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 with Module s - when they’re assigned as Module attributes they are automatically added to the list of its parameters, and will appear e.g. in parameters() 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 as Parameter, these temporaries would get registered too.

Parameters

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 torch-nn-init).

Parameters

fn (Module -> None) – function to be applied to each submodule

Returns

self

Return type

Module

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

cpu()[source]

Moves all model parameters and buffers to the CPU.

Returns

self

Return type

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.

Parameters

device (int, optional) – if specified, all parameters will be copied to that device

Returns

self

Return type

Module

double()[source]

Casts all floating point parameters and buffers to double datatype.

Returns

self

Return type

Module

dump_patches = False

This allows better BC support for load_state_dict(). In state_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.

This is equivalent with self.train(False).

Returns

self

Return type

Module

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 single-line and multi-line strings are acceptable.

float()[source]

Casts all floating point parameters and buffers to float datatype.

Returns

self

Return type

Module

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

Module

load_state_dict(state_dict, strict=True)[source]

Copies parameters and buffers from state_dict into this module and its descendants. If strict is True, then the keys of state_dict must exactly match the keys returned by this module’s state_dict() function.

Parameters
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 with missing_keys and unexpected_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
• prefix (str) – prefix to prepend to all buffer names.

• 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

(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
• prefix (str) – prefix to prepend to all parameter names.

• 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

(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 and grad_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 of grad_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 and grad_output will only contain the gradients for a subset of the inputs and outputs. For such Module, you should use torch.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 or modified output


The hook can modify the output. It can modify the input inplace but it will not have effect on forward since this is called after forward() is called.

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 pre-hook on the module.

The hook will be called every time before forward() is invoked. It should have the following signature:

hook(module, input) -> None or modified input


The hook can modify the input. User can either return a tuple or a single modified value in the hook. We will wrap the value into a tuple if a single value is returned(unless that value is already a tuple).

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.

requires_grad_(requires_grad=True)[source]

Change if autograd should record operations on parameters in this module.

This method sets the parameters’ requires_grad attributes in-place.

This method is helpful for freezing part of the module for finetuning or training parts of a model individually (e.g., GAN training).

Parameters

requires_grad (bool) – whether autograd should record operations on parameters in this module. Default: True.

Returns

self

Return type

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

dict

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 desired dtype s. In addition, this method will only cast the floating point parameters and buffers to dtype (if given). The integral parameters and buffers will be moved device, if that is given, but with dtypes unchanged. When non_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 in-place.

Parameters
• device (torch.device) – the desired device of the parameters and buffers in this module

• dtype (torch.dtype) – the desired floating point type of the floating point parameters and buffers in this module

• tensor (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

Module

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.

Parameters

mode (bool) – whether to set training mode (True) or evaluation mode (False). Default: True.

Returns

self

Return type

Module

type(dst_type)[source]

Casts all parameters and buffers to dst_type.

Parameters

dst_type (type or string) – the desired type

Returns

self

Return type

Module

zero_grad()[source]

Sets gradients of all model parameters to zero.

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 all Module 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

extend(modules)[source]

Appends modules from a Python iterable to the end of the list.

Parameters

modules (iterable) – iterable of modules to append

insert(index, module)[source]

Insert a given module before a given index in the list.

Parameters
• index (int) – index to insert.

• module (nn.Module) – module to insert

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 all Module methods.

ModuleDict is an ordered dictionary that respects

Note that update() with other unordered mapping types (e.g., Python’s plain dict) does not preserve the order of the merged mapping.

Parameters

modules (iterable, optional) – a mapping (dictionary) of (string: module) or an iterable of key-value 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

clear()[source]

Remove all items from the ModuleDict.

items()[source]

Return an iterable of the ModuleDict key/value pairs.

keys()[source]

Return an iterable of the ModuleDict keys.

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 key-value pairs from a mapping or an iterable, overwriting existing keys.

Note

If modules is an OrderedDict, a ModuleDict, or an iterable of key-value pairs, the order of new elements in it is preserved.

Parameters

modules (iterable) – a mapping (dictionary) from string to Module, or an iterable of key-value pairs of type (string, Module)

values()[source]

Return an iterable of the ModuleDict values.

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 all Module 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

extend(parameters)[source]

Appends parameters from a Python iterable to the end of the list.

Parameters

parameters (iterable) – iterable of parameters 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 respects

Note that update() with other unordered mapping types (e.g., Python’s plain dict) does not preserve the order of the merged mapping.

Parameters

parameters (iterable, optional) – a mapping (dictionary) of (string : Parameter) or an iterable of key-value 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

clear()[source]

Remove all items from the ParameterDict.

items()[source]

Return an iterable of the ParameterDict key/value pairs.

keys()[source]

Return an iterable of the ParameterDict keys.

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 key-value pairs from a mapping or an iterable, overwriting existing keys.

Note

If parameters is an OrderedDict, a ParameterDict, or an iterable of key-value pairs, the order of new elements in it is preserved.

Parameters

parameters (iterable) – a mapping (dictionary) from string to Parameter, or an iterable of key-value pairs of type (string, Parameter)

values()[source]

Return an iterable of the ParameterDict values.

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 cross-correlation 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 cross-correlation, a single number or a one-element tuple.

• padding controls the amount of implicit zero-paddings on both sides for padding 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 what dilation does.

• groups controls the connections between inputs and outputs. in_channels and out_channels must both be divisible by groups. 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 cross-correlation, and not a full cross-correlation. 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

• kernel_size (int or tuple) – Size of the convolving kernel

• stride (int or tuple, optional) – Stride of the convolution. Default: 1

• padding (int or tuple, optional) – Zero-padding 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 is True, 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 cross-correlation 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 cross-correlation, a single number or a tuple.

• padding controls the amount of implicit zero-paddings on both sides for padding 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 what dilation does.

• groups controls the connections between inputs and outputs. in_channels and out_channels must both be divisible by groups. 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 dimension

• a 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 cross-correlation, and not a full cross-correlation. 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

• kernel_size (int or tuple) – Size of the convolving kernel

• stride (int or tuple, optional) – Stride of the convolution. Default: 1

• padding (int or tuple, optional) – Zero-padding 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 is True, 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)
>>> # non-square kernels and unequal stride and with padding
>>> m = nn.Conv2d(16, 33, (3, 5), stride=(2, 1), padding=(4, 2))
>>> # non-square 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 cross-correlation operator

• stride controls the stride for the cross-correlation.

• padding controls the amount of implicit zero-paddings on both sides for padding 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 what dilation does.

• groups controls the connections between inputs and outputs. in_channels and out_channels must both be divisible by groups. 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 dimension

• a 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 cross-correlation, and not a full cross-correlation. 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

• kernel_size (int or tuple) – Size of the convolving kernel

• stride (int or tuple, optional) – Stride of the convolution. Default: 1

• padding (int or tuple, optional) – Zero-padding 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 is True, 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)
>>> # non-square 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 fractionally-strided convolution or a deconvolution (although it is not an actual deconvolution operation).

• stride controls the stride for the cross-correlation.

• padding controls the amount of implicit zero-paddings on both sides for dilation * (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 what dilation does.

• groups controls the connections between inputs and outputs. in_channels and out_channels must both be divisible by groups. 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 cross-correlation, and not a full cross-correlation. It is up to the user to add proper padding.

Note

The padding argument effectively adds dilation * (kernel_size - 1) - padding amount of zero padding to both sizes of the input. This is set so that when a Conv1d and a ConvTranspose1d are initialized with same parameters, they are inverses of each other in regard to the input and output shapes. However, when stride > 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 that output_padding is only used to find output shape, but does not actually add zero-padding 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

• kernel_size (int or tuple) – Size of the convolving kernel

• stride (int or tuple, optional) – Stride of the convolution. Default: 1

• padding (int or tuple, optional) – dilation * (kernel_size - 1) - padding zero-padding will be added to both sides of the input. Default: 0

• output_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 is True, 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 fractionally-strided convolution or a deconvolution (although it is not an actual deconvolution operation).

• stride controls the stride for the cross-correlation.

• padding controls the amount of implicit zero-paddings on both sides for dilation * (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 what dilation does.

• groups controls the connections between inputs and outputs. in_channels and out_channels must both be divisible by groups. 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 dimensions

• a 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 cross-correlation, and not a full cross-correlation. It is up to the user to add proper padding.

Note

The padding argument effectively adds dilation * (kernel_size - 1) - padding amount of zero padding to both sizes of the input. This is set so that when a Conv2d and a ConvTranspose2d are initialized with same parameters, they are inverses of each other in regard to the input and output shapes. However, when stride > 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 that output_padding is only used to find output shape, but does not actually add zero-padding 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

• kernel_size (int or tuple) – Size of the convolving kernel

• stride (int or tuple, optional) – Stride of the convolution. Default: 1

• padding (int or tuple, optional) – dilation * (kernel_size - 1) - padding zero-padding will be added to both sides of each dimension in the input. Default: 0

• output_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 is True, 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)
>>> # non-square 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 element-wise 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 fractionally-strided convolution or a deconvolution (although it is not an actual deconvolution operation).

• stride controls the stride for the cross-correlation.

• padding controls the amount of implicit zero-paddings on both sides for dilation * (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 what dilation does.

• groups controls the connections between inputs and outputs. in_channels and out_channels must both be divisible by groups. 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 dimensions

• a 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 cross-correlation, and not a full cross-correlation. It is up to the user to add proper padding.

Note

The padding argument effectively adds dilation * (kernel_size - 1) - padding amount of zero padding to both sizes of the input. This is set so that when a Conv3d and a ConvTranspose3d are initialized with same parameters, they are inverses of each other in regard to the input and output shapes. However, when stride > 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 that output_padding is only used to find output shape, but does not actually add zero-padding 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

• kernel_size (int or tuple) – Size of the convolving kernel

• stride (int or tuple, optional) – Stride of the convolution. Default: 1

• padding (int or tuple, optional) – dilation * (kernel_size - 1) - padding zero-padding will be added to both sides of each dimension in the input. Default: 0

• output_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 is True, 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)
>>> # non-square 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 sliding kernel_size-sized block within the spatial dimensions of input into a column (i.e., last dimension) of a 3-D output 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 and dilation arguments specify how the sliding blocks are retrieved.

• stride controls the stride for the sliding blocks.

• padding controls the amount of implicit zero-paddings on both sides for padding 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 what dilation does.

Parameters
• kernel_size (int or tuple) – the size of the sliding blocks

• 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 or stride 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 4-D input tensors (batched image-like 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(1.9073e-06)


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 of Unfold.) This operation combines these local blocks into the large output tensor of shape $(N, C, \text{output\_size}[0], \text{output\_size}[1], \dots)$ by summing the overlapping values. Similar to Unfold, 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., with stride > 0.

The padding, stride and dilation arguments specify how the sliding blocks are retrieved.

• stride controls the stride for the sliding blocks.

• padding controls the amount of implicit zero-paddings on both sides for padding 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 what dilation does.

Parameters
• output_size (int or tuple) – the shape of the spatial dimensions of the output (i.e., output.sizes()[2:])

• kernel_size (int or tuple) – the size of the sliding blocks

• 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 or stride 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 4-D output tensors (batched image-like 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 non-zero, then the input is implicitly zero-padded on both sides for padding number of points. dilation controls the spacing between the kernel points. It is harder to describe, but this link has a nice visualization of what dilation 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

• 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 for torch.nn.MaxUnpool1d later

• 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

$L_{out} = \left\lfloor \frac{L_{in} + 2 \times \text{padding} - \text{dilation} \times (\text{kernel\_size} - 1) - 1}{\text{stride}} + 1\right\rfloor$

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, kH-1} \max_{n=0, \ldots, kW-1} \\ & \text{input}(N_i, C_j, \text{stride[0]} \times h + m, \text{stride[1]} \times w + n) \end{aligned}

If padding is non-zero, then the input is implicitly zero-padded on both sides for padding number of points. dilation controls the spacing between the kernel points. It is harder to describe, but this link has a nice visualization of what dilation 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 dimension

• a 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

• 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 for torch.nn.MaxUnpool2d later

• 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

$H_{out} = \left\lfloor\frac{H_{in} + 2 * \text{padding[0]} - \text{dilation[0]} \times (\text{kernel\_size[0]} - 1) - 1}{\text{stride[0]}} + 1\right\rfloor$
$W_{out} = \left\lfloor\frac{W_{in} + 2 * \text{padding[1]} - \text{dilation[1]} \times (\text{kernel\_size[1]} - 1) - 1}{\text{stride[1]}} + 1\right\rfloor$

Examples:

>>> # pool of square window of size=3, stride=2
>>> m = nn.MaxPool2d(3, stride=2)
>>> # pool of non-square 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, kD-1} \max_{m=0, \ldots, kH-1} \max_{n=0, \ldots, kW-1} \\ & \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 non-zero, then the input is implicitly zero-padded on both sides for padding number of points. dilation controls the spacing between the kernel points. It is harder to describe, but this link has a nice visualization of what dilation 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 dimension

• a 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

• 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 for torch.nn.MaxUnpool3d later

• ceil_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 non-square 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 non-maximal values are lost.

MaxUnpool1d takes in as input the output of MaxPool1d including the indices of the maximal values and computes a partial inverse in which all non-maximal 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 argument output_size in the forward call. See the Inputs and Example below.

Parameters
• kernel_size (int or tuple) – Size of the max pooling window.

• stride (int or tuple) – Stride of the max pooling window. It is set to kernel_size by default.

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 non-maximal values are lost.

MaxUnpool2d takes in as input the output of MaxPool2d including the indices of the maximal values and computes a partial inverse in which all non-maximal 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 argument output_size in the forward call. See the Inputs and Example below.

Parameters
• kernel_size (int or tuple) – Size of the max pooling window.

• stride (int or tuple) – Stride of the max pooling window. It is set to kernel_size by default.

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 non-maximal values are lost. MaxUnpool3d takes in as input the output of MaxPool3d including the indices of the maximal values and computes a partial inverse in which all non-maximal 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 argument output_size in the forward call. See the Inputs section below.

Parameters
• kernel_size (int or tuple) – Size of the max pooling window.

• stride (int or tuple) – Stride of the max pooling window. It is set to kernel_size by default.

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:

$\text{out}(N_i, C_j, l) = \frac{1}{k} \sum_{m=0}^{k-1} \text{input}(N_i, C_j, \text{stride} \times l + m)$

If padding is non-zero, then the input is implicitly zero-padded on both sides for padding number of points.

The parameters kernel_size, stride, padding can each be an int or a one-element tuple.

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

• count_include_pad – when True, will include the zero-padding 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, divisor_override=None)[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:

$out(N_i, C_j, h, w) = \frac{1}{kH * kW} \sum_{m=0}^{kH-1} \sum_{n=0}^{kW-1} input(N_i, C_j, stride[0] \times h + m, stride[1] \times w + n)$

If padding is non-zero, then the input is implicitly zero-padded on both sides for padding 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 dimension

• a 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

• ceil_mode – when True, will use ceil instead of floor to compute the output shape

• count_include_pad – when True, will include the zero-padding in the averaging calculation

• divisor_override – if specified, it will be used as divisor, otherwise attr:kernel_size will be used

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 non-square 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, divisor_override=None)[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}^{kD-1} \sum_{m=0}^{kH-1} \sum_{n=0}^{kW-1} \\ & \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 non-zero, then the input is implicitly zero-padded on all three sides for padding 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 dimension

• a 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

• ceil_mode – when True, will use ceil instead of floor to compute the output shape

• count_include_pad – when True, will include the zero-padding in the averaging calculation

• divisor_override – if specified, it will be used as divisor, otherwise attr:kernel_size will be used

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 non-square 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 max-pooling 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 to nn.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 power-average 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::
>>> # power-2 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 power-average 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 dimension

• a 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:

>>> # power-2 pool of square window of size=3, stride=2
>>> m = nn.LPPool2d(2, 3, stride=2)
>>> # pool of non-square 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)


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
>>> input = torch.randn(1, 64, 8)
>>> output = m(input)


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, or None 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
>>> input = torch.randn(1, 64, 8, 9)
>>> output = m(input)
>>> # target output size of 7x7 (square)
>>> input = torch.randn(1, 64, 10, 9)
>>> output = m(input)
>>> # target output size of 10x7
>>> input = torch.randn(1, 64, 10, 9)
>>> output = m(input)


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, or None 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
>>> input = torch.randn(1, 64, 8, 9, 10)
>>> output = m(input)
>>> # target output size of 7x7x7 (cube)
>>> 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)


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
>>> input = torch.randn(1, 64, 8)
>>> output = m(input)


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, or None which means the size will be the same as that of the input.

Examples

>>> # target output size of 5x7
>>> input = torch.randn(1, 64, 8, 9)
>>> output = m(input)
>>> # target output size of 7x7 (square)
>>> input = torch.randn(1, 64, 10, 9)
>>> output = m(input)
>>> # target output size of 10x7
>>> input = torch.randn(1, 64, 10, 9)
>>> output = m(input)


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, or None which means the size will be the same as that of the input.

Examples

>>> # target output size of 5x7x9
>>> input = torch.randn(1, 64, 8, 9, 10)
>>> output = m(input)
>>> # target output size of 7x7x7 (cube)
>>> 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)


class torch.nn.ReflectionPad1d(padding)[source]

Pads the input tensor using the reflection of the input boundary.

For N-dimensional 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 2-tuple, 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(input)
tensor([[[3., 2., 1., 0., 1., 2., 3., 2.],
[7., 6., 5., 4., 5., 6., 7., 6.]]])


class torch.nn.ReflectionPad2d(padding)[source]

Pads the input tensor using the reflection of the input boundary.

For N-dimensional 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 4-tuple, 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.]]]])


class torch.nn.ReplicationPad1d(padding)[source]

Pads the input tensor using replication of the input boundary.

For N-dimensional 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 2-tuple, 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(input)
tensor([[[0., 0., 0., 0., 1., 2., 3., 3.],
[4., 4., 4., 4., 5., 6., 7., 7.]]])


class torch.nn.ReplicationPad2d(padding)[source]

Pads the input tensor using replication of the input boundary.

For N-dimensional 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 4-tuple, 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.]]]])


class torch.nn.ReplicationPad3d(padding)[source]

Pads the input tensor using replication of the input boundary.

For N-dimensional 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 6-tuple, 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)


class torch.nn.ZeroPad2d(padding)[source]

Pads the input tensor boundaries with zero.

For N-dimensional 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 4-tuple, 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]]]])


class torch.nn.ConstantPad1d(padding, value)[source]

Pads the input tensor boundaries with a constant value.

For N-dimensional 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 2-tuple, 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]]])
>>> 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]]])


class torch.nn.ConstantPad2d(padding, value)[source]

Pads the input tensor boundaries with a constant value.

For N-dimensional 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 4-tuple, 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]]])


class torch.nn.ConstantPad3d(padding, value)[source]

Pads the input tensor boundaries with a constant value.

For N-dimensional 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 6-tuple, 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

$D_{out} = D_{in} + \text{padding\_front} + \text{padding\_back}$

$H_{out} = H_{in} + \text{padding\_top} + \text{padding\_bottom}$

$W_{out} = W_{in} +$