weights[0, :].zero_() >>> embedding_matrix = weights >>> input = torch.tensor([[0,2,0,5]]) >>> F.embedding(input, embedding_matrix, padding_idx=0) tensor([[[ 0.0000, 0.0000, 0.0000], [ 0.5609, 0.5384, 0.8720], [ 0.0000, 0.0000, 0.0000], [ 0.6262, 0.2438, 0.7471]]])
embedding_bag¶

torch.nn.functional.
embedding_bag
(input, weight, offsets=None, max_norm=None, norm_type=2, scale_grad_by_freq=False, mode='mean', sparse=False, per_sample_weights=None)[source]¶ Computes sums, means or maxes of bags of embeddings, without instantiating the intermediate embeddings.
See
torch.nn.EmbeddingBag
for more details.Note
When using the CUDA backend, this operation may induce nondeterministic behaviour in be backward that is not easily switched off. Please see the notes on Reproducibility for background.
 Parameters
input (LongTensor) – Tensor containing bags of indices into the embedding matrix
weight (Tensor) – The embedding matrix with number of rows equal to the maximum possible index + 1, and number of columns equal to the embedding size
offsets (LongTensor, optional) – Only used when
input
is 1D.offsets
determines the starting index position of each bag (sequence) ininput
.max_norm (float, optional) – If given, each embedding vector with norm larger than
max_norm
is renormalized to have normmax_norm
. Note: this will modifyweight
inplace.norm_type (float, optional) – The
p
in thep
norm to compute for themax_norm
option. Default2
.scale_grad_by_freq (boolean, optional) – if given, this will scale gradients by the inverse of frequency of the words in the minibatch. Default
False
. Note: this option is not supported whenmode="max"
.mode (string, optional) –
"sum"
,"mean"
or"max"
. Specifies the way to reduce the bag. Default:"mean"
sparse (bool, optional) – if
True
, gradient w.r.t.weight
will be a sparse tensor. See Notes undertorch.nn.Embedding
for more details regarding sparse gradients. Note: this option is not supported whenmode="max"
.per_sample_weights (Tensor, optional) – a tensor of float / double weights, or None to indicate all weights should be taken to be 1. If specified,
per_sample_weights
must have exactly the same shape as input and is treated as having the sameoffsets
, if those are not None.
Shape:
input
(LongTensor) andoffsets
(LongTensor, optional)If
input
is 2D of shape (B, N),it will be treated as
B
bags (sequences) each of fixed lengthN
, and this will returnB
values aggregated in a way depending on themode
.offsets
is ignored and required to beNone
in this case.If
input
is 1D of shape (N),it will be treated as a concatenation of multiple bags (sequences).
offsets
is required to be a 1D tensor containing the starting index positions of each bag ininput
. Therefore, foroffsets
of shape (B),input
will be viewed as havingB
bags. Empty bags (i.e., having 0length) will have returned vectors filled by zeros.
weight
(Tensor): the learnable weights of the module of shape (num_embeddings, embedding_dim)per_sample_weights
(Tensor, optional). Has the same shape asinput
.output
: aggregated embedding values of shape (B, embedding_dim)
Examples:
>>> # an Embedding module containing 10 tensors of size 3 >>> embedding_matrix = torch.rand(10, 3) >>> # a batch of 2 samples of 4 indices each >>> input = torch.tensor([1,2,4,5,4,3,2,9]) >>> offsets = torch.tensor([0,4]) >>> F.embedding_bag(embedding_matrix, input, offsets) tensor([[ 0.3397, 0.3552, 0.5545], [ 0.5893, 0.4386, 0.5882]])
one_hot¶

torch.nn.functional.
one_hot
(tensor, num_classes=0) → LongTensor¶ Takes LongTensor with index values of shape
(*)
and returns a tensor of shape(*, num_classes)
that have zeros everywhere except where the index of last dimension matches the corresponding value of the input tensor, in which case it will be 1.See also Onehot on Wikipedia .
 Parameters
tensor (LongTensor) – class values of any shape.
num_classes (int) – Total number of classes. If set to 1, the number of classes will be inferred as one greater than the largest class value in the input tensor.
 Returns
LongTensor that has one more dimension with 1 values at the index of last dimension indicated by the input, and 0 everywhere else.
Examples
>>> F.one_hot(torch.arange(0, 5) % 3) tensor([[1, 0, 0], [0, 1, 0], [0, 0, 1], [1, 0, 0], [0, 1, 0]]) >>> F.one_hot(torch.arange(0, 5) % 3, num_classes=5) tensor([[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0]]) >>> F.one_hot(torch.arange(0, 6).view(3,2) % 3) tensor([[[1, 0, 0], [0, 1, 0]], [[0, 0, 1], [1, 0, 0]], [[0, 1, 0], [0, 0, 1]]])
Distance functions¶
pairwise_distance¶

torch.nn.functional.
pairwise_distance
(x1, x2, p=2.0, eps=1e06, keepdim=False)[source]¶ See
torch.nn.PairwiseDistance
for details
cosine_similarity¶

torch.nn.functional.
cosine_similarity
(x1, x2, dim=1, eps=1e8) → Tensor¶ Returns cosine similarity between x1 and x2, computed along dim.
\[\text{similarity} = \dfrac{x_1 \cdot x_2}{\max(\Vert x_1 \Vert _2 \cdot \Vert x_2 \Vert _2, \epsilon)} \] Parameters
 Shape:
Input: \((\ast_1, D, \ast_2)\) where D is at position dim.
Output: \((\ast_1, \ast_2)\) where 1 is at position dim.
Example:
>>> input1 = torch.randn(100, 128) >>> input2 = torch.randn(100, 128) >>> output = F.cosine_similarity(input1, input2) >>> print(output)
pdist¶

torch.nn.functional.
pdist
(input, p=2) → Tensor¶ Computes the pnorm distance between every pair of row vectors in the input. This is identical to the upper triangular portion, excluding the diagonal, of torch.norm(input[:, None]  input, dim=2, p=p). This function will be faster if the rows are contiguous.
If input has shape \(N \times M\) then the output will have shape \(\frac{1}{2} N (N  1)\).
This function is equivalent to scipy.spatial.distance.pdist(input, ‘minkowski’, p=p) if \(p \in (0, \infty)\). When \(p = 0\) it is equivalent to scipy.spatial.distance.pdist(input, ‘hamming’) * M. When \(p = \infty\), the closest scipy function is scipy.spatial.distance.pdist(xn, lambda x, y: np.abs(x  y).max()).
 Parameters
input – input tensor of shape \(N \times M\).
p – p value for the pnorm distance to calculate between each vector pair \(\in [0, \infty]\).
Loss functions¶
binary_cross_entropy¶

torch.nn.functional.
binary_cross_entropy
(input, target, weight=None, size_average=None, reduce=None, reduction='mean')[source]¶ Function that measures the Binary Cross Entropy between the target and the output.
See
BCELoss
for details. Parameters
input – Tensor of arbitrary shape
target – Tensor of the same shape as input
weight (Tensor, optional) – a manual rescaling weight if provided it’s repeated to match input tensor shape
size_average (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the fieldsize_average
is set toFalse
, the losses are instead summed for each minibatch. Ignored when reduce isFalse
. Default:True
reduce (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged or summed over observations for each minibatch depending onsize_average
. Whenreduce
isFalse
, returns a loss per batch element instead and ignoressize_average
. Default:True
reduction (string, optional) – Specifies the reduction to apply to the output:
'none'
'mean'
'sum'
.'none'
: no reduction will be applied,'mean'
: the sum of the output will be divided by the number of elements in the output,'sum'
: the output will be summed. Note:size_average
andreduce
are in the process of being deprecated, and in the meantime, specifying either of those two args will overridereduction
. Default:'mean'
Examples:
>>> input = torch.randn((3, 2), requires_grad=True) >>> target = torch.rand((3, 2), requires_grad=False) >>> loss = F.binary_cross_entropy(F.sigmoid(input), target) >>> loss.backward()
binary_cross_entropy_with_logits¶

torch.nn.functional.
binary_cross_entropy_with_logits
(input, target, weight=None, size_average=None, reduce=None, reduction='mean', pos_weight=None)[source]¶ Function that measures Binary Cross Entropy between target and output logits.
See
BCEWithLogitsLoss
for details. Parameters
input – Tensor of arbitrary shape
target – Tensor of the same shape as input
weight (Tensor, optional) – a manual rescaling weight if provided it’s repeated to match input tensor shape
size_average (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the fieldsize_average
is set toFalse
, the losses are instead summed for each minibatch. Ignored when reduce isFalse
. Default:True
reduce (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged or summed over observations for each minibatch depending onsize_average
. Whenreduce
isFalse
, returns a loss per batch element instead and ignoressize_average
. Default:True
reduction (string, optional) – Specifies the reduction to apply to the output:
'none'
'mean'
'sum'
.'none'
: no reduction will be applied,'mean'
: the sum of the output will be divided by the number of elements in the output,'sum'
: the output will be summed. Note:size_average
andreduce
are in the process of being deprecated, and in the meantime, specifying either of those two args will overridereduction
. Default:'mean'
pos_weight (Tensor, optional) – a weight of positive examples. Must be a vector with length equal to the number of classes.
Examples:
>>> input = torch.randn(3, requires_grad=True) >>> target = torch.empty(3).random_(2) >>> loss = F.binary_cross_entropy_with_logits(input, target) >>> loss.backward()
poisson_nll_loss¶

torch.nn.functional.
poisson_nll_loss
(input, target, log_input=True, full=False, size_average=None, eps=1e08, reduce=None, reduction='mean')[source]¶ Poisson negative log likelihood loss.
See
PoissonNLLLoss
for details. Parameters
input – expectation of underlying Poisson distribution.
target – random sample \(target \sim \text{Poisson}(input)\).
log_input – if
True
the loss is computed as \(\exp(\text{input})  \text{target} * \text{input}\), ifFalse
then loss is \(\text{input}  \text{target} * \log(\text{input}+\text{eps})\). Default:True
full – whether to compute full loss, i. e. to add the Stirling approximation term. Default:
False
\(\text{target} * \log(\text{target})  \text{target} + 0.5 * \log(2 * \pi * \text{target})\).size_average (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the fieldsize_average
is set toFalse
, the losses are instead summed for each minibatch. Ignored when reduce isFalse
. Default:True
eps (float, optional) – Small value to avoid evaluation of \(\log(0)\) when
log_input`=``False`
. Default: 1e8reduce (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged or summed over observations for each minibatch depending onsize_average
. Whenreduce
isFalse
, returns a loss per batch element instead and ignoressize_average
. Default:True
reduction (string, optional) – Specifies the reduction to apply to the output:
'none'
'mean'
'sum'
.'none'
: no reduction will be applied,'mean'
: the sum of the output will be divided by the number of elements in the output,'sum'
: the output will be summed. Note:size_average
andreduce
are in the process of being deprecated, and in the meantime, specifying either of those two args will overridereduction
. Default:'mean'
cosine_embedding_loss¶

torch.nn.functional.
cosine_embedding_loss
(input1, input2, target, margin=0, size_average=None, reduce=None, reduction='mean') → Tensor[source]¶ See
CosineEmbeddingLoss
for details.
cross_entropy¶

torch.nn.functional.
cross_entropy
(input, target, weight=None, size_average=None, ignore_index=100, reduce=None, reduction='mean')[source]¶ This criterion combines log_softmax and nll_loss in a single function.
See
CrossEntropyLoss
for details. Parameters
input (Tensor) – \((N, C)\) where C = number of classes or \((N, C, H, W)\) in case of 2D Loss, or \((N, C, d_1, d_2, ..., d_K)\) where \(K \geq 1\) in the case of Kdimensional loss.
target (Tensor) – \((N)\) where each value is \(0 \leq \text{targets}[i] \leq C1\), or \((N, d_1, d_2, ..., d_K)\) where \(K \geq 1\) for Kdimensional loss.
weight (Tensor, optional) – a manual rescaling weight given to each class. If given, has to be a Tensor of size C
size_average (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the fieldsize_average
is set toFalse
, the losses are instead summed for each minibatch. Ignored when reduce isFalse
. Default:True
ignore_index (int, optional) – Specifies a target value that is ignored and does not contribute to the input gradient. When
size_average
isTrue
, the loss is averaged over nonignored targets. Default: 100reduce (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged or summed over observations for each minibatch depending onsize_average
. Whenreduce
isFalse
, returns a loss per batch element instead and ignoressize_average
. Default:True
reduction (string, optional) – Specifies the reduction to apply to the output:
'none'
'mean'
'sum'
.'none'
: no reduction will be applied,'mean'
: the sum of the output will be divided by the number of elements in the output,'sum'
: the output will be summed. Note:size_average
andreduce
are in the process of being deprecated, and in the meantime, specifying either of those two args will overridereduction
. Default:'mean'
Examples:
>>> input = torch.randn(3, 5, requires_grad=True) >>> target = torch.randint(5, (3,), dtype=torch.int64) >>> loss = F.cross_entropy(input, target) >>> loss.backward()
ctc_loss¶

torch.nn.functional.
ctc_loss
(log_probs, targets, input_lengths, target_lengths, blank=0, reduction='mean', zero_infinity=False)[source]¶ The Connectionist Temporal Classification loss.
See
CTCLoss
for details.Note
In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting
torch.backends.cudnn.deterministic = True
. Please see the notes on Reproducibility for background.Note
When using the CUDA backend, this operation may induce nondeterministic behaviour in be backward that is not easily switched off. Please see the notes on Reproducibility for background.
 Parameters
log_probs – \((T, N, C)\) where C = number of characters in alphabet including blank, T = input length, and N = batch size. The logarithmized probabilities of the outputs (e.g. obtained with
torch.nn.functional.log_softmax()
).targets – \((N, S)\) or (sum(target_lengths)). Targets cannot be blank. In the second form, the targets are assumed to be concatenated.
input_lengths – \((N)\). Lengths of the inputs (must each be \(\leq T\))
target_lengths – \((N)\). Lengths of the targets
blank (int, optional) – Blank label. Default \(0\).
reduction (string, optional) – Specifies the reduction to apply to the output:
'none'
'mean'
'sum'
.'none'
: no reduction will be applied,'mean'
: the output losses will be divided by the target lengths and then the mean over the batch is taken,'sum'
: the output will be summed. Default:'mean'
zero_infinity (bool, optional) – Whether to zero infinite losses and the associated gradients. Default:
False
Infinite losses mainly occur when the inputs are too short to be aligned to the targets.
Example:
>>> log_probs = torch.randn(50, 16, 20).log_softmax(2).detach().requires_grad_() >>> targets = torch.randint(1, 20, (16, 30), dtype=torch.long) >>> input_lengths = torch.full((16,), 50, dtype=torch.long) >>> target_lengths = torch.randint(10,30,(16,), dtype=torch.long) >>> loss = F.ctc_loss(log_probs, targets, input_lengths, target_lengths) >>> loss.backward()
hinge_embedding_loss¶

torch.nn.functional.
hinge_embedding_loss
(input, target, margin=1.0, size_average=None, reduce=None, reduction='mean') → Tensor[source]¶ See
HingeEmbeddingLoss
for details.
kl_div¶

torch.nn.functional.
kl_div
(input, target, size_average=None, reduce=None, reduction='mean')[source]¶ The KullbackLeibler divergence Loss.
See
KLDivLoss
for details. Parameters
input – Tensor of arbitrary shape
target – Tensor of the same shape as input
size_average (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the fieldsize_average
is set toFalse
, the losses are instead summed for each minibatch. Ignored when reduce isFalse
. Default:True
reduce (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged or summed over observations for each minibatch depending onsize_average
. Whenreduce
isFalse
, returns a loss per batch element instead and ignoressize_average
. Default:True
reduction (string, optional) – Specifies the reduction to apply to the output:
'none'
'batchmean'
'sum'
'mean'
.'none'
: no reduction will be applied'batchmean'
: the sum of the output will be divided by the batchsize'sum'
: the output will be summed'mean'
: the output will be divided by the number of elements in the output Default:'mean'
Note
size_average
andreduce
are in the process of being deprecated, and in the meantime, specifying either of those two args will overridereduction
.Note
:attr:
reduction
='mean'
doesn’t return the true kl divergence value, please use :attr:reduction
='batchmean'
which aligns with KL math definition. In the next major release,'mean'
will be changed to be the same as ‘batchmean’.
l1_loss¶
mse_loss¶
margin_ranking_loss¶

torch.nn.functional.
margin_ranking_loss
(input1, input2, target, margin=0, size_average=None, reduce=None, reduction='mean') → Tensor[source]¶ See
MarginRankingLoss
for details.
multilabel_margin_loss¶

torch.nn.functional.
multilabel_margin_loss
(input, target, size_average=None, reduce=None, reduction='mean') → Tensor[source]¶ See
MultiLabelMarginLoss
for details.
multilabel_soft_margin_loss¶

torch.nn.functional.
multilabel_soft_margin_loss
(input, target, weight=None, size_average=None) → Tensor[source]¶ See
MultiLabelSoftMarginLoss
for details.
multi_margin_loss¶

torch.nn.functional.
multi_margin_loss
(input, target, p=1, margin=1.0, weight=None, size_average=None, reduce=None, reduction='mean')[source]¶  multi_margin_loss(input, target, p=1, margin=1, weight=None, size_average=None,
reduce=None, reduction=’mean’) > Tensor
See
MultiMarginLoss
for details.
nll_loss¶

torch.nn.functional.
nll_loss
(input, target, weight=None, size_average=None, ignore_index=100, reduce=None, reduction='mean')[source]¶ The negative log likelihood loss.
See
NLLLoss
for details. Parameters
input – \((N, C)\) where C = number of classes or \((N, C, H, W)\) in case of 2D Loss, or \((N, C, d_1, d_2, ..., d_K)\) where \(K \geq 1\) in the case of Kdimensional loss.
target – \((N)\) where each value is \(0 \leq \text{targets}[i] \leq C1\), or \((N, d_1, d_2, ..., d_K)\) where \(K \geq 1\) for Kdimensional loss.
weight (Tensor, optional) – a manual rescaling weight given to each class. If given, has to be a Tensor of size C
size_average (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the fieldsize_average
is set toFalse
, the losses are instead summed for each minibatch. Ignored when reduce isFalse
. Default:True
ignore_index (int, optional) – Specifies a target value that is ignored and does not contribute to the input gradient. When
size_average
isTrue
, the loss is averaged over nonignored targets. Default: 100reduce (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged or summed over observations for each minibatch depending onsize_average
. Whenreduce
isFalse
, returns a loss per batch element instead and ignoressize_average
. Default:True
reduction (string, optional) – Specifies the reduction to apply to the output:
'none'
'mean'
'sum'
.'none'
: no reduction will be applied,'mean'
: the sum of the output will be divided by the number of elements in the output,'sum'
: the output will be summed. Note:size_average
andreduce
are in the process of being deprecated, and in the meantime, specifying either of those two args will overridereduction
. Default:'mean'
Example:
>>> # input is of size N x C = 3 x 5 >>> input = torch.randn(3,