# 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: data (Tensor) – parameter tensor. requires_grad (bool, optional) – if the parameter requires gradient. See Excluding subgraphs from backward for more details. Default: True

## Containers¶

### Module¶

class torch.nn.Module[source]

Base class for all neural network modules.

Your models should also subclass this class.

Modules can also contain other Modules, allowing to nest them in a tree structure. You can assign the submodules as regular attributes:

import torch.nn as nn
import torch.nn.functional as F

class Model(nn.Module):
def __init__(self):
super(Model, self).__init__()
self.conv1 = nn.Conv2d(1, 20, 5)
self.conv2 = nn.Conv2d(20, 20, 5)

def forward(self, x):
x = F.relu(self.conv1(x))
return F.relu(self.conv2(x))


Submodules assigned in this way will be registered, and will have their parameters converted too when you call .cuda(), 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 parameter (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 self 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)
)

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 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 self Module
double()[source]

Casts all floating point parameters and buffers to double datatype.

Returns: self 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 follow the naming convention of state dict. See _load_from_state_dict on how to use this information in loading.

If new parameters/buffers are added/removed from a module, this number shall be bumped, and the module’s _load_from_state_dict method can compare the version number and do appropriate changes if the state dict is from before the change.

eval()[source]

Sets the module in evaluation mode.

This has any effect only on certain modules. See documentations of particular modules for details of their behaviors in training/evaluation mode, if they are affected, e.g. Dropout, BatchNorm, etc.

extra_repr()[source]

Set the extra representation of the module

To print customized extra information, you should reimplement this method in your own modules. Both single-line and multi-line strings are acceptable.

float()[source]

Casts all floating point parameters and buffers to float datatype.

Returns: self 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 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: state_dict (dict) – a dict containing parameters and persistent buffers. strict (bool, optional) – whether to strictly enforce that the keys in state_dict match the keys returned by this module’s state_dict() function. Default: True
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 (2 -> 2)
(1): Linear (2 -> 2)
)
1 -> Linear (2 -> 2)

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 (2 -> 2)
(1): Linear (2 -> 2)
))
1 -> ('0', Linear (2 -> 2))

named_parameters(memo=None, prefix='')[source]

Returns an iterator over module parameters, yielding both the name of the parameter as well as the parameter itself

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()[source]

Returns an iterator over module parameters.

This is typically passed to an optimizer.

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() torch.utils.hooks.RemovableHandle
register_buffer(name, tensor)[source]

Adds a persistent buffer to the module.

This is typically used to register a buffer that should not to be considered a model parameter. For example, BatchNorm’s running_mean is not a parameter, but is part of the persistent state.

Buffers can be accessed as attributes using given names.

Parameters: name (string) – name of the buffer. The buffer can be accessed from this module using the given name tensor (Tensor) – buffer to be registered.

Example:

>>> self.register_buffer('running_mean', torch.zeros(num_features))

register_forward_hook(hook)[source]

Registers a forward hook on the module.

The hook will be called every time after forward() has computed an output. It should have the following signature:

hook(module, input, output) -> None


The hook should not modify the input or output.

Returns: a handle that can be used to remove the added hook by calling handle.remove() 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


The hook should not modify the input.

Returns: a handle that can be used to remove the added hook by calling handle.remove() 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 parameter (Parameter) – parameter to be added to the module.
state_dict(destination=None, prefix='', keep_vars=False)[source]

Returns a dictionary containing a whole state of the module.

Both parameters and persistent buffers (e.g. running averages) are included. Keys are corresponding parameter and buffer names.

Returns: a dictionary containing a whole state of the module 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)[source]
to(dtype)[source]
to(device, dtype)[source]

It has similar signature as torch.Tensor.to(), but does not take a Tensor and only takes in floating point dtype s. In particular, this method will only cast the floating point parameters and buffers to dtype. It will still move the integral parameters and buffers to device, if that is given. 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 self 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)
Linear(in_features=2, out_features=2, bias=True)
>>> linear.weight
Parameter containing:
tensor([[ 0.1914, -0.3420],
[-0.5112, -0.2324]], dtype=torch.float16, device='cuda:1')
>>> cpu = torch.device("cpu")
>>> linear.to(cpu)
Linear(in_features=2, out_features=2, bias=True)
>>> linear.weight
Parameter containing:
tensor([[ 0.1914, -0.3420],
[-0.5112, -0.2324]], dtype=torch.float16)

train(mode=True)[source]

Sets the module in training mode.

This has any effect only on certain modules. See documentations of particular modules for details of their behaviors in training/evaluation mode, if they are affected, e.g. Dropout, BatchNorm, etc.

Returns: self Module
type(dst_type)[source]

Casts all parameters and buffers to dst_type.

Parameters: dst_type (type or string) – the desired type self 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

### 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

## Convolution layers¶

### Conv1d¶

class torch.nn.Conv1d(in_channels, out_channels, kernel_size, stride=1, padding=0, dilation=1, groups=1, bias=True)[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 $$(N, C_{in}, L)$$ and output $$(N, C_{out}, L_{out})$$ can be precisely described as:

$\begin{equation*} \text{out}(N_i, C_{out_j}) = \text{bias}(C_{out_j}) + \sum_{k = 0}^{C_{in} - 1} \text{weight}(C_{out_j}, k) \star \text{input}(N_i, k) \end{equation*},$

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 $$\left\lfloor \frac{\text{out_channels}}{\text{in_channels}} \right\rfloor$$).

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 configuration when groups == in_channels and out_channels == K * in_channels where K is a positive integer is termed in literature as depthwise convolution.

In other words, for an input of size $$(N, C_{in}, L_{in})$$, if you want a depthwise convolution with a depthwise multiplier K, then you use the constructor arguments $$(\text{in_channels}=C_{in}, \text{out_channels}=C_{in} * K, ..., \text{groups}=C_{in})$$

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 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

$L_{out} = \left\lfloor\frac{L_{in} + 2 * \text{padding} - \text{dilation} * (\text{kernel_size} - 1) - 1}{\text{stride}} + 1\right\rfloor$
Variables: weight (Tensor) – the learnable weights of the module of shape (out_channels, in_channels, kernel_size) bias (Tensor) – the learnable bias of the module of shape (out_channels)

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)[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 $$(N, C_{in}, H, W)$$ and output $$(N, C_{out}, H_{out}, W_{out})$$ can be precisely described as:

$\begin{equation*} \text{out}(N_i, C_{out_j}) = \text{bias}(C_{out_j}) + \sum_{k = 0}^{C_{in} - 1} \text{weight}(C_{out_j}, k) \star \text{input}(N_i, k) \end{equation*},$

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 $$\left\lfloor\frac{\text{out_channels}}{\text{in_channels}}\right\rfloor$$).

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

The configuration when groups == in_channels and out_channels == K * in_channels where K is a positive integer is termed in literature as depthwise convolution.

In other words, for an input of size $$(N, C_{in}, H_{in}, W_{in})$$, if you want a depthwise convolution with a depthwise multiplier K, then you use the constructor arguments $$(\text{in_channels}=C_{in}, \text{out_channels}=C_{in} * K, ..., \text{groups}=C_{in})$$

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 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

\begin{align}\begin{aligned}H_{out} = \left\lfloor\frac{H_{in} + 2 * \text{padding}[0] - \text{dilation}[0] * (\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] * (\text{kernel_size}[1] - 1) - 1}{\text{stride}[1]} + 1\right\rfloor\end{aligned}\end{align}
Variables: weight (Tensor) – the learnable weights of the module of shape (out_channels, in_channels, kernel_size[0], kernel_size[1]) bias (Tensor) – the learnable bias of the module of shape (out_channels)

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)[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:

$\begin{equation*} \text{out}(N_i, C_{out_j}) = \text{bias}(C_{out_j}) + \sum_{k = 0}^{C_{in} - 1} \text{weight}(C_{out_j}, k) \star \text{input}(N_i, k) \end{equation*},$

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 $$\left\lfloor\frac{\text{out_channels}}{\text{in_channels}}\right\rfloor$$).

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

The configuration when groups == in_channels and out_channels == K * in_channels where K is a positive integer is termed in literature as depthwise convolution.

In other words, for an input of size $$(N, C_{in}, D_{in}, H_{in}, W_{in})$$, if you want a depthwise convolution with a depthwise multiplier K, then you use the constructor arguments $$(\text{in_channels}=C_{in}, \text{out_channels}=C_{in} * K, ..., \text{groups}=C_{in})$$

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 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

\begin{align}\begin{aligned}D_{out} = \left\lfloor\frac{D_{in} + 2 * \text{padding}[0] - \text{dilation}[0] * (\text{kernel_size}[0] - 1) - 1}{\text{stride}[0]} + 1\right\rfloor\\H_{out} = \left\lfloor\frac{H_{in} + 2 * \text{padding}[1] - \text{dilation}[1] * (\text{kernel_size}[1] - 1) - 1}{\text{stride}[1]} + 1\right\rfloor\\W_{out} = \left\lfloor\frac{W_{in} + 2 * \text{padding}[2] - \text{dilation}[2] * (\text{kernel_size}[2] - 1) - 1}{\text{stride}[2]} + 1\right\rfloor\end{aligned}\end{align}
Variables: weight (Tensor) – the learnable weights of the module of shape (out_channels, in_channels, kernel_size[0], kernel_size[1], kernel_size[2]) bias (Tensor) – the learnable bias of the module of shape (out_channels)

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)[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 padding number of points.

• output_padding controls the amount of implicit zero-paddings on both sides of the output for output_padding number of points. 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 $$\left\lfloor\frac{\text{out_channels}}{\text{in_channels}}\right\rfloor$$).

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 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 :attrstride >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.

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) – 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

$L_{out} = (L_{in} - 1) * \text{stride} - 2 * \text{padding} + \text{kernel_size} + \text{output_padding}$
Variables: weight (Tensor) – the learnable weights of the module of shape (in_channels, out_channels, kernel_size[0], kernel_size[1]) bias (Tensor) – the learnable bias of the module of shape (out_channels)

### ConvTranspose2d¶

class torch.nn.ConvTranspose2d(in_channels, out_channels, kernel_size, stride=1, padding=0, output_padding=0, groups=1, bias=True, dilation=1)[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 padding number of points for each dimension.

• output_padding controls the amount of implicit zero-paddings on both sides of the output for output_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 $$\left\lfloor\frac{\text{out_channels}}{\text{in_channels}}\right\rfloor$$).

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 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 :attrstride >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.

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) – 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

\begin{align}\begin{aligned}H_{out} = (H_{in} - 1) * \text{stride}[0] - 2 * \text{padding}[0] + \text{kernel_size}[0] + \text{output_padding}[0]\\W_{out} = (W_{in} - 1) * \text{stride}[1] - 2 * \text{padding}[1] + \text{kernel_size}[1] + \text{output_padding}[1]\end{aligned}\end{align}
Variables: weight (Tensor) – the learnable weights of the module of shape (in_channels, out_channels, kernel_size[0], kernel_size[1]) bias (Tensor) – the learnable bias of the module of shape (out_channels)

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)[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 padding number of points for each dimension.

• output_padding controls the amount of implicit zero-paddings on both sides of the output for output_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 $$\left\lfloor\frac{\text{out_channels}}{\text{in_channels}}\right\rfloor$$).

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 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 :attrstride >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.

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) – 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

\begin{align}\begin{aligned}D_{out} = (D_{in} - 1) * \text{stride}[0] - 2 * \text{padding}[0] + \text{kernel_size}[0] + \text{output_padding}[0]\\H_{out} = (H_{in} - 1) * \text{stride}[1] - 2 * \text{padding}[1] + \text{kernel_size}[1] + \text{output_padding}[1]\\W_{out} = (W_{in} - 1) * \text{stride}[2] - 2 * \text{padding}[2] + \text{kernel_size}[2] + \text{output_padding}[2]\end{aligned}\end{align}
Variables: weight (Tensor) – the learnable weights of the module of shape (in_channels, out_channels, kernel_size[0], kernel_size[1], kernel_size[2]) bias (Tensor) – the learnable bias of the module of shape (out_channels)

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.Conv3d(16, 33, (3, 5, 2), stride=(2, 1, 1), padding=(0, 4, 2))
>>> input = torch.randn(20, 16, 10, 50, 100)
>>> output = m(input)


## 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:

$\begin{equation*} \text{out}(N_i, C_j, k) = \max_{m=0, \ldots, \text{kernel_size}-1} \text{input}(N_i, C_j, \text{stride} * k + m) \end{equation*}$

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 padding – implicit zero padding to be added on both sides dilation – a parameter that controls the stride of elements in the window return_indices – if True, will return the max indices along with the outputs. Useful when Unpooling 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

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

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:

$\begin{equation*} \text{out}(N_i, C_j, h, w) = \max_{m=0, \ldots, kH-1} \max_{n=0, \ldots, kW-1} \text{input}(N_i, C_j, \text{stride}[0] * h + m, \text{stride}[1] * w + n) \end{equation*}$

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 padding – implicit zero padding to be added on both sides dilation – a parameter that controls the stride of elements in the window return_indices – if True, will return the max indices along with the outputs. Useful when Unpooling 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

\begin{align}\begin{aligned}H_{out} = \left\lfloor\frac{H_{in} + 2 * \text{padding}[0] - \text{dilation}[0] * (\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] * (\text{kernel_size}[1] - 1) - 1}{\text{stride}[1]} + 1\right\rfloor\end{aligned}\end{align}

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{split}\begin{align*} \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] * k + d,\\ &\text{stride}[1] * h + m, \text{stride}[2] * w + n) \end{align*}\end{split}

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 padding – implicit zero padding to be added on all three sides dilation – a parameter that controls the stride of elements in the window return_indices – if True, will return the max indices along with the outputs. Useful when Unpooling 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

\begin{align}\begin{aligned}D_{out} = \left\lfloor\frac{D_{in} + 2 * \text{padding}[0] - \text{dilation}[0] * (\text{kernel_size}[0] - 1) - 1}{\text{stride}[0]} + 1\right\rfloor\\H_{out} = \left\lfloor\frac{H_{in} + 2 * \text{padding}[1] - \text{dilation}[1] * (\text{kernel_size}[1] - 1) - 1}{\text{stride}[1]} + 1\right\rfloor\\W_{out} = \left\lfloor\frac{W_{in} + 2 * \text{padding}[2] - \text{dilation}[2] * (\text{kernel_size}[2] - 1) - 1}{\text{stride}[2]} + 1\right\rfloor\end{aligned}\end{align}

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. padding (int or tuple) – Padding that was added to the input
Inputs:
• input: the input Tensor to invert
• indices: the indices given out by MaxPool1d
• output_size (optional) : a torch.Size that specifies the targeted output size
Shape:
• Input: $$(N, C, H_{in})$$

• Output: $$(N, C, H_{out})$$ where

$H_{out} = (H_{in} - 1) * \text{stride}[0] - 2 * \text{padding}[0] + \text{kernel_size}[0]$

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. padding (int or tuple) – Padding that was added to the input
Inputs:
• input: the input Tensor to invert
• indices: the indices given out by MaxPool2d
• output_size (optional) : a torch.Size that specifies the targeted output size
Shape:
• Input: $$(N, C, H_{in}, W_{in})$$

• Output: $$(N, C, H_{out}, W_{out})$$ where

\begin{align}\begin{aligned}H_{out} = (H_{in} - 1) * \text{stride}[0] - 2 * \text{padding}[0] + \text{kernel_size}[0]\\W_{out} = (W_{in} - 1) * \text{stride}[1] - 2 * \text{padding}[1] + \text{kernel_size}[1]\end{aligned}\end{align}

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. padding (int or tuple) – Padding that was added to the input
Inputs:
• input: the input Tensor to invert
• indices: the indices given out by MaxPool3d
• output_size (optional) : a torch.Size that specifies the targeted output size
Shape:
• Input: $$(N, C, D_{in}, H_{in}, W_{in})$$

• Output: $$(N, C, D_{out}, H_{out}, W_{out})$$ where

\begin{align}\begin{aligned}D_{out} = (D_{in} - 1) * \text{stride}[0] - 2 * \text{padding}[0] + \text{kernel_size}[0]\\H_{out} = (H_{in} - 1) * \text{stride}[1] - 2 * \text{padding}[1] + \text{kernel_size}[1]\\W_{out} = (W_{in} - 1) * \text{stride}[2] - 2 * \text{padding}[2] + \text{kernel_size}[2]\end{aligned}\end{align}

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:

$\begin{equation*} \text{out}(N_i, C_j, l) = \frac{1}{k} \sum_{m=0}^{k} \text{input}(N_i, C_j, \text{stride} * l + m) \end{equation*}$

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 padding – implicit zero padding to be added on both sides ceil_mode – when True, will use ceil instead of floor to compute the output shape count_include_pad – when True, will include the zero-padding in the averaging calculation
Shape:
• Input: $$(N, C, L_{in})$$

• Output: $$(N, C, L_{out})$$ where

$L_{out} = \left\lfloor \frac{L_{in} + 2 * \text{padding} - \text{kernel_size}}{\text{stride}} + 1\right\rfloor$

Examples:

>>> # pool with window of size=3, stride=2
>>> m = nn.AvgPool1d(3, stride=2)
>>> m(torch.tensor([[[1.,2,3,4,5,6,7]]]))
tensor([[[ 2.,  4.,  6.]]])


### AvgPool2d¶

class torch.nn.AvgPool2d(kernel_size, stride=None, padding=0, ceil_mode=False, count_include_pad=True)[source]

Applies a 2D average pooling over an input signal composed of several input planes.

In the simplest case, the output value of the layer with input size $$(N, C, H, W)$$, output $$(N, C, H_{out}, W_{out})$$ and kernel_size $$(kH, kW)$$ can be precisely described as:

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

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 padding – implicit zero padding to be added on both sides ceil_mode – when True, will use ceil instead of floor to compute the output shape count_include_pad – when True, will include the zero-padding in the averaging calculation
Shape:
• Input: $$(N, C, H_{in}, W_{in})$$

• Output: $$(N, C, H_{out}, W_{out})$$ where

\begin{align}\begin{aligned}H_{out} = \left\lfloor\frac{H_{in} + 2 * \text{padding}[0] - \text{kernel_size}[0]}{\text{stride}[0]} + 1\right\rfloor\\W_{out} = \left\lfloor\frac{W_{in} + 2 * \text{padding}[1] - \text{kernel_size}[1]}{\text{stride}[1]} + 1\right\rfloor\end{aligned}\end{align}

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)[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:

$\begin{equation*} \text{out}(N_i, C_j, d, h, w) = \sum_{k=0}^{kD-1} \sum_{m=0}^{kH-1} \sum_{n=0}^{kW-1} \frac{\text{input}(N_i, C_j, \text{stride}[0] * d + k, \text{stride}[1] * h + m, \text{stride}[2] * w + n)} {kD * kH * kW} \end{equation*}$

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 padding – implicit zero padding to be added on all three sides ceil_mode – when True, will use ceil instead of floor to compute the output shape count_include_pad – when True, will include the zero-padding in the averaging calculation
Shape:
• Input: $$(N, C, D_{in}, H_{in}, W_{in})$$

• Output: $$(N, C, D_{out}, H_{out}, W_{out})$$ where

\begin{align}\begin{aligned}D_{out} = \left\lfloor\frac{D_{in} + 2 * \text{padding}[0] - \text{kernel_size}[0]}{\text{stride}[0]} + 1\right\rfloor\\H_{out} = \left\lfloor\frac{H_{in} + 2 * \text{padding}[1] - \text{kernel_size}[1]}{\text{stride}[1]} + 1\right\rfloor\\W_{out} = \left\lfloor\frac{W_{in} + 2 * \text{padding}[2] - \text{kernel_size}[2]}{\text{stride}[2]} + 1\right\rfloor\end{aligned}\end{align}

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 $$kHxkW$$ 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 x 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 = infinity, one gets Max Pooling
• At p = 1, one gets Sum Pooling (which is proportional to Average Pooling)
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

$L_{out} = \left\lfloor\frac{L_{in} + 2 * \text{padding} - \text{kernel_size}}{\text{stride}} + 1\right\rfloor$
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
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

\begin{align}\begin{aligned}H_{out} = \left\lfloor\frac{H_{in} + 2 * \text{padding}[0] - \text{dilation}[0] * (\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] * (\text{kernel_size}[1] - 1) - 1}{\text{stride}[1]} + 1\right\rfloor\end{aligned}\end{align}

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
>>> m = nn.AdaptiveMaxPool1d(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
>>> m = nn.AdaptiveMaxPool2d((5,7))
>>> input = torch.randn(1, 64, 8, 9)
>>> output = m(input)
>>> # target output size of 7x7 (square)
>>> m = nn.AdaptiveMaxPool2d(7)
>>> input = torch.randn(1, 64, 10, 9)
>>> output = m(input)
>>> # target output size of 10x7
>>> m = nn.AdaptiveMaxPool2d((None, 7))
>>> input = torch.randn(1, 64, 10, 9)
>>> output = m(input)


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
>>> m = nn.AdaptiveMaxPool3d((5,7,9))
>>> input = torch.randn(1, 64, 8, 9, 10)
>>> output = m(input)
>>> # target output size of 7x7x7 (cube)
>>> m = nn.AdaptiveMaxPool3d(7)
>>> input = torch.randn(1, 64, 10, 9, 8)
>>> output = m(input)
>>> # target output size of 7x9x8
>>> m = nn.AdaptiveMaxPool3d((7, None, None))
>>> input = torch.randn(1, 64, 10, 9, 8)
>>> output = m(input)


class torch.nn.AdaptiveAvgPool1d(output_size)[source]

Applies a 1D adaptive average pooling over an input signal composed of several input planes.

The output size is H, for any input size. The number of output features is equal to the number of input planes.

Parameters: output_size – the target output size H

Examples

>>> # target output size of 5
>>> m = nn.AdaptiveAvgPool1d(5)
>>> input = torch.randn(1, 64, 8)
>>> output = m(input)


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
>>> m = nn.AdaptiveAvgPool2d((5,7))
>>> input = torch.randn(1, 64, 8, 9)
>>> output = m(input)
>>> # target output size of 7x7 (square)
>>> m = nn.AdaptiveAvgPool2d(7)
>>> input = torch.randn(1, 64, 10, 9)
>>> output = m(input)
>>> # target output size of 10x7
>>> m = nn.AdaptiveMaxPool2d((None, 7))
>>> input = torch.randn(1, 64, 10, 9)
>>> output = m(input)


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
>>> m = nn.AdaptiveAvgPool3d((5,7,9))
>>> input = torch.randn(1, 64, 8, 9, 10)
>>> output = m(input)
>>> # target output size of 7x7x7 (cube)
>>> m = nn.AdaptiveAvgPool3d(7)
>>> input = torch.randn(1, 64, 10, 9, 8)
>>> output = m(input)
>>> # target output size of 7x9x8
>>> m = nn.AdaptiveMaxPool3d((7, None, None))
>>> input = torch.randn(1, 64, 10, 9, 8)
>>> output = m(input)


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

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

For Nd-padding, use :func: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 (paddingLeft, paddingRight)
Shape:
• Input: $$(N, C, W_{in})$$
• Output: $$(N, C, W_{out})$$ where $$W_{out} = W_{in} + \textit{paddingLeft} + \textit{paddingRight}$$

Examples:

>>> m = nn.ReflectionPad1d(2)
>>> input = torch.arange(8).reshape(1, 2, 4)
>>> input

(0 ,.,.) =
0  1  2  3
4  5  6  7
[torch.FloatTensor of size (1,2,4)]

>>> m(input)

(0 ,.,.) =
2   1   0   1   2   3   2   1
6   5   4   5   6   7   6   5
[torch.FloatTensor of size (1,2,8)]

>>> # using different paddings
>>> m = nn.ReflectionPad1d((3, 1))
>>> m(input)

(0 ,.,.) =
3   2   1   0   1   2   3   2
7   6   5   4   5   6   7   6
[torch.FloatTensor of size (1,2,8)]


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

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

For Nd-padding, use :func: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 (paddingLeft, paddingRight, paddingTop, paddingBottom)
Shape:
• Input: $$(N, C, H_{in}, W_{in})$$
• Output: $$(N, C, H_{out}, W_{out})$$ where $$H_{out} = H_{in} + \textit{paddingTop} + \textit{paddingBottom}$$ $$W_{out} = W_{in} + \textit{paddingLeft} + \textit{paddingRight}$$

Examples:

>>> m = nn.ReflectionPad2d(2)
>>> input = torch.arange(9).reshape(1, 1, 3, 3)
>>> input

(0 ,0 ,.,.) =
0  1  2
3  4  5
6  7  8
[torch.FloatTensor of size (1,1,3,3)]

>>> m(input)

(0 ,0 ,.,.) =
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
[torch.FloatTensor of size (1,1,7,7)]

>>> # using different paddings
>>> m = nn.ReflectionPad2d((1, 1, 2, 0))
>>> m(input)

(0 ,0 ,.,.) =
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
[torch.FloatTensor of size (1,1,5,5)]


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

Pads the input tensor using replication of the input boundary.

For Nd-padding, use :func: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 (paddingLeft, paddingRight)
Shape:
• Input: $$(N, C, W_{in})$$
• Output: $$(N, C, W_{out})$$ where $$W_{out} = W_{in} + \textit{paddingLeft} + \textit{paddingRight}$$

Examples:

>>> m = nn.ReplicationPad1d(2)
>>> input = torch.arange(8).reshape(1, 2, 4)
>>> input

(0 ,.,.) =
0  1  2  3
4  5  6  7
[torch.FloatTensor of size (1,2,4)]

>>> m(input)

(0 ,.,.) =
0   0   0   1   2   3   3   3
4   4   4   5   6   7   7   7
[torch.FloatTensor of size (1,2,8)]

>>> # using different paddings
>>> m = nn.ReplicationPad1d((3, 1))
>>> m(input)

(0 ,.,.) =
0   0   0   0   1   2   3   3
4   4   4   4   5   6   7   7
[torch.FloatTensor of size (1,2,8)]


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

Pads the input tensor using replication of the input boundary.

For Nd-padding, use :func: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 (paddingLeft, paddingRight, paddingTop, paddingBottom)
Shape:
• Input: $$(N, C, H_{in}, W_{in})$$
• Output: $$(N, C, H_{out}, W_{out})$$ where $$H_{out} = H_{in} + \textit{paddingTop} + \textit{paddingBottom}$$ $$W_{out} = W_{in} + \textit{paddingLeft} + \textit{paddingRight}$$

Examples:

>>> m = nn.ReplicationPad2d(2)
>>> input = torch.arange(9).reshape(1, 1, 3, 3)
>>> input

(0 ,0 ,.,.) =
0  1  2
3  4  5
6  7  8
[torch.FloatTensor of size (1,1,3,3)]

>>> m(input)

(0 ,0 ,.,.) =
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
[torch.FloatTensor of size (1,1,7,7)]

>>> # using different paddings
>>> m = nn.ReplicationPad2d((1, 1, 2, 0))
>>> m(input)

(0 ,0 ,.,.) =
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
[torch.FloatTensor of size (1,1,5,5)]


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

Pads the input tensor using replication of the input boundary.

For Nd-padding, use :func: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 (paddingLeft, paddingRight, paddingTop, paddingBottom, paddingFront, paddingBack)
Shape:
• Input: $$(N, C, D_{in}, H_{in}, W_{in})$$
• Output: $$(N, C, D_{out}, H_{out}, W_{out})$$ where $$D_{out} = D_{in} + \textit{paddingFront} + \textit{paddingBack}$$ $$H_{out} = H_{in} + \textit{paddingTop} + \textit{paddingBottom}$$ $$W_{out} = W_{in} + \textit{paddingLeft} + \textit{paddingRight}$$

Examples:

>>> m = nn.ReplicationPad3d(3)
>>> input = torch.randn(16, 3, 8, 320, 480)
>>> output = m(input)
>>> # using different paddings
>>> 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 Nd-padding, use :func: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 (paddingLeft, paddingRight, paddingTop, paddingBottom)
Shape:
• Input: $$(N, C, H_{in}, W_{in})$$
• Output: $$(N, C, H_{out}, W_{out})$$ where $$H_{out} = H_{in} + \textit{paddingTop} + \textit{paddingBottom}$$ $$W_{out} = W_{in} + \textit{paddingLeft} + \textit{paddingRight}$$

Examples:

>>> m = nn.ZeroPad2d(2)
>>> input = torch.randn(1, 1, 3, 3)
>>> input

(0 ,0 ,.,.) =
1.4418 -1.9812 -0.3815
-0.3828 -0.6833 -0.2376
0.1433  0.0211  0.4311
[torch.FloatTensor of size (1,1,3,3)]

>>> m(input)

(0 ,0 ,.,.) =
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  1.4418 -1.9812 -0.3815  0.0000  0.0000
0.0000  0.0000 -0.3828 -0.6833 -0.2376  0.0000  0.0000
0.0000  0.0000  0.1433  0.0211  0.4311  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
[torch.FloatTensor of size (1,1,7,7)]

>>> # using different paddings
>>> m = nn.ZeroPad2d((1, 1, 2, 0))
>>> m(input)

(0 ,0 ,.,.) =
0.0000  0.0000  0.0000  0.0000  0.0000
0.0000  0.0000  0.0000  0.0000  0.0000
0.0000  1.4418 -1.9812 -0.3815  0.0000
0.0000 -0.3828 -0.6833 -0.2376  0.0000
0.0000  0.1433  0.0211  0.4311  0.0000
[torch.FloatTensor of size (1,1,5,5)]


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

Pads the input tensor boundaries with a constant value.

For Nd-padding, use :func: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 (paddingLeft, paddingRight)
Shape:
• Input: $$(N, C, W_{in})$$
• Output: $$(N, C, W_{out})$$ where $$W_{out} = W_{in} + \textit{paddingLeft} + \textit{paddingRight}$$

Examples:

>>> m = nn.ConstantPad1d(2, 3.5)
>>> input = torch.randn(1, 2, 4)
>>> input

(0 ,.,.) =
0.1875  0.5046 -1.0074  2.0005
-0.3540 -1.8645  1.1530  0.0632
[torch.FloatTensor of size (1,2,4)]

>>> m(input)

(0 ,.,.) =
3.5000  3.5000  0.1875  0.5046 -1.0074  2.0005  3.5000  3.5000
3.5000  3.5000 -0.3540 -1.8645  1.1530  0.0632  3.5000  3.5000
[torch.FloatTensor of size (1,2,8)]

>>> # using different paddings
>>> m = nn.ConstantPad1d((3, 1), 3.5)
>>> m(input)

(0 ,.,.) =
3.5000  3.5000  3.5000  0.1875  0.5046 -1.0074  2.0005  3.5000
3.5000  3.5000  3.5000 -0.3540 -1.8645  1.1530  0.0632  3.5000
[torch.FloatTensor of size (1,2,8)]


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

Pads the input tensor boundaries with a constant value.

For Nd-padding, use :func: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 (paddingLeft, paddingRight, paddingTop, paddingBottom)
Shape:
• Input: $$(N, C, H_{in}, W_{in})$$
• Output: $$(N, C, H_{out}, W_{out})$$ where $$H_{out} = H_{in} + \textit{paddingTop} + \textit{paddingBottom}$$ $$W_{out} = W_{in} + \textit{paddingLeft} + \textit{paddingRight}$$

Examples:

>>> m = nn.ConstantPad2d(2, 3.5)
>>> input = torch.randn(1, 2, 2)
>>> input

(0 ,.,.) =
-0.2295 -0.9774
-0.3335 -1.4178
[torch.FloatTensor of size (1,2,2)]

>>> m(input)

(0 ,.,.) =
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 -0.2295 -0.9774  3.5000  3.5000
3.5000  3.5000 -0.3335 -1.4178  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
[torch.FloatTensor of size (1,6,6)]

>>> # using different paddings
>>> m = nn.ConstantPad2d((3, 0, 2, 1), 3.5)
>>> m(input)

(0 ,.,.) =
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 -0.2295 -0.9774
3.5000  3.5000  3.5000 -0.3335 -1.4178
3.5000  3.5000  3.5000  3.5000  3.5000
[torch.FloatTensor of size (1,5,5)]


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

Pads the input tensor boundaries with a constant value.

For Nd-padding, use :func: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 (paddingLeft, paddingRight, paddingTop, paddingBottom, paddingFront, paddingBack)
Shape:
• Input: $$(N, C, D_{in}, H_{in}, W_{in})$$
• Output: $$(N, C, D_{out}, H_{out}, W_{out})$$ where $$D_{out} = D_{in} + \textit{paddingFront} + \textit{paddingBack}$$ $$H_{out} = H_{in} + \textit{paddingTop} + \textit{paddingBottom}$$ $$W_{out} = W_{in} + \textit{paddingLeft} + \textit{paddingRight}$$

Examples:

>>> m = nn.ConstantPad3d(3, 3.5)
>>> input = torch.randn(16, 3, 10, 20, 30)
>>> output = m(input)
>>> # using different paddings
>>> m = nn.ConstantPad3d((3, 3, 6, 6, 0, 1), 3.5)
>>> output = m(input)


## Non-linear activations (weighted sum, nonlinearity)¶

### ELU¶

class torch.nn.ELU(alpha=1.0, inplace=False)[source]

Applies element-wise, $$\text{ELU}(x) = \max(0,x) + \min(0, \alpha * (\exp(x) - 1))$$

Parameters: alpha – the $$\alpha$$ value for the ELU formulation. Default: 1.0 inplace – can optionally do the operation in-place. Default: False
Shape:
• Input: $$(N, *)$$ where * means, any number of additional dimensions
• Output: $$(N, *)$$, same shape as the input

Examples:

>>> m = nn.ELU()
>>> input = torch.randn(2)
>>> output = m(input)


### Hardshrink¶

class torch.nn.Hardshrink(lambd=0.5)[source]

Applies the hard shrinkage function element-wise Hardshrink is defined as:

$\begin{split}\text{HardShrink}(x) = \begin{cases} x, & \text{ if } x > \lambda \\ x, & \text{ if } x < -\lambda \\ 0, & \text{ otherwise } \end{cases}\end{split}$
Parameters: lambd – the $$\lambda$$ value for the Hardshrink formulation. Default: 0.5
Shape:
• Input: $$(N, *)$$ where * means, any number of additional dimensions
• Output: $$(N, *)$$, same shape as the input

Examples:

>>> m = nn.Hardshrink()
>>> input = torch.randn(2)
>>> output = m(input)


### Hardtanh¶

class torch.nn.Hardtanh(min_val=-1, max_val=1, inplace=False, min_value=None, max_value=None)[source]

Applies the HardTanh function element-wise

HardTanh is defined as:

$\begin{split}\text{HardTanh}(x) = \begin{cases} 1 & \text{ if } x > 1 \\ -1 & \text{ if } x < -1 \\ x & \text{ otherwise } \\ \end{cases}\end{split}$

The range of the linear region $$[-1, 1]$$ can be adjusted using min_val and max_val.

Parameters: min_val – minimum value of the linear region range. Default: -1 max_val – maximum value of the linear region range. Default: 1 inplace – can optionally do the operation in-place. Default: False

Keyword arguments min_value and max_value have been deprecated in favor of min_val and max_val.

Shape:
• Input: $$(N, *)$$ where * means, any number of additional dimensions
• Output: $$(N, *)$$, same shape as the input

Examples:

>>> m = nn.Hardtanh(-2, 2)
>>> input = torch.randn(2)
>>> output = m(input)


### LeakyReLU¶

class torch.nn.LeakyReLU(negative_slope=0.01, inplace=False)[source]

Applies element-wise, $$\text{LeakyReLU}(x) = \max(0, x) + \text{negative_slope} * \min(0, x)$$ or

$\begin{split}\text{LeakyRELU}(x) = \begin{cases} x, & \text{ if } x \geq 0 \\ \text{negative_slope} \times x, & \text{ otherwise } \end{cases}\end{split}$
Parameters: negative_slope – Controls the angle of the negative slope. Default: 1e-2 inplace – can optionally do the operation in-place. Default: False
Shape:
• Input: $$(N, *)$$ where * means, any number of additional dimensions
• Output: $$(N, *)$$, same shape as the input

Examples:

>>> m = nn.LeakyReLU(0.1)
>>> input = torch.randn(2)
>>> output = m(input)


### LogSigmoid¶

class torch.nn.LogSigmoid[source]

Applies element-wise $$\text{LogSigmoid}(x) = \log\left(\frac{ 1 }{ 1 + \exp(-x)}\right)$$

Shape:
• Input: $$(N, *)$$ where * means, any number of additional dimensions
• Output: $$(N, *)$$, same shape as the input

Examples:

>>> m = nn.LogSigmoid()
>>> input = torch.randn(2)
>>> output = m(input)


### PReLU¶

class torch.nn.PReLU(num_parameters=1, init=0.25)[source]

Applies element-wise the function $$\text{PReLU}(x) = \max(0,x) + a * \min(0,x)$$ or

$\begin{split}\text{PReLU}(x) = \begin{cases} x, & \text{ if } x \geq 0 \\ ax, & \text{ otherwise } \end{cases}\end{split}$

Here $$a$$ is a learnable parameter. When called without arguments, nn.PReLU() uses a single parameter $$a$$ across all input channels. If called with nn.PReLU(nChannels), a separate $$a$$ is used for each input channel.

Note

weight decay should not be used when learning $$a$$ for good performance.

Parameters: num_parameters – number of $$a$$ to learn. Default: 1 init – the initial value of $$a$$. Default: 0.25
Shape:
• Input: $$(N, *)$$ where * means, any number of additional dimensions
• Output: $$(N, *)$$, same shape as the input

Examples:

>>> m = nn.PReLU()
>>> input = torch.randn(2)
>>> output = m(input)


### ReLU¶

class torch.nn.ReLU(inplace=False)[source]

Applies the rectified linear unit function element-wise $$\text{ReLU}(x)= \max(0, x)$$

Parameters: inplace – can optionally do the operation in-place. Default: False
Shape:
• Input: $$(N, *)$$ where * means, any number of additional dimensions
• Output: $$(N, *)$$, same shape as the input

Examples:

>>> m = nn.ReLU()
>>> input = torch.randn(2)
>>> output = m(input)


### ReLU6¶

class torch.nn.ReLU6(inplace=False)[source]

Applies the element-wise function $$\text{ReLU6}(x) = \min(\max(0,x), 6)$$

Parameters: inplace – can optionally do the operation in-place. Default: False
Shape:
• Input: $$(N, *)$$ where * means, any number of additional dimensions
• Output: $$(N, *)$$, same shape as the input

Examples:

>>> m = nn.ReLU6()
>>> input = torch.randn(2)
>>> output = m(input)


### RReLU¶

class torch.nn.RReLU(lower=0.125, upper=0.3333333333333333, inplace=False)[source]

Applies the randomized leaky rectified liner unit function element-wise described in the paper Empirical Evaluation of Rectified Activations in Convolutional Network.

The function is defined as:

$\begin{split}\text{RReLU}(x) = \begin{cases} x & \text{if } x \geq 0 \\ ax & \text{ otherwise } \end{cases},\end{split}$

where $$a$$ is randomly sampled from uniform distribution $$\mathcal{U}(\text{lower}, \text{upper})$$.

Parameters: lower – lower bound of the uniform distribution. Default: $$\frac{1}{8}$$ upper – upper bound of the uniform distribution. Default: $$\frac{1}{3}$$ inplace – can optionally do the operation in-place. Default: False
Shape:
• Input: $$(N, *)$$ where * means, any number of additional dimensions
• Output: $$(N, *)$$, same shape as the input

Examples:

>>> m = nn.RReLU(0.1, 0.3)
>>> input = torch.randn(2)
>>> output = m(input)


### SELU¶

class torch.nn.SELU(inplace=False)[source]

Applies element-wise, $$\text{SELU}(x) = \text{scale} * (\max(0,x) + \min(0, \alpha * (\exp(x) - 1)))$$, with $$\alpha = 1.6732632423543772848170429916717$$ and $$\text{scale} = 1.0507009873554804934193349852946$$.

More details can be found in the paper Self-Normalizing Neural Networks .

Parameters: inplace (bool, optional) – can optionally do the operation in-place. Default: False
Shape:
• Input: $$(N, *)$$ where * means, any number of additional dimensions
• Output: $$(N, *)$$, same shape as the input

Examples:

>>> m = nn.SELU()
>>> input = torch.randn(2)
>>> output = m(input)


### Sigmoid¶

class torch.nn.Sigmoid[source]

Applies the element-wise function $$\text{Sigmoid}(x) = \frac{1}{1 + \exp(-x)}$$

Shape:
• Input: $$(N, *)$$ where * means, any number of additional dimensions
• Output: $$(N, *)$$, same shape as the input

Examples:

>>> m = nn.Sigmoid()
>>> input = torch.randn(2)
>>> output = m(input)


### Softplus¶

class torch.nn.Softplus(beta=1, threshold=20)[source]

Applies element-wise $$\text{Softplus}(x) = \frac{1}{\beta} * \log(1 + \exp(\beta * x))$$

SoftPlus is a smooth approximation to the ReLU function and can be used to constrain the output of a machine to always be positive.

For numerical stability the implementation reverts to the linear function for inputs above a certain value.

Parameters: beta – the $$\beta$$ value for the Softplus formulation. Default: 1 threshold – values above this revert to a linear function. Default: 20
Shape:
• Input: $$(N, *)$$ where * means, any number of additional dimensions
• Output: $$(N, *)$$, same shape as the input

Examples:

>>> m = nn.Softplus()
>>> input = torch.randn(2)
>>> output = m(input)


### Softshrink¶

class torch.nn.Softshrink(lambd=0.5)[source]

Applies the soft shrinkage function elementwise

SoftShrinkage function is defined as:

$\begin{split}\text{SoftShrinkage}(x) = \begin{cases} x - \lambda, & \text{ if } x > \lambda \\ x + \lambda, & \text{ if } x < -\lambda \\ 0, & \text{ otherwise } \end{cases}\end{split}$
Parameters: lambd – the $$\lambda$$ value for the Softshrink formulation. Default: 0.5
Shape:
• Input: $$(N, *)$$ where * means, any number of additional dimensions
• Output: $$(N, *)$$, same shape as the input

Examples:

>>> m = nn.Softshrink()
>>> input = torch.randn(2)
>>> output = m(input)


### Softsign¶

class torch.nn.Softsign[source]

Applies element-wise, the function $$\text{SoftSign}(x) = \frac{x}{ 1 + |x|}$$

Shape:
• Input: $$(N, *)$$ where * means, any number of additional dimensions
• Output: $$(N, *)$$, same shape as the input

Examples:

>>> m = nn.Softsign()
>>> input = torch.randn(2)
>>> output = m(input)


### Tanh¶

class torch.nn.Tanh[source]

Applies element-wise, $$\text{Tanh}(x) = \tanh(x) = \frac{e^x - e^{-x}} {e^x + e^{-x}}$$

Shape:
• Input: $$(N, *)$$ where * means, any number of additional dimensions
• Output: $$(N, *)$$, same shape as the input

Examples:

>>> m = nn.Tanh()
>>> input = torch.randn(2)
>>> output = m(input)


### Tanhshrink¶

class torch.nn.Tanhshrink[source]

Applies element-wise, $$\text{Tanhshrink}(x) = x - \text{Tanh}(x)$$

Shape:
• Input: $$(N, *)$$ where * means, any number of additional dimensions
• Output: $$(N, *)$$, same shape as the input

Examples:

>>> m = nn.Tanhshrink()
>>> input = torch.randn(2)
>>> output = m(input)


### Threshold¶

class torch.nn.Threshold(threshold, value, inplace=False)[source]

Thresholds each element of the input Tensor

Threshold is defined as:

$\begin{split}y = \begin{cases} x, &\text{ if } x > \text{threshold} \\ \text{value}, &\text{ otherwise } \end{cases}\end{split}$
Parameters: threshold – The value to threshold at value – The value to replace with inplace – can optionally do the operation in-place. Default: False
Shape:
• Input: $$(N, *)$$ where * means, any number of additional dimensions
• Output: $$(N, *)$$, same shape as the input

Examples:

>>> m = nn.Threshold(0.1, 20)
>>> input = torch.randn(2)
>>> output = m(input)


## Non-linear activations (other)¶

### Softmin¶

class torch.nn.Softmin(dim=None)[source]

Applies the Softmin function to an n-dimensional input Tensor rescaling them so that the elements of the n-dimensional output Tensor lie in the range (0, 1) and sum to 1

$$\text{Softmin}(x_{i}) = \frac{\exp(-x_i)}{\sum_j \exp(-x_j)}$$

Shape:
• Input: any shape
• Output: same as input
Parameters: dim (int) – A dimension along which Softmax will be computed (so every slice along dim will sum to 1). a Tensor of the same dimension and shape as the input, with values in the range [0, 1]

Examples:

>>> m = nn.Softmin()
>>> input = torch.randn(2, 3)
>>> output = m(input)


### Softmax¶

class torch.nn.Softmax(dim=None)[source]

Applies the Softmax function to an n-dimensional input Tensor rescaling them so that the elements of the n-dimensional output Tensor lie in the range (0,1) and sum to 1

Softmax is defined as $$\text{Softmax}(x_{i}) = \frac{\exp(x_i)}{\sum_j \exp(x_j)}$$

Shape:
• Input: any shape
• Output: same as input
Returns: a Tensor of the same dimension and shape as the input with values in the range [0, 1] dim (int) – A dimension along which Softmax will be computed (so every slice along dim will sum to 1).

Note

This module doesn’t work directly with NLLLoss, which expects the Log to be computed between the Softmax and itself. Use LogSoftmax instead (it’s faster and has better numerical properties).

Examples:

>>> m = nn.Softmax()
>>> input = torch.randn(2, 3)
>>> output = m(input)


### Softmax2d¶

class torch.nn.Softmax2d[source]

Applies SoftMax over features to each spatial location.

When given an image of Channels x Height x Width, it will apply Softmax to each location $$(Channels, h_i, w_j)$$

Shape:
• Input: $$(N, C, H, W)$$
• Output: $$(N, C, H, W)$$ (same shape as input)
Returns: a Tensor of the same dimension and shape as the input with values in the range [0, 1]

Examples:

>>> m = nn.Softmax2d()
>>> # you softmax over the 2nd dimension
>>> input = torch.randn(2, 3, 12, 13)
>>> output = m(input)


### LogSoftmax¶

class torch.nn.LogSoftmax(dim=None)[source]

Applies the Log(Softmax(x)) function to an n-dimensional input Tensor. The LogSoftmax formulation can be simplified as

$$\text{LogSoftmax}(x_{i}) = \log\left(\frac{\exp(x_i) }{ \sum_j \exp(x_j)} \right)$$

Shape:
• Input: any shape
• Output: same as input
Parameters: dim (int) – A dimension along which Softmax will be computed (so every slice along dim will sum to 1). a Tensor of the same dimension and shape as the input with values in the range [-inf, 0)

Examples:

>>> m = nn.LogSoftmax()
>>> input = torch.randn(2, 3)
>>> output = m(input)


## Normalization layers¶

### BatchNorm1d¶

class torch.nn.BatchNorm1d(num_features, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)[source]

Applies Batch Normalization over a 2D or 3D input (a mini-batch of 1D inputs with optional additional channel dimension) as described in the paper Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift .

$y = \frac{x - \mathrm{E}[x]}{\sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta$

The mean and standard-deviation are calculated per-dimension over the mini-batches and $$\gamma$$ and $$\beta$$ are learnable parameter vectors of size C (where C is the input size).

By default, during training this layer keeps running estimates of its computed mean and variance, which are then used for normalization during evaluation. The running estimates are kept with a default momentum of 0.1.

If track_running_stats is set to False, this layer then does not keep running estimates, and batch statistics are instead used during evaluation time as well.

Note

This momentum argument is different from one used in optimizer classes and the conventional notion of momentum. Mathematically, the update rule for running statistics here is $$\hat{x}_\text{new} = (1 - \text{momentum}) \times \hat{x} + \text{momemtum} \times x_t$$, where $$\hat{x}$$ is the estimated statistic and $$x_t$$ is the new observed value.

Because the Batch Normalization is done over the C dimension, computing statistics on (N, L) slices, it’s common terminology to call this Temporal Batch Normalization.

Parameters: num_features – $$C$$ from an expected input of size $$(N, C, L)$$ or $$L$$ from input of size $$(N, L)$$ eps – a value added to the denominator for numerical stability. Default: 1e-5 momentum – the value used for the running_mean and running_var computation. Default: 0.1 affine – a boolean value that when set to True, this module has learnable affine parameters. Default: True track_running_stats – a boolean value that when set to True, this module tracks the running mean and variance, and when set to False, this module does not track such statistics and always uses batch statistics in both training and eval modes. Default: True
Shape:
• Input: $$(N, C)$$ or $$(N, C, L)$$
• Output: $$(N, C)$$ or $$(N, C, L)$$ (same shape as input)

Examples:

>>> # With Learnable Parameters
>>> m = nn.BatchNorm1d(100)
>>> # Without Learnable Parameters
>>> m = nn.BatchNorm1d(100, affine=False)
>>> input = torch.randn(20, 100)
>>> output = m(input)


### BatchNorm2d¶

class torch.nn.BatchNorm2d(num_features, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)[source]

Applies Batch Normalization over a 4D input (a mini-batch of 2D inputs with additional channel dimension) as described in the paper Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift .

$y = \frac{x - \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta$

The mean and standard-deviation are calculated per-dimension over the mini-batches and $$\gamma$$ and $$\beta$$ are learnable parameter vectors of size C (where C is the input size).

By default, during training this layer keeps running estimates of its computed mean and variance, which are then used for normalization during evaluation. The running estimates are kept with a default momentum of 0.1.

If track_running_stats is set to False, this layer then does not keep running estimates, and batch statistics are instead used during evaluation time as well.

Note

This momentum argument is different from one used in optimizer classes and the conventional notion of momentum. Mathematically, the update rule for running statistics here is $$\hat{x}_\text{new} = (1 - \text{momentum}) \times \hat{x} + \text{momemtum} \times x_t$$, where $$\hat{x}$$ is the estimated statistic and $$x_t$$ is the new observed value.

Because the Batch Normalization is done over the C dimension, computing statistics on (N, H, W) slices, it’s common terminology to call this Spatial Batch Normalization.

Parameters: num_features – $$C$$ from an expected input of size $$(N, C, H, W)$$ eps – a value added to the denominator for numerical stability. Default: 1e-5 momentum – the value used for the running_mean and running_var computation. Default: 0.1 affine – a boolean value that when set to True, this module has learnable affine parameters. Default: True track_running_stats – a boolean value that when set to True, this module tracks the running mean and variance, and when set to False, this module does not track such statistics and always uses batch statistics in both training and eval modes. Default: True
Shape:
• Input: $$(N, C, H, W)$$
• Output: $$(N, C, H, W)$$ (same shape as input)

Examples:

>>> # With Learnable Parameters
>>> m = nn.BatchNorm2d(100)
>>> # Without Learnable Parameters
>>> m = nn.BatchNorm2d(100, affine=False)
>>> input = torch.randn(20, 100, 35, 45)
>>> output = m(input)


### BatchNorm3d¶

class torch.nn.BatchNorm3d(num_features, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)[source]

Applies Batch Normalization over a 5D input (a mini-batch of 3D inputs with additional channel dimension) as described in the paper Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift .

$y = \frac{x - \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta$

The mean and standard-deviation are calculated per-dimension over the mini-batches and $$\gamma$$ and $$\beta$$ are learnable parameter vectors of size C (where C is the input size).

By default, during training this layer keeps running estimates of its computed mean and variance, which are then used for normalization during evaluation. The running estimates are kept with a default momentum of 0.1.

If track_running_stats is set to False, this layer then does not keep running estimates, and batch statistics are instead used during evaluation time as well.

Note

This momentum argument is different from one used in optimizer classes and the conventional notion of momentum. Mathematically, the update rule for running statistics here is $$\hat{x}_\text{new} = (1 - \text{momentum}) \times \hat{x} + \text{momemtum} \times x_t$$, where $$\hat{x}$$ is the estimated statistic and $$x_t$$ is the new observed value.

Because the Batch Normalization is done over the C dimension, computing statistics on (N, D, H, W) slices, it’s common terminology to call this Volumetric Batch Normalization or Spatio-temporal Batch Normalization.

Parameters: num_features – $$C$$ from an expected input of size $$(N, C, D, H, W)$$ eps – a value added to the denominator for numerical stability. Default: 1e-5 momentum – the value used for the running_mean and running_var computation. Default: 0.1 affine – a boolean value that when set to True, this module has learnable affine parameters. Default: True track_running_stats – a boolean value that when set to True, this module tracks the running mean and variance, and when set to False, this module does not track such statistics and always uses batch statistics in both training and eval modes. Default: True
Shape:
• Input: $$(N, C, D, H, W)$$
• Output: $$(N, C, D, H, W)$$ (same shape as input)

Examples:

>>> # With Learnable Parameters
>>> m = nn.BatchNorm3d(100)
>>> # Without Learnable Parameters
>>> m = nn.BatchNorm3d(100, affine=False)
>>> input = torch.randn(20, 100, 35, 45, 10)
>>> output = m(input)


### InstanceNorm1d¶

class torch.nn.InstanceNorm1d(num_features, eps=1e-05, momentum=0.1, affine=False, track_running_stats=False)[source]

Applies Instance Normalization over a 2D or 3D input (a mini-batch of 1D inputs with optional additional channel dimension) as described in the paper Instance Normalization: The Missing Ingredient for Fast Stylization .

$y = \frac{x - \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x]} + \epsilon} * \gamma + \beta$

The mean and standard-deviation are calculated per-dimension separately for each object in a mini-batch. $$\gamma$$ and $$\beta$$ are learnable parameter vectors of size C (where C is the input size) if affine is True.

By default, this layer uses instance statistics computed from input data in both training and evaluation modes.

If track_running_stats is set to True, during training this layer keeps running estimates of its computed mean and variance, which are then used for normalization during evaluation. The running estimates are kept with a default momentum of 0.1.

Note

This momentum argument is different from one used in optimizer classes and the conventional notion of momentum. Mathematically, the update rule for running statistics here is $$\hat{x}_\text{new} = (1 - \text{momentum}) \times \hat{x} + \text{momemtum} \times x_t$$, where $$\hat{x}$$ is the estimated statistic and $$x_t$$ is the new observed value.

Parameters: num_features – $$C$$ from an expected input of size $$(N, C, L)$$ or $$L$$ from input of size $$(N, L)$$ eps – a value added to the denominator for numerical stability. Default: 1e-5 momentum – the value used for the running_mean and running_var computation. Default: 0.1 affine – a boolean value that when set to True, this module has learnable affine parameters. Default: True track_running_stats – a boolean value that when set to True, this module tracks the running mean and variance, and when set to False, this module does not track such statistics and always uses batch statistics in both training and eval modes. Default: False
Shape:
• Input: $$(N, C, L)$$
• Output: $$(N, C, L)$$ (same shape as input)

Examples:

>>> # Without Learnable Parameters
>>> m = nn.InstanceNorm1d(100)
>>> # With Learnable Parameters
>>> m = nn.InstanceNorm1d(100, affine=True)
>>> input = torch.randn(20, 100, 40)
>>> output = m(input)


### InstanceNorm2d¶

class torch.nn.InstanceNorm2d(num_features, eps=1e-05, momentum=0.1, affine=False, track_running_stats=False)[source]

Applies Instance Normalization over a 4D input (a mini-batch of 2D inputs with additional channel dimension) as described in the paper Instance Normalization: The Missing Ingredient for Fast Stylization .

$y = \frac{x - \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x]} + \epsilon} * \gamma + \beta$

The mean and standard-deviation are calculated per-dimension separately for each object in a mini-batch. $$\gamma$$ and $$\beta$$ are learnable parameter vectors of size C (where C is the input size) if affine is True.

By default, this layer uses instance statistics computed from input data in both training and evaluation modes.

If track_running_stats is set to True, during training this layer keeps running estimates of its computed mean and variance, which are then used for normalization during evaluation. The running estimates are kept with a default momentum of 0.1.

Note

This momentum argument is different from one used in optimizer classes and the conventional notion of momentum. Mathematically, the update rule for running statistics here is $$\hat{x}_\text{new} = (1 - \text{momentum}) \times \hat{x} + \text{momemtum} \times x_t$$, where $$\hat{x}$$ is the estimated statistic and $$x_t$$ is the new observed value.

Parameters: num_features – $$C$$ from an expected input of size $$(N, C, H, W)$$ eps – a value added to the denominator for numerical stability. Default: 1e-5 momentum – the value used for the running_mean and running_var computation. Default: 0.1 affine – a boolean value that when set to True, this module has learnable affine parameters. Default: True track_running_stats – a boolean value that when set to True, this module tracks the running mean and variance, and when set to False, this module does not track such statistics and always uses batch statistics in both training and eval modes. Default: False
Shape:
• Input: $$(N, C, H, W)$$
• Output: $$(N, C, H, W)$$ (same shape as input)

Examples:

>>> # Without Learnable Parameters
>>> m = nn.InstanceNorm2d(100)
>>> # With Learnable Parameters
>>> m = nn.InstanceNorm2d(100, affine=True)
>>> input = torch.randn(20, 100, 35, 45)
>>> output = m(input)


### InstanceNorm3d¶

class torch.nn.InstanceNorm3d(num_features, eps=1e-05, momentum=0.1, affine=False, track_running_stats=False)[source]

Applies Instance Normalization over a 5D input (a mini-batch of 3D inputs with additional channel dimension) as described in the paper Instance Normalization: The Missing Ingredient for Fast Stylization .

$y = \frac{x - \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x]} + \epsilon} * \gamma + \beta$

The mean and standard-deviation are calculated per-dimension separately for each object in a mini-batch. $$\gamma$$ and $$\beta$$ are learnable parameter vectors of size C (where C is the input size) if affine is True.

By default, this layer uses instance statistics computed from input data in both training and evaluation modes.

If track_running_stats is set to True, during training this layer keeps running estimates of its computed mean and variance, which are then used for normalization during evaluation. The running estimates are kept with a default momentum of 0.1.

Note

This momentum argument is different from one used in optimizer classes and the conventional notion of momentum. Mathematically, the update rule for running statistics here is $$\hat{x}_\text{new} = (1 - \text{momentum}) \times \hat{x} + \text{momemtum} \times x_t$$, where $$\hat{x}$$ is the estimated statistic and $$x_t$$ is the new observed value.

Parameters: num_features – $$C$$ from an expected input of size $$(N, C, D, H, W)$$ eps – a value added to the denominator for numerical stability. Default: 1e-5 momentum – the value used for the running_mean and running_var computation. Default: 0.1 affine – a boolean value that when set to True, this module has learnable affine parameters. Default: True track_running_stats – a boolean value that when set to True, this module tracks the running mean and variance, and when set to False, this module does not track such statistics and always uses batch statistics in both training and eval modes. Default: False
Shape:
• Input: $$(N, C, D, H, W)$$
• Output: $$(N, C, D, H, W)$$ (same shape as input)

Examples:

>>> # Without Learnable Parameters
>>> m = nn.InstanceNorm3d(100)
>>> # With Learnable Parameters
>>> m = nn.InstanceNorm3d(100, affine=True)
>>> input = torch.randn(20, 100, 35, 45, 10)
>>> output = m(input)


### LayerNorm¶

class torch.nn.LayerNorm(normalized_shape, eps=1e-05, elementwise_affine=True)[source]

Applies Layer Normalization over a mini-batch of inputs as described in the paper Layer Normalization .

$y = \frac{x - \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x]} + \epsilon} * \gamma + \beta$

The mean and standard-deviation are calculated separately over the last certain number dimensions with shape specified by normalized_shape. $$\gamma$$ and $$\beta$$ are learnable affine transform parameters of normalized_shape if elementwise_affine is True.

Note

Unlike Batch Normalization and Instance Normalization, which applies scalar scale and bias for each entire channel/plane with the affine option, Layer Normalization applies per-element scale and bias with elementwise_affine.

This layer uses statistics computed from input data in both training and evaluation modes.

Parameters: normalized_shape (int or list or torch.Size) – input shape from an expected input of size $[* \times \text{normalized_shape}[0] \times \text{normalized_shape}[1] \times \ldots \times \text{normalized_shape}[-1]]$ If a single integer is used, it is treated as a singleton list, and this module will normalize over the last dimension with that specific size. eps – a value added to the denominator for numerical stability. Default: 1e-5 elementwise_affine – a boolean value that when set to True, this module has learnable per-element affine parameters. Default: True
Shape:
• Input: $$(N, *)$$
• Output: $$(N, *)$$ (same shape as input)

Examples:

>>> input = torch.randn(20, 5, 10, 10)
>>> # With Learnable Parameters
>>> m = nn.LayerNorm(input.size()[1:])
>>> # Without Learnable Parameters
>>> m = nn.LayerNorm(input.size()[1:], elementwise_affine=False)
>>> # Normalize over last two dimensions
>>> m = nn.LayerNorm([10, 10])
>>> # Normalize over last dimension of size 10
>>> m = nn.LayerNorm(10)
>>> # Activating the module
>>> output = m(input)


### LocalResponseNorm¶

class torch.nn.LocalResponseNorm(size, alpha=0.0001, beta=0.75, k=1)[source]

Applies local response normalization over an input signal composed of several input planes, where channels occupy the second dimension. Applies normalization across channels.

$b_{c} = a_{c}\left(k + \frac{\alpha}{n} \sum_{c'=\max(0, c-n/2)}^{\min(N-1,c+n/2)}a_{c'}^2\right)^{-\beta}$
Parameters: size – amount of neighbouring channels used for normalization alpha – multiplicative factor. Default: 0.0001 beta – exponent. Default: 0.75 k – additive factor. Default: 1
Shape:
• Input: $$(N, C, ...)$$
• Output: $$(N, C, ...)$$ (same shape as input)

Examples:

>>> lrn = nn.LocalResponseNorm(2)
>>> signal_2d = torch.randn(32, 5, 24, 24)
>>> signal_4d = torch.randn(16, 5, 7, 7, 7, 7)
>>> output_2d = lrn(signal_2d)
>>> output_4d = lrn(signal_4d)


## Recurrent layers¶

### RNN¶

class torch.nn.RNN(*args, **kwargs)[source]

Applies a multi-layer Elman RNN with tanh or ReLU non-linearity to an input sequence.

For each element in the input sequence, each layer computes the following function:

$h_t = \tanh(w_{ih} x_t + b_{ih} + w_{hh} h_{(t-1)} + b_{hh})$

where $$h_t$$ is the hidden state at time t, $$x_t$$ is the input at time t, and $$h_{(t-1)}$$ is the hidden state of the previous layer at time t-1 or the initial hidden state at time 0. If nonlinearity='relu', then ReLU is used instead of tanh.

Parameters: input_size – The number of expected features in the input x hidden_size – The number of features in the hidden state h num_layers – Number of recurrent layers. E.g., setting num_layers=2 would mean stacking two RNNs together to form a stacked RNN, with the second RNN taking in outputs of the first RNN and computing the final results. Default: 1 nonlinearity – The non-linearity to use. Can be either ‘tanh’ or ‘relu’. Default: ‘tanh’ bias – If False, then the layer does not use bias weights b_ih and b_hh. Default: True batch_first – If True, then the input and output tensors are provided as (batch, seq, feature) dropout – If non-zero, introduces a Dropout layer on the outputs of each RNN layer except the last layer, with dropout probability equal to dropout. Default: 0 bidirectional – If True, becomes a bidirectional RNN. Default: False
Inputs: input, h_0
Outputs: output, h_n
• output of shape (seq_len, batch, hidden_size * num_directions): tensor containing the output features (h_k) from the last layer of the RNN, for each k. If a torch.nn.utils.rnn.PackedSequence has been given as the input, the output will also be a packed sequence.
• h_n (num_layers * num_directions, batch, hidden_size): tensor containing the hidden state for k = seq_len.
Variables: weight_ih_l[k] – the learnable input-hidden weights of the k-th layer, of shape (hidden_size * input_size) for k = 0. Otherwise, the shape is (hidden_size * hidden_size) weight_hh_l[k] – the learnable hidden-hidden weights of the k-th layer, of shape (hidden_size * hidden_size) bias_ih_l[k] – the learnable input-hidden bias of the k-th layer, of shape (hidden_size) bias_hh_l[k] – the learnable hidden-hidden bias of the k-th layer, of shape (hidden_size)

Examples:

>>> rnn = nn.RNN(10, 20, 2)
>>> input = torch.randn(5, 3, 10)
>>> h0 = torch.randn(2, 3, 20)
>>> output, hn = rnn(input, h0)


### LSTM¶

class torch.nn.LSTM(*args, **kwargs)[source]

Applies a multi-layer long short-term memory (LSTM) RNN to an input sequence.

For each element in the input sequence, each layer computes the following function:

$\begin{split}\begin{array}{ll} i_t = \sigma(W_{ii} x_t + b_{ii} + W_{hi} h_{(t-1)} + b_{hi}) \\ f_t = \sigma(W_{if} x_t + b_{if} + W_{hf} h_{(t-1)} + b_{hf}) \\ g_t = \tanh(W_{ig} x_t + b_{ig} + W_{hg} h_{(t-1)} + b_{hg}) \\ o_t = \sigma(W_{io} x_t + b_{io} + W_{ho} h_{(t-1)} + b_{ho}) \\ c_t = f_t c_{(t-1)} + i_t g_t \\ h_t = o_t \tanh(c_t) \end{array}\end{split}$

where $$h_t$$ is the hidden state at time t, $$c_t$$ is the cell state at time t, $$x_t$$ is the input at time t, $$h_{(t-1)}$$ is the hidden state of the previous layer at time t-1 or the initial hidden state at time 0, and $$i_t$$, $$f_t$$, $$g_t$$, $$o_t$$ are the input, forget, cell, and output gates, respectively. $$\sigma$$ is the sigmoid function.

Parameters: input_size – The number of expected features in the input x hidden_size – The number of features in the hidden state h num_layers – Number of recurrent layers. E.g., setting num_layers=2 would mean stacking two LSTMs together to form a stacked LSTM, with the second LSTM taking in outputs of the first LSTM and computing the final results. Default: 1 bias – If False, then the layer does not use bias weights b_ih and b_hh. Default: True batch_first – If True, then the input and output tensors are provided as (batch, seq, feature) dropout – If non-zero, introduces a Dropout layer on the outputs of each LSTM layer except the last layer, with dropout probability equal to dropout. Default: 0 bidirectional – If True, becomes a bidirectional LSTM. Default: False
Inputs: input, (h_0, c_0)
• input of shape (seq_len, batch, input_size): tensor containing the features of the input sequence. The input can also be a packed variable length sequence. See torch.nn.utils.rnn.pack_padded_sequence() or torch.nn.utils.rnn.pack_sequence() for details.

• h_0 of shape (num_layers * num_directions, batch, hidden_size): tensor containing the initial hidden state for each element in the batch.

• c_0 of shape (num_layers * num_directions, batch, hidden_size): tensor containing the initial cell state for each element in the batch.

If (h_0, c_0) is not provided, both h_0 and c_0 default to zero.

Outputs: output, (h_n, c_n)
• output of shape (seq_len, batch, hidden_size * num_directions): tensor containing the output features (h_t) from the last layer of the LSTM, for each t. If a torch.nn.utils.rnn.PackedSequence has been given as the input, the output will also be a packed sequence.
• h_n of shape (num_layers * num_directions, batch, hidden_size): tensor containing the hidden state for t = seq_len
• c_n (num_layers * num_directions, batch, hidden_size): tensor containing the cell state for t = seq_len
Variables: weight_ih_l[k] – the learnable input-hidden weights of the $$\text{k}^{th}$$ layer (W_ii|W_if|W_ig|W_io), of shape (4*hidden_size x input_size) weight_hh_l[k] – the learnable hidden-hidden weights of the $$\text{k}^{th}$$ layer (W_hi|W_hf|W_hg|W_ho), of shape (4*hidden_size x hidden_size) bias_ih_l[k] – the learnable input-hidden bias of the $$\text{k}^{th}$$ layer (b_ii|b_if|b_ig|b_io), of shape (4*hidden_size) bias_hh_l[k] – the learnable hidden-hidden bias of the $$\text{k}^{th}$$ layer (b_hi|b_hf|b_hg|b_ho), of shape (4*hidden_size)

Examples:

>>> rnn = nn.LSTM(10, 20, 2)
>>> input = torch.randn(5, 3, 10)
>>> h0 = torch.randn(2, 3, 20)
>>> c0 = torch.randn(2, 3, 20)
>>> output, hn = rnn(input, (h0, c0))


### GRU¶

class torch.nn.GRU(*args, **kwargs)[source]

Applies a multi-layer gated recurrent unit (GRU) RNN to an input sequence.

For each element in the input sequence, each layer computes the following function:

$\begin{split}\begin{array}{ll} r_t = \sigma(W_{ir} x_t + b_{ir} + W_{hr} h_{(t-1)} + b_{hr}) \\ z_t = \sigma(W_{iz} x_t + b_{iz} + W_{hz} h_{(t-1)} + b_{hz}) \\ n_t = \tanh(W_{in} x_t + b_{in} + r_t (W_{hn} h_{(t-1)}+ b_{hn})) \\ h_t = (1 - z_t) n_t + z_t h_{(t-1)} \\ \end{array}\end{split}$

where $$h_t$$ is the hidden state at time t, $$x_t$$ is the input at time t, $$h_{(t-1)}$$ is the hidden state of the previous layer at time t-1 or the initial hidden state at time 0, and $$r_t$$, $$z_t$$, $$n_t$$ are the reset, update, and new gates, respectively. $$\sigma$$ is the sigmoid function.

Parameters: input_size – The number of expected features in the input x hidden_size – The number of features in the hidden state h num_layers – Number of recurrent layers. E.g., setting num_layers=2 would mean stacking two GRUs together to form a stacked GRU, with the second GRU taking in outputs of the first GRU and computing the final results. Default: 1 bias – If False, then the layer does not use bias weights b_ih and b_hh. Default: True batch_first – If True, then the input and output tensors are provided as (batch, seq, feature) dropout – If non-zero, introduces a Dropout layer on the outputs of each GRU layer except the last layer, with dropout probability equal to dropout. Default: 0 bidirectional – If True, becomes a bidirectional GRU. Default: False
Inputs: input, h_0
• input of shape (seq_len, batch, input_size): tensor containing the features of the input sequence. The input can also be a packed variable length sequence. See torch.nn.utils.rnn.pack_padded_sequence() for details.
• h_0 of shape (num_layers * num_directions, batch, hidden_size): tensor containing the initial hidden state for each element in the batch. Defaults to zero if not provided.
Outputs: output, h_n
• output of shape (seq_len, batch, hidden_size * num_directions): tensor containing the output features h_t from the last layer of the GRU, for each t. If a torch.nn.utils.rnn.PackedSequence has been given as the input, the output will also be a packed sequence.
• h_n of shape (num_layers * num_directions, batch, hidden_size): tensor containing the hidden state for t = seq_len
Variables: weight_ih_l[k] – the learnable input-hidden weights of the $$\text{k}^{th}$$ layer (W_ir|W_iz|W_in), of shape (3*hidden_size x input_size) weight_hh_l[k] – the learnable hidden-hidden weights of the $$\text{k}^{th}$$ layer (W_hr|W_hz|W_hn), of shape (3*hidden_size x hidden_size) bias_ih_l[k] – the learnable input-hidden bias of the $$\text{k}^{th}$$ layer (b_ir|b_iz|b_in), of shape (3*hidden_size) bias_hh_l[k] – the learnable hidden-hidden bias of the $$\text{k}^{th}$$ layer (b_hr|b_hz|b_hn), of shape (3*hidden_size)

Examples:

>>> rnn = nn.GRU(10, 20, 2)
>>> input = torch.randn(5, 3, 10)
>>> h0 = torch.randn(2, 3, 20)
>>> output, hn = rnn(input, h0)


### RNNCell¶

class torch.nn.RNNCell(input_size, hidden_size, bias=True, nonlinearity='tanh')[source]

An Elman RNN cell with tanh or ReLU non-linearity.

$h' = \tanh(w_{ih} x + b_{ih} + w_{hh} h + b_{hh})$

If :attr:nonlinearity=’relu’, then ReLU is used in place of tanh.

Parameters: input_size – The number of expected features in the input x hidden_size – The number of features in the hidden state h bias – If False, then the layer does not use bias weights b_ih and b_hh. Default: True nonlinearity – The non-linearity to use. Can be either ‘tanh’ or ‘relu’. Default: ‘tanh’
Inputs: input, hidden
• input of shape (batch, input_size): tensor containing input features
• hidden of shape (batch, hidden_size): tensor containing the initial hidden state for each element in the batch. Defaults to zero if not provided.
Outputs: h’
• h’ of shape (batch, hidden_size): tensor containing the next hidden state for each element in the batch
Variables: weight_ih – the learnable input-hidden weights, of shape (input_size x hidden_size) weight_hh – the learnable hidden-hidden weights, of shape (hidden_size x hidden_size) bias_ih – the learnable input-hidden bias, of shape (hidden_size) bias_hh – the learnable hidden-hidden bias, of shape (hidden_size)

Examples:

>>> rnn = nn.RNNCell(10, 20)
>>> input = torch.randn(6, 3, 10)
>>> hx = torch.randn(3, 20)
>>> output = []
>>> for i in range(6):
hx = rnn(input[i], hx)
output.append(hx)


### LSTMCell¶

class torch.nn.LSTMCell(input_size, hidden_size, bias=True)[source]

A long short-term memory (LSTM) cell.

$\begin{split}\begin{array}{ll} i = \sigma(W_{ii} x + b_{ii} + W_{hi} h + b_{hi}) \\ f = \sigma(W_{if} x + b_{if} + W_{hf} h + b_{hf}) \\ g = \tanh(W_{ig} x + b_{ig} + W_{hc} h + b_{hg}) \\ o = \sigma(W_{io} x + b_{io} + W_{ho} h + b_{ho}) \\ c' = f * c + i * g \\ h' = o \tanh(c') \\ \end{array}\end{split}$

where $$\sigma$$ is the sigmoid function.

Parameters: input_size – The number of expected features in the input x hidden_size – The number of features in the hidden state h bias – If False, then the layer does not use bias weights b_ih and b_hh. Default: True
Inputs: input, (h_0, c_0)
• input of shape (batch, input_size): tensor containing input features

• h_0 of shape (batch, hidden_size): tensor containing the initial hidden state for each element in the batch.

• c_0 of shape (batch, hidden_size): tensor containing the initial cell state for each element in the batch.

If (h_0, c_0) is not provided, both h_0 and c_0 default to zero.

Outputs: h_1, c_1
• h_1 of shape (batch, hidden_size): tensor containing the next hidden state for each element in the batch
• c_1 of shape (batch, hidden_size): tensor containing the next cell state for each element in the batch
Variables: weight_ih – the learnable input-hidden weights, of shape (4*hidden_size x input_size) weight_hh – the learnable hidden-hidden weights, of shape (4*hidden_size x hidden_size) bias_ih – the learnable input-hidden bias, of shape (4*hidden_size) bias_hh – the learnable hidden-hidden bias, of shape (4*hidden_size)

Examples:

>>> rnn = nn.LSTMCell(10, 20)
>>> input = torch.randn(6, 3, 10)
>>> hx = torch.randn(3, 20)
>>> cx = torch.randn(3, 20)
>>> output = []
>>> for i in range(6):
hx, cx = rnn(input[i], (hx, cx))
output.append(hx)


### GRUCell¶

class torch.nn.GRUCell(input_size, hidden_size, bias=True)[source]

A gated recurrent unit (GRU) cell

$\begin{split}\begin{array}{ll} r = \sigma(W_{ir} x + b_{ir} + W_{hr} h + b_{hr}) \\ z = \sigma(W_{iz} x + b_{iz} + W_{hz} h + b_{hz}) \\ n = \tanh(W_{in} x + b_{in} + r * (W_{hn} h + b_{hn})) \\ h' = (1 - z) * n + z * h \end{array}\end{split}$

where $$\sigma$$ is the sigmoid function.

Parameters: input_size – The number of expected features in the input x hidden_size – The number of features in the hidden state h bias – If False, then the layer does not use bias weights b_ih and b_hh. Default: True
Inputs: input, hidden
• input of shape (batch, input_size): tensor containing input features
• hidden of shape (batch, hidden_size): tensor containing the initial hidden state for each element in the batch. Defaults to zero if not provided.
Outputs: h’
• h’ of shape (batch, hidden_size): tensor containing the next hidden state for each element in the batch
Variables: weight_ih – the learnable input-hidden weights, of shape (3*hidden_size x input_size) weight_hh – the learnable hidden-hidden weights, of shape (3*hidden_size x hidden_size) bias_ih – the learnable input-hidden bias, of shape (3*hidden_size) bias_hh – the learnable hidden-hidden bias, of shape (3*hidden_size)

Examples:

>>> rnn = nn.GRUCell(10, 20)
>>> input = torch.randn(6, 3, 10)
>>> hx = torch.randn(3, 20)
>>> output = []
>>> for i in range(6):
hx = rnn(input[i], hx)
output.append(hx)


## Linear layers¶

### Linear¶

class torch.nn.Linear(in_features, out_features, bias=True)[source]

Applies a linear transformation to the incoming data: $$y = Ax + b$$

Parameters: in_features – size of each input sample out_features – size of each output sample bias – If set to False, the layer will not learn an additive bias. Default: True
Shape:
• Input: $$(N, *, in\_features)$$ where $$*$$ means any number of additional dimensions
• Output: $$(N, *, out\_features)$$ where all but the last dimension are the same shape as the input.
Variables: weight – the learnable weights of the module of shape (out_features x in_features) bias – the learnable bias of the module of shape (out_features)

Examples:

>>> m = nn.Linear(20, 30)
>>> input = torch.randn(128, 20)
>>> output = m(input)
>>> print(output.size())


### Bilinear¶

class torch.nn.Bilinear(in1_features, in2_features, out_features, bias=True)[source]

Applies a bilinear transformation to the incoming data: $$y = x_1 A x_2 + b$$

Parameters: in1_features – size of each first input sample in2_features – size of each second input sample out_features – size of each output sample bias – If set to False, the layer will not learn an additive bias. Default: True
Shape:
• Input: $$(N, *, \text{in1_features})$$, $$(N, *, \text{in2_features})$$ where $$*$$ means any number of additional dimensions. All but the last dimension of the inputs should be the same.
• Output: $$(N, *, \text{out_features})$$ where all but the last dimension are the same shape as the input.
Variables: weight – the learnable weights of the module of shape (out_features x in1_features x in2_features) bias – the learnable bias of the module of shape (out_features)

Examples:

>>> m = nn.Bilinear(20, 30, 40)
>>> input1 = torch.randn(128, 20)
>>> input2 = torch.randn(128, 30)
>>> output = m(input1, input2)
>>> print(output.size())


## Dropout layers¶

### Dropout¶

class torch.nn.Dropout(p=0.5, inplace=False)[source]

During training, randomly zeroes some of the elements of the input tensor with probability p using samples from a Bernoulli distribution. The elements to zero are randomized on every forward call.

This has proven to be an effective technique for regularization and preventing the co-adaptation of neurons as described in the paper Improving neural networks by preventing co-adaptation of feature detectors .

Furthermore, the outputs are scaled by a factor of $$\frac{1}{1-p}$$ during training. This means that during evaluation the module simply computes an identity function.

Parameters: p – probability of an element to be zeroed. Default: 0.5 inplace – If set to True, will do this operation in-place. Default: False
Shape:
• Input: Any. Input can be of any shape
• Output: Same. Output is of the same shape as input

Examples:

>>> m = nn.Dropout(p=0.2)
>>> input = torch.randn(20, 16)
>>> output = m(input)


### Dropout2d¶

class torch.nn.Dropout2d(p=0.5, inplace=False)[source]

Randomly zeroes whole channels of the input tensor. The channels to zero-out are randomized on every forward call.

Usually the input comes from nn.Conv2d modules.

As described in the paper Efficient Object Localization Using Convolutional Networks , if adjacent pixels within feature maps are strongly correlated (as is normally the case in early convolution layers) then i.i.d. dropout will not regularize the activations and will otherwise just result in an effective learning rate decrease.

In this case, nn.Dropout2d() will help promote independence between feature maps and should be used instead.

Parameters: p (float, optional) – probability of an element to be zero-ed. inplace (bool, optional) – If set to True, will do this operation in-place
Shape:
• Input: $$(N, C, H, W)$$
• Output: $$(N, C, H, W)$$ (same shape as input)

Examples:

>>> m = nn.Dropout2d(p=0.2)
>>> input = torch.randn(20, 16, 32, 32)
>>> output = m(input)


### Dropout3d¶

class torch.nn.Dropout3d(p=0.5, inplace=False)[source]

Randomly zeroes whole channels of the input tensor. The channels to zero are randomized on every forward call.

Usually the input comes from nn.Conv3d modules.

As described in the paper Efficient Object Localization Using Convolutional Networks , if adjacent pixels within feature maps are strongly correlated (as is normally the case in early convolution layers) then i.i.d. dropout will not regularize the activations and will otherwise just result in an effective learning rate decrease.

In this case, nn.Dropout3d() will help promote independence between feature maps and should be used instead.

Parameters: p (float, optional) – probability of an element to be zeroed. inplace (bool, optional) – If set to True, will do this operation in-place
Shape:
• Input: $$(N, C, D, H, W)$$
• Output: $$(N, C, D, H, W)$$ (same shape as input)

Examples:

>>> m = nn.Dropout3d(p=0.2)
>>> input = torch.randn(20, 16, 4, 32, 32)
>>> output = m(input)


class torch.nn.AlphaDropout(p=0.5)[source]

Applies Alpha Dropout over the input.

Alpha Dropout is a type of Dropout that maintains the self-normalizing property. For an input with zero mean and unit standard deviation, the output of Alpha Dropout maintains the original mean and standard deviation of the input. Alpha Dropout goes hand-in-hand with SELU activation function, which ensures that the outputs have zero mean and unit standard deviation.

During training, it randomly masks some of the elements of the input tensor with probability p using samples from a bernoulli distribution. The elements to masked are randomized on every forward call, and scaled and shifted to maintain zero mean and unit standard deviation.

During evaluation the module simply computes an identity function.

More details can be found in the paper Self-Normalizing Neural Networks .

Parameters: p (float) – probability of an element to be dropped. Default: 0.5
Shape:
• Input: Any. Input can be of any shape
• Output: Same. Output is of the same shape as input

Examples:

>>> m = nn.AlphaDropout(p=0.2)
>>> input = torch.randn(20, 16)
>>> output = m(input)


## Sparse layers¶

### Embedding¶

class torch.nn.Embedding(num_embeddings, embedding_dim, padding_idx=None, max_norm=None, norm_type=2, scale_grad_by_freq=False, sparse=False, _weight=None)[source]

A simple lookup table that stores embeddings of a fixed dictionary and size.

This module is often used to store word embeddings and retrieve them using indices. The input to the module is a list of indices, and the output is the corresponding word embeddings.

Parameters: num_embeddings (int) – size of the dictionary of embeddings embedding_dim (int) – the size of each embedding vector padding_idx (int, optional) – If given, pads the output with the embedding vector at padding_idx (initialized to zeros) whenever it encounters the index. max_norm (float, optional) – If given, will renormalize the embeddings to always have a norm lesser than this norm_type (float, optional) – The p of the p-norm to compute for the max_norm option scale_grad_by_freq (bool, optional) – if given, this will scale gradients by the frequency of the words in the mini-batch. sparse (bool, optional) – if True, gradient w.r.t. weight matrix will be a sparse tensor. See Notes for more details regarding sparse gradients. weight (Tensor) – the learnable weights of the module of shape (num_embeddings, embedding_dim)
Shape:
• Input: LongTensor of arbitrary shape containing the indices to extract
• Output: (*, embedding_dim), where * is the input shape

Note

Keep in mind that only a limited number of optimizers support sparse gradients: currently it’s optim.SGD (CUDA and CPU), optim.SparseAdam (CUDA and CPU) and optim.Adagrad (CPU)

Note

With padding_idx set, the embedding vector at padding_idx is initialized to all zeros. However, note that this vector can be modified afterwards, e.g., using a customized initialization method, and thus changing the vector used to pad the output. The gradient for this vector from Embedding is always zero.

Examples:

>>> # an Embedding module containing 10 tensors of size 3
>>> embedding = nn.Embedding(10, 3)
>>> # a batch of 2 samples of 4 indices each
>>> input = torch.LongTensor([[1,2,4,5],[4,3,2,9]])
>>> embedding(input)
tensor([[[-0.0251, -1.6902,  0.7172],
[-0.6431,  0.0748,  0.6969],
[ 1.4970,  1.3448, -0.9685],
[-0.3677, -2.7265, -0.1685]],

[[ 1.4970,  1.3448, -0.9685],
[ 0.4362, -0.4004,  0.9400],
[-0.6431,  0.0748,  0.6969],
[ 0.9124, -2.3616,  1.1151]]])

>>> # example with padding_idx
>>> embedding = nn.Embedding(10, 3, padding_idx=0)
>>> input = torch.LongTensor([[0,2,0,5]])
>>> embedding(input)
tensor([[[ 0.0000,  0.0000,  0.0000],
[ 0.1535, -2.0309,  0.9315],
[ 0.0000,  0.0000,  0.0000],
[-0.1655,  0.9897,  0.0635]]])

classmethod from_pretrained(embeddings, freeze=True)[source]

Creates Embedding instance from given 2-dimensional FloatTensor.

Parameters: embeddings (Tensor) – FloatTensor containing weights for the Embedding. First dimension is being passed to Embedding as ‘num_embeddings’, second as ‘embedding_dim’. freeze (boolean, optional) – If True, the tensor does not get updated in the learning process. Equivalent to embedding.weight.requires_grad = False. Default: True

Examples:

>>> # FloatTensor containing pretrained weights
>>> weight = torch.FloatTensor([[1, 2.3, 3], [4, 5.1, 6.3]])
>>> embedding = nn.Embedding.from_pretrained(weight)
>>> # Get embeddings for index 1
>>> input = torch.LongTensor([1])
>>> embedding(input)
tensor([[ 4.0000,  5.1000,  6.3000]])


### EmbeddingBag¶

class torch.nn.EmbeddingBag(num_embeddings, embedding_dim, max_norm=None, norm_type=2, scale_grad_by_freq=False, mode='mean', sparse=False)[source]

Computes sums or means of ‘bags’ of embeddings, without instantiating the intermediate embeddings.

For bags of constant length,
• nn.EmbeddingBag with mode=sum is equivalent to nn.Embedding followed by torch.sum(dim=1)
• with mode=mean is equivalent to nn.Embedding followed by torch.mean(dim=1)

However, nn.EmbeddingBag is much more time and memory efficient than using a chain of these operations.

Parameters: num_embeddings (int) – size of the dictionary of embeddings embedding_dim (int) – the size of each embedding vector max_norm (float, optional) – If given, will renormalize the embeddings to always have a norm lesser than this norm_type (float, optional) – The p of the p-norm to compute for the max_norm option scale_grad_by_freq (bool, optional) – if given, this will scale gradients by the frequency of the words in the dictionary. mode (string, optional) – ‘sum’ | ‘mean’. Specifies the way to reduce the bag. Default: ‘mean’ sparse (bool, optional) – if True, gradient w.r.t. weight matrix will be a sparse tensor. See Notes for more details regarding sparse gradients. weight (Tensor) – the learnable weights of the module of shape (num_embeddings, embedding_dim)
Inputs: input, offsets
• input (N or B x N): LongTensor containing the indices of the embeddings
to extract. When input is 1D Tensor of shape N, an offsets Tensor is given, that contains the starting position of each new sequence in the mini-batch.
• offsets (B or None): LongTensor containing the starting positions of
each sample in a mini-batch of variable length sequences. If input is 2D (B x N), then offsets does not need to be given, as the input is treated as a mini-batch of fixed length sequences of length N each.
Shape:
• Input: LongTensor N, N = number of embeddings to extract
(or) LongTensor B x N, B = number of sequences in mini-batch,
N = number of embeddings per sequence
• Offsets: LongTensor B, B = number of bags. The values are the
offsets in input for each bag, i.e. the cumsum of lengths. Offsets is not given if Input is 2D B x N Tensor, the input is considered to be of fixed-length sequences
• Output: (B, embedding_dim)

Examples:

>>> # an Embedding module containing 10 tensors of size 3
>>> embedding_sum = nn.EmbeddingBag(10, 3, mode='sum')
>>> # a batch of 2 samples of 4 indices each
>>> input = torch.LongTensor([1,2,4,5,4,3,2,9])
>>> offsets = torch.LongTensor([0,4])
>>> embedding_sum(input, offsets)
tensor([[-0.8861, -5.4350, -0.0523],
[ 1.1306, -2.5798, -1.0044]])


## Distance functions¶

### CosineSimilarity¶

class torch.nn.CosineSimilarity(dim=1, eps=1e-08)[source]

Returns cosine similarity between $$x_1$$ and $$x_2$$, computed along dim.

$\text{similarity} = \dfrac{x_1 \cdot x_2}{\max(\Vert x_1 \Vert _2 \cdot \Vert x_2 \Vert _2, \epsilon)}$
Parameters: dim (int, optional) – Dimension where cosine similarity is computed. Default: 1 eps (float, optional) – Small value to avoid division by zero. Default: 1e-8
Shape:
• Input1: $$(\ast_1, D, \ast_2)$$ where D is at position dim
• Input2: $$(\ast_1, D, \ast_2)$$, same shape as the Input1
• Output: $$(\ast_1, \ast_2)$$

Examples:

>>> input1 = torch.randn(100, 128)
>>> input2 = torch.randn(100, 128)
>>> cos = nn.CosineSimilarity(dim=1, eps=1e-6)
>>> output = cos(input1, input2)


### PairwiseDistance¶

class torch.nn.PairwiseDistance(p=2, eps=1e-06, keepdim=False)[source]

Computes the batchwise pairwise distance between vectors $$v_1$$,:math:v_2 using the p-norm:

$\Vert x \Vert _p := \left( \sum_{i=1}^n \vert x_i \vert ^ p \right) ^ {1/p}$
Parameters: p (real) – the norm degree. Default: 2 eps (float, optional) – Small value to avoid division by zero. Default: 1e-6 keepdim (bool, optional) – Determines whether or not to keep the batch dimension. Default: False
Shape:
• Input1: $$(N, D)$$ where D = vector dimension
• Input2: $$(N, D)$$, same shape as the Input1
• Output: $$(N)$$. If keepdim is False, then $$(N, 1)$$.

Examples:

>>> pdist = nn.PairwiseDistance(p=2)
>>> input1 = torch.randn(100, 128)
>>> input2 = torch.randn(100, 128)
>>> output = pdist(input1, input2)


## Loss functions¶

### L1Loss¶

class torch.nn.L1Loss(size_average=True, reduce=True)[source]

Creates a criterion that measures the mean absolute value of the element-wise difference between input x and target y:

The loss can be described as:

$\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = \left| x_n - y_n \right|,$

where $$N$$ is the batch size. If reduce is True, then:

$\begin{split}\ell(x, y) = \begin{cases} \operatorname{mean}(L), & \text{if}\; \text{size_average} = \text{True},\\ \operatorname{sum}(L), & \text{if}\; \text{size_average} = \text{False}. \end{cases}\end{split}$

x and y arbitrary shapes with a total of n elements each.

The sum operation still operates over all the elements, and divides by n.

The division by n can be avoided if one sets the constructor argument size_average=False.

Parameters: size_average (bool, optional) – By default, the losses are averaged over observations for each minibatch. However, if the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True reduce (bool, optional) – By default, the losses are averaged or summed for each minibatch. When reduce is False, the loss function returns a loss per input/target element instead and ignores size_average. Default: True
Shape:
• Input: $$(N, *)$$ where * means, any number of additional dimensions
• Target: $$(N, *)$$, same shape as the input
• Output: scalar. If reduce is False, then $$(N, *)$$, same shape as the input

Examples:

>>> loss = nn.L1Loss()
>>> input = torch.randn(3, 5, requires_grad=True)
>>> target = torch.randn(3, 5)
>>> output = loss(input, target)
>>> output.backward()


### MSELoss¶

class torch.nn.MSELoss(size_average=True, reduce=True)[source]

Creates a criterion that measures the mean squared error between n elements in the input x and target y.

The loss can be described as:

$\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = \left( x_n - y_n \right)^2,$

where $$N$$ is the batch size. If reduce is True, then:

$\begin{split}\ell(x, y) = \begin{cases} \operatorname{mean}(L), & \text{if}\; \text{size_average} = \text{True},\\ \operatorname{sum}(L), & \text{if}\; \text{size_average} = \text{False}. \end{cases}\end{split}$

The sum operation still operates over all the elements, and divides by n.

The division by n can be avoided if one sets size_average to False.

To get a batch of losses, a loss per batch element, set reduce to False. These losses are not averaged and are not affected by size_average.

Parameters: size_average (bool, optional) – By default, the losses are averaged over observations for each minibatch. However, if the field size_average is set to False, the losses are instead summed for each minibatch. Only applies when reduce is True. Default: True reduce (bool, optional) – By default, the losses are averaged over observations for each minibatch, or summed, depending on size_average. When reduce is False, returns a loss per input/target element instead and ignores size_average. Default: True
Shape:
• Input: $$(N, *)$$ where * means, any number of additional dimensions
• Target: $$(N, *)$$, same shape as the input

Examples:

>>> loss = nn.MSELoss()
>>> input = torch.randn(3, 5, requires_grad=True)
>>> target = torch.randn(3, 5)
>>> output = loss(input, target)
>>> output.backward()


### CrossEntropyLoss¶

class torch.nn.CrossEntropyLoss(weight=None, size_average=True, ignore_index=-100, reduce=True)[source]

This criterion combines nn.LogSoftmax() and nn.NLLLoss() in one single class.

It is useful when training a classification problem with C classes. If provided, the optional argument weight should be a 1D Tensor assigning weight to each of the classes. This is particularly useful when you have an unbalanced training set.

The input is expected to contain scores for each class.

input has to be a Tensor of size either $$(minibatch, C)$$ or $$(minibatch, C, d_1, d_2, ..., d_K)$$ with $$K \geq 2$$ for the K-dimensional case (described later).

This criterion expects a class index (0 to C-1) as the target for each value of a 1D tensor of size minibatch

The loss can be described as:

$\text{loss}(x, class) = -\log\left(\frac{\exp(x[class])}{\sum_j \exp(x[j])}\right) = -x[class] + \log\left(\sum_j \exp(x[j])\right)$

or in the case of the weight argument being specified:

$\text{loss}(x, class) = weight[class] \left(-x[class] + \log\left(\sum_j \exp(x[j])\right)\right)$

The losses are averaged across observations for each minibatch.

Can also be used for higher dimension inputs, such as 2D images, by providing an input of size $$(minibatch, C, d_1, d_2, ..., d_K)$$ with $$K \geq 2$$, where $$K$$ is the number of dimensions, and a target of appropriate shape (see below).

Parameters: weight (Tensor, optional) – a manual rescaling weight given to each class. If given, has to be a Tensor of size C size_average (bool, optional) – By default, the losses are averaged over observations for each minibatch. However, if the field size_average is set to False, the losses are instead summed for each minibatch. Ignored if reduce is False. ignore_index (int, optional) – Specifies a target value that is ignored and does not contribute to the input gradient. When size_average is True, the loss is averaged over non-ignored targets. reduce (bool, optional) – By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch instead and ignores size_average. Default: True
Shape:
• Input: $$(N, C)$$ where C = number of classes, or
$$(N, C, d_1, d_2, ..., d_K)$$ with $$K \geq 2$$ in the case of K-dimensional loss.
• Target: $$(N)$$ where each value is $$0 \leq \text{targets}[i] \leq C-1$$, or
$$(N, d_1, d_2, ..., d_K)$$ with $$K \geq 2$$ in the case of K-dimensional loss.
• Output: scalar. If reduce is False, then the same size
as the target: $$(N)$$, or $$(N, d_1, d_2, ..., d_K)$$ with $$K \geq 2$$ in the case of K-dimensional loss.

Examples:

>>> loss = nn.CrossEntropyLoss()
>>> input = torch.randn(3, 5, requires_grad=True)
>>> target = torch.empty(3, dtype=torch.long).random_(5)
>>> output = loss(input, target)
>>> output.backward()


### NLLLoss¶

class torch.nn.NLLLoss(weight=None, size_average=True, ignore_index=-100, reduce=True)[source]

The negative log likelihood loss. It is useful to train a classification problem with C classes.

If provided, the optional argument weight should be a 1D Tensor assigning weight to each of the classes. This is particularly useful when you have an unbalanced training set.

The input given through a forward call is expected to contain log-probabilities of each class. input has to be a Tensor of size either $$(minibatch, C)$$ or $$(minibatch, C, d_1, d_2, ..., d_K)$$ with $$K \geq 2$$ for the K-dimensional case (described later).

Obtaining log-probabilities in a neural network is easily achieved by adding a LogSoftmax layer in the last layer of your network. You may use CrossEntropyLoss instead, if you prefer not to add an extra layer.

The target that this loss expects is a class index (0 to C-1, where C = number of classes)

If reduce is False, the loss can be described as:

$\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = - w_{y_n} x_{n,y_n}, \quad w_{c} = \text{weight}[c] \cdot \mathbb{1}\{c \not= \text{ignore_index}\},$

where $$N$$ is the batch size. If reduce is True (default), then

$\begin{split}\ell(x, y) = \begin{cases} \sum_{n=1}^N \frac{1}{\sum_{n=1}^N w_{y_n}} l_n, & \text{if}\; \text{size_average} = \text{True},\\ \sum_{n=1}^N l_n, & \text{if}\; \text{size_average} = \text{False}. \end{cases}\end{split}$

Can also be used for higher dimension inputs, such as 2D images, by providing an input of size $$(minibatch, C, d_1, d_2, ..., d_K)$$ with $$K \geq 2$$, where $$K$$ is the number of dimensions, and a target of appropriate shape (see below). In the case of images, it computes NLL loss per-pixel.

Parameters: weight (Tensor, optional) – a manual rescaling weight given to each class. If given, it has to be a Tensor of size C. Otherwise, it is treated as if having all ones. size_average (bool, optional) – By default, the losses are averaged over observations for each minibatch with weights set by weight. However, if the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True ignore_index (int, optional) – Specifies a target value that is ignored and does not contribute to the input gradient. When size_average is True, the loss is averaged over non-ignored targets. reduce (bool, optional) – By default, the losses are averaged or summed for each minibatch. When reduce is False, the loss function returns a loss per batch instead and ignores size_average. Default: True
Shape:
• Input: $$(N, C)$$ where C = number of classes, or
$$(N, C, d_1, d_2, ..., d_K)$$ with $$K \geq 2$$ in the case of K-dimensional loss.
• Target: $$(N)$$ where each value is $$0 \leq \text{targets}[i] \leq C-1$$, or
$$(N, d_1, d_2, ..., d_K)$$ with $$K \geq 2$$ in the case of K-dimensional loss.
• Output: scalar. If reduce is False, then the same size
as the target: $$(N)$$, or $$(N, d_1, d_2, ..., d_K)$$ with $$K \geq 2$$ in the case of K-dimensional loss.

Examples:

>>> m = nn.LogSoftmax()
>>> loss = nn.NLLLoss()
>>> # input is of size N x C = 3 x 5
>>> input = torch.randn(3, 5, requires_grad=True)
>>> # each element in target has to have 0 <= value < C
>>> target = torch.tensor([1, 0, 4])
>>> output = loss(m(input), target)
>>> output.backward()
>>>
>>>
>>> # 2D loss example (used, for example, with image inputs)
>>> N, C = 5, 4
>>> loss = nn.NLLLoss()
>>> # input is of size N x C x height x width
>>> data = torch.randn(N, 16, 10, 10)
>>> m = nn.Conv2d(16, C, (3, 3))
>>> # each element in target has to have 0 <= value < C
>>> target = torch.tensor(N, 8, 8).random_(0, C)
>>> output = loss(m(data), target)
>>> output.backward()


### PoissonNLLLoss¶

class torch.nn.PoissonNLLLoss(log_input=True, full=False, size_average=True, eps=1e-08, reduce=True)[source]

Negative log likelihood loss with Poisson distribution of target.

The loss can be described as:

\begin{align}\begin{aligned}\text{target} \sim \mathrm{Poisson}(\text{input})\\\text{loss}(\text{input}, \text{target}) = \text{input} - \text{target} * \log(\text{input}) + \log(\text{target!})\end{aligned}\end{align}

The last term can be omitted or approximated with Stirling formula. The approximation is used for target values more than 1. For targets less or equal to 1 zeros are added to the loss.

Parameters: log_input (bool, optional) – if True the loss is computed as $$\exp(\text{input}) - \text{target}*\text{input}$$, if False the loss is $$\text{input} - \text{target}*\log(\text{input}+\text{eps})$$. full (bool, optional) – whether to compute full loss, i. e. to add the Stirling approximation term $\text{target}*\log(\text{target}) - \text{target} + 0.5 * \log(2\pi\text{target}).$ size_average (bool, optional) – By default, the losses are averaged over observations for each minibatch. However, if the field size_average is set to False, the losses are instead summed for each minibatch. eps (float, optional) – Small value to avoid evaluation of $$\log(0)$$ when log_input == False. Default: 1e-8 reduce (bool, optional) – By default, the losses are averaged over observations for each minibatch, or summed, depending on size_average. When reduce is False, returns a loss per input/target element instead and ignores size_average. Default: True

Examples:

>>> loss = nn.PoissonNLLLoss()
>>> log_input = torch.randn(5, 2, requires_grad=True)
>>> target = torch.randn(5, 2)
>>> output = loss(log_input, target)
>>> output.backward()


### KLDivLoss¶

class torch.nn.KLDivLoss(size_average=True, reduce=True)[source]

The Kullback-Leibler divergence Loss

KL divergence is a useful distance measure for continuous distributions and is often useful when performing direct regression over the space of (discretely sampled) continuous output distributions.

As with NLLLoss, the input given is expected to contain log-probabilities, however unlike ClassNLLLoss, input is not restricted to a 2D Tensor, because the criterion is applied element-wise.

This criterion expects a target Tensor of the same size as the input Tensor.

The loss can be described as:

$\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = y_n \odot \left( \log y_n - x_n \right),$

where $$N$$ is the batch size. If reduce is True, then:

$\begin{split}\ell(x, y) = \begin{cases} \operatorname{mean}(L), & \text{if}\; \text{size_average} = \text{True},\\ \operatorname{sum}(L), & \text{if}\; \text{size_average} = \text{False}. \end{cases}\end{split}$

By default, the losses are averaged for each minibatch over observations as well as over dimensions. However, if the field size_average is set to False, the losses are instead summed.

Parameters: (bool, optional (size_average) – By default, the losses are averaged for each minibatch over observations as well as over dimensions. However, if False the losses are instead summed. reduce (bool, optional) – By default, the losses are averaged over observations for each minibatch, or summed, depending on size_average. When reduce is False, returns a loss per input/target element instead and ignores size_average. Default: True
Shape:
• input: $$(N, *)$$ where * means, any number of additional dimensions
• target: $$(N, *)$$, same shape as the input
• output: scalar. If reduce is True, then $$(N, *)$$,
same shape as the input

### BCELoss¶

class torch.nn.BCELoss(weight=None, size_average=True, reduce=True)[source]

Creates a criterion that measures the Binary Cross Entropy between the target and the output:

The loss can be described as:

$\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = - w_n \left[ y_n \cdot \log x_n + (1 - y_n) \cdot \log (1 - x_n) \right],$

where $$N$$ is the batch size. If reduce is True, then

$\begin{split}\ell(x, y) = \begin{cases} \operatorname{mean}(L), & \text{if}\; \text{size_average} = \text{True},\\ \operatorname{sum}(L), & \text{if}\; \text{size_average} = \text{False}. \end{cases}\end{split}$

This is used for measuring the error of a reconstruction in for example an auto-encoder. Note that the targets y should be numbers between 0 and 1.

Parameters: weight (Tensor, optional) – a manual rescaling weight given to the loss of each batch element. If given, has to be a Tensor of size “nbatch”. size_average (bool, optional) – By default, the losses are averaged over observations for each minibatch. However, if the field size_average is set to False, the losses are instead summed for each minibatch. Default: True reduce (bool, optional) – By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per input/target element instead and ignores size_average. Default: True
Shape:
• Input: $$(N, *)$$ where * means, any number of additional dimensions
• Target: $$(N, *)$$, same shape as the input
• Output: scalar. If reduce is False, then (N, *), same shape as input.

Examples:

>>> m = nn.Sigmoid()
>>> loss = nn.BCELoss()
>>> input = torch.randn(3, requires_grad=True)
>>> target = torch.empty(3).random_(2)
>>> output = loss(m(input), target)
>>> output.backward()


### BCEWithLogitsLoss¶

class torch.nn.BCEWithLogitsLoss(weight=None, size_average=True, reduce=True)[source]

This loss combines a Sigmoid layer and the BCELoss in one single class. This version is more numerically stable than using a plain Sigmoid followed by a BCELoss as, by combining the operations into one layer, we take advantage of the log-sum-exp trick for numerical stability.

The loss can be described as:

$\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = - w_n \left[ t_n \cdot \log \sigma(x_n) + (1 - t_n) \cdot \log (1 - \sigma(x_n)) \right],$

where $$N$$ is the batch size. If reduce is True, then

$\begin{split}\ell(x, y) = \begin{cases} \operatorname{mean}(L), & \text{if}\; \text{size_average} = \text{True},\\ \operatorname{sum}(L), & \text{if}\; \text{size_average} = \text{False}. \end{cases}\end{split}$

This is used for measuring the error of a reconstruction in for example an auto-encoder. Note that the targets t[i] should be numbers between 0 and 1.

Parameters: weight (Tensor, optional) – a manual rescaling weight given to the loss of each batch element. If given, has to be a Tensor of size “nbatch”. size_average (bool, optional) – By default, the losses are averaged over observations for each minibatch. However, if the field size_average is set to False, the losses are instead summed for each minibatch. Default: True reduce – By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per input/target element instead and ignores size_average. Default: True

### MarginRankingLoss¶

class torch.nn.MarginRankingLoss(margin=0, size_average=True, reduce=True)[source]

Creates a criterion that measures the loss given inputs x1, x2, two 1D mini-batch Tensors, and a label 1D mini-batch tensor y with values (1 or -1).

If y == 1 then it assumed the first input should be ranked higher (have a larger value) than the second input, and vice-versa for y == -1.

The loss function for each sample in the mini-batch is:

$\text{loss}(x, y) = \max(0, -y * (x1 - x2) + \text{margin})$
Parameters: margin (float, optional) – Has a default value of 0. size_average (bool, optional) – By default, the losses are averaged over observations for each minibatch. However, if the field size_average is set to False, the losses are instead summed for each minibatch. Default: True reduce (bool, optional) – By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
Shape:
• Input: $$(N, D)$$ where N is the batch size and D is the size of a sample.
• Target: $$(N)$$
• Output: scalar. If reduce is False, then (N).

### HingeEmbeddingLoss¶

class torch.nn.HingeEmbeddingLoss(margin=1.0, size_average=True, reduce=True)[source]

Measures the loss given an input tensor x and a labels tensor y containing values (1 or -1). This is usually used for measuring whether two inputs are similar or dissimilar, e.g. using the L1 pairwise distance as x, and is typically used for learning nonlinear embeddings or semi-supervised learning:

The loss function for $$n$$-th sample in the mini-batch is:

$\begin{split}l_n = \begin{cases} x_n, & \text{if}\; y_n = 1,\\ \max \{0, \Delta - x_n\}, & \text{if}\; y_n = -1, \end{cases}\end{split}$

and the total loss functions is

$\begin{split}\ell(x, y) = \begin{cases} \operatorname{mean}(L), & \text{if}\; \text{size_average} = \text{True},\\ \operatorname{sum}(L), & \text{if}\; \text{size_average} = \text{False}. \end{cases}\end{split}$

where $$L = \{l_1,\dots,l_N\}^\top$$.

Parameters: margin (float, optional) – Has a default value of 1. size_average (bool, optional) – By default, the losses are averaged over observations for each minibatch. However, if the field size_average is set to False, the losses are instead summed for each minibatch. Default: True reduce (bool, optional) – By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
Shape:
• Input: Tensor of arbitrary shape. The sum operation operates over all the elements.
• Target: Same shape as input.
• Output: scalar. If reduce is False, then same shape as the input

### MultiLabelMarginLoss¶

class torch.nn.MultiLabelMarginLoss(size_average=True, reduce=True)[source]

Creates a criterion that optimizes a multi-class multi-classification hinge loss (margin-based loss) between input x (a 2D mini-batch Tensor) and output y (which is a 2D Tensor of target class indices). For each sample in the mini-batch:

$\text{loss}(x, y) = \sum_{ij}\frac{\max(0, 1 - (x[y[j]] - x[i]))}{\text{x.size}(0)}$

where i == 0 to x.size(0), j == 0 to y.size(0), $$y[j] \geq 0$$, and $$i \neq y[j]$$ for all i and j.

y and x must have the same size.

The criterion only considers a contiguous block of non-negative targets that starts at the front.

This allows for different samples to have variable amounts of target classes

Parameters: size_average (bool, optional) – By default, the losses are averaged over observations for each minibatch. However, if the field size_average is set to False, the losses are instead summed for each minibatch. Default: True reduce (bool, optional) – By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
Shape:
• Input: $$(C)$$ or $$(N, C)$$ where N is the batch size and C is the number of classes.
• Target: $$(C)$$ or $$(N, C)$$, same shape as the input.
• Output: scalar. If reduce is False, then (N).

### SmoothL1Loss¶

class torch.nn.SmoothL1Loss(size_average=True, reduce=True)[source]

Creates a criterion that uses a squared term if the absolute element-wise error falls below 1 and an L1 term otherwise. It is less sensitive to outliers than the MSELoss and in some cases prevents exploding gradients (e.g. see “Fast R-CNN” paper by Ross Girshick). Also known as the Huber loss:

$\text{loss}(x, y) = \frac{1}{n} \sum_{i} z_{i}$

where $$z_{i}$$ is given by:

$\begin{split}z_{i} = \begin{cases} 0.5 (x_i - y_i)^2, & \text{if } |x_i - y_i| < 1 \\ |x_i - y_i| - 0.5, & \text{otherwise } \end{cases}\end{split}$

x and y arbitrary shapes with a total of n elements each the sum operation still operates over all the elements, and divides by n.

The division by n can be avoided if one sets size_average to False

Parameters: size_average (bool, optional) – By default, the losses are averaged over all elements. However, if the field size_average is set to False, the losses are instead summed. Ignored when reduce is False. Default: True reduce (bool, optional) – By default, the losses are averaged or summed over elements. When reduce is False, the loss function returns a loss per input/target element instead and ignores size_average. Default: True
Shape:
• Input: $$(N, *)$$ where * means, any number of additional dimensions
• Target: $$(N, *)$$, same shape as the input
• Output: scalar. If reduce is False, then $$(N, *)$$, same shape as the input

### SoftMarginLoss¶

class torch.nn.SoftMarginLoss(size_average=True, reduce=True)[source]

Creates a criterion that optimizes a two-class classification logistic loss between input tensor x and target tensor y (containing 1 or -1).

$\text{loss}(x, y) = \sum_i \frac{\log(1 + \exp(-y[i]*x[i]))}{\text{x.nelement}()}$
Parameters: size_average (bool, optional) – By default, the losses are averaged over observations for each minibatch. However, if the field size_average is set to False, the losses are instead summed for each minibatch. Default: True reduce (bool, optional) – By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
Shape:
• Input: Tensor of arbitrary shape.
• Target: Same shape as input.
• Output: scalar. If reduce is False, then same shape as the input

### MultiLabelSoftMarginLoss¶

class torch.nn.MultiLabelSoftMarginLoss(weight=None, size_average=True, reduce=True)[source]

Creates a criterion that optimizes a multi-label one-versus-all loss based on max-entropy, between input x and target y of size (N, C). For each sample in the minibatch:

$loss(x, y) = - \sum_i y[i] * \log((1 + \exp(-x[i]))^{-1}) + (1-y[i]) * \log\left(\frac{\exp(-x[i])}{(1 + \exp(-x[i]))}\right)$

where i == 0 to x.nElement()-1, y[i] in {0,1}.

Parameters: weight (Tensor, optional) – a manual rescaling weight given to each class. If given, it has to be a Tensor of size C. Otherwise, it is treated as if having all ones. size_average (bool, optional) – By default, the losses are averaged over observations for each minibatch. However, if the field size_average is set to False, the losses are instead summed for each minibatch. Default: True reduce (bool, optional) – By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
Shape:
• Input: $$(N, C)$$ where N is the batch size and C is the number of classes.
• Target: $$(N, C)$$, same shape as the input.
• Output: scalar. If reduce is False, then (N).

### CosineEmbeddingLoss¶

class torch.nn.CosineEmbeddingLoss(margin=0, size_average=True, reduce=True)[source]

Creates a criterion that measures the loss given input tensors $$x_1$$, $$x_2$$ and a Tensor label y with values 1 or -1. This is used for measuring whether two inputs are similar or dissimilar, using the cosine distance, and is typically used for learning nonlinear embeddings or semi-supervised learning.

The loss function for each sample is:

$\begin{split}\text{loss}(x, y) = \begin{cases} 1 - \cos(x_1, x_2), & \text{if } y == 1 \\ \max(0, \cos(x_1, x_2) - \text{margin}), & \text{if } y == -1 \end{cases}\end{split}$
Parameters: margin (float, optional) – Should be a number from -1 to 1, 0 to 0.5 is suggested. If margin is missing, the default value is 0. size_average (bool, optional) – By default, the losses are averaged over observations for each minibatch. However, if the field size_average is set to False, the losses are instead summed for each minibatch. Default: True reduce (bool, optional) – By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True

### MultiMarginLoss¶

class torch.nn.MultiMarginLoss(p=1, margin=1, weight=None, size_average=True, reduce=True)[source]

Creates a criterion that optimizes a multi-class classification hinge loss (margin-based loss) between input x (a 2D mini-batch Tensor) and output y (which is a 1D tensor of target class indices, $$0 \leq y \leq \text{x.size}(1)$$):

For each mini-batch sample, the loss in terms of the 1D input x and scalar output y is:

$\text{loss}(x, y) = \frac{\sum_i \max(0, \text{margin} - x[y] + x[i]))^p}{\text{x.size}(0)}$

where i == 0 to x.size(0) and $$i \neq y$$.

Optionally, you can give non-equal weighting on the classes by passing a 1D weight tensor into the constructor.

The loss function then becomes:

$\text{loss}(x, y) = \frac{\sum_i \max(0, w[y] * (\text{margin} - x[y] - x[i]))^p)}{\text{x.size}(0)}$
Parameters: p (int, optional) – Has a default value of 1. 1 and 2 are the only supported values margin (float, optional) – Has a default value of 1. weight (Tensor, optional) – a manual rescaling weight given to each class. If given, it has to be a Tensor of size C. Otherwise, it is treated as if having all ones. size_average (bool, optional) – By default, the losses are averaged over observations for each minibatch. However, if the field size_average is set to False, the losses are instead summed for each minibatch. Default: True reduce (bool, optional) – By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True

### TripletMarginLoss¶

class torch.nn.TripletMarginLoss(margin=1.0, p=2, eps=1e-06, swap=False, size_average=True, reduce=True)[source]

Creates a criterion that measures the triplet loss given an input tensors x1, x2, x3 and a margin with a value greater than 0. This is used for measuring a relative similarity between samples. A triplet is composed by a, p and n: anchor, positive examples and negative example respectively. The shapes of all input tensors should be $$(N, D)$$.

The distance swap is described in detail in the paper Learning shallow convolutional feature descriptors with triplet losses by V. Balntas, E. Riba et al.

The loss function for each sample in the mini-batch is:

$L(a, p, n) = \max \{d(a_i, p_i) - d(a_i, n_i) + {\rm margin}, 0\}$

where $$d(x_i, y_i) = \left\lVert {\bf x}_i - {\bf y}_i \right\rVert_p$$.

Parameters: margin (float, optional) – Default: 1. p (int, optional) – The norm degree for pairwise distance. Default: 2. swap (float, optional) – The distance swap is described in detail in the paper Learning shallow convolutional feature descriptors with triplet losses by V. Balntas, E. Riba et al. Default: False. size_average (bool, optional) – By default, the losses are averaged over observations for each minibatch. However, if the field size_average is set to False, the losses are instead summed for each minibatch. Default: True reduce (bool, optional) – By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True
Shape:
• Input: $$(N, D)$$ where D is the vector dimension.
• Output: scalar. If reduce is False, then (N).
>>> triplet_loss = nn.TripletMarginLoss(margin=1.0, p=2)
>>> input1 = torch.randn(100, 128, requires_grad=True)
>>> input2 = torch.randn(100, 128, requires_grad=True)
>>> input3 = torch.randn(100, 128, requires_grad=True)
>>> output = triplet_loss(input1, input2, input3)
>>> output.backward()


## Vision layers¶

### PixelShuffle¶

class torch.nn.PixelShuffle(upscale_factor)[source]

Rearranges elements in a Tensor of shape $$(*, r^2C, H, W)$$ to a tensor of shape $$(C, rH, rW)$$.

This is useful for implementing efficient sub-pixel convolution with a stride of $$1/r$$.

Look at the paper: Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network by Shi et. al (2016) for more details

Parameters: upscale_factor (int) – factor to increase spatial resolution by
Shape:
• Input: $$(N, C * \text{upscale_factor}^2, H, W)$$
• Output: $$(N, C, H * \text{upscale_factor}, W * \text{upscale_factor})$$

Examples:

>>> ps = nn.PixelShuffle(3)
>>> input = torch.tensor(1, 9, 4, 4)
>>> output = ps(input)
>>> print(output.size())
torch.Size([1, 1, 12, 12])


### Upsample¶

class torch.nn.Upsample(size=None, scale_factor=None, mode='nearest', align_corners=None)[source]

Upsamples a given multi-channel 1D (temporal), 2D (spatial) or 3D (volumetric) data.

The input data is assumed to be of the form minibatch x channels x [optional depth] x [optional height] x width. Hence, for spatial inputs, we expect a 4D Tensor and for volumetric inputs, we expect a 5D Tensor.

The algorithms available for upsampling are nearest neighbor and linear, bilinear and trilinear for 3D, 4D and 5D input Tensor, respectively.

One can either give a scale_factor or the target output size to calculate the output size. (You cannot give both, as it is ambiguous)

Parameters: size (tuple, optional) – a tuple of ints ([optional D_out], [optional H_out], W_out) output sizes scale_factor (int / tuple of python:ints, optional) – the multiplier for the image height / width / depth mode (string, optional) – the upsampling algorithm: one of nearest, linear, bilinear and trilinear. Default: nearest align_corners (bool, optional) – if True, the corner pixels of the input and output tensors are aligned, and thus preserving the values at those pixels. This only has effect when mode is linear, bilinear, or trilinear. Default: False
Shape:
• Input: $$(N, C, W_{in})$$, $$(N, C, H_{in}, W_{in})$$ or $$(N, C, D_{in}, H_{in}, W_{in})$$

• Output: $$(N, C, W_{out})$$, $$(N, C, H_{out}, W_{out})$$ or $$(N, C, D_{out}, H_{out}, W_{out})$$, where

\begin{align}\begin{aligned}D_{out} = \left\lfloor D_{in} \times \text{scale_factor} \right\rfloor \text{ or size}[-3]\\H_{out} = \left\lfloor H_{in} \times \text{scale_factor} \right\rfloor \text{ or size}[-2]\\W_{out} = \left\lfloor W_{in} \times \text{scale_factor} \right\rfloor \text{ or size}[-1]\end{aligned}\end{align}

Warning

With align_corners = True, the linearly interpolating modes (linear, bilinear, and trilinear) don’t proportionally align the output and input pixels, and thus the output values can depend on the input size. This was the default behavior for these modes up to version 0.3.1. Since then, the default behavior is align_corners = False. See below for concrete examples on how this affects the outputs.

Examples:

>>> input = torch.arange(1, 5).view(1, 1, 2, 2)
>>> input
tensor([[[[ 1.,  2.],
[ 3.,  4.]]]])

>>> m = nn.Upsample(scale_factor=2, mode='nearest')
>>> m(input)
tensor([[[[ 1.,  1.,  2.,  2.],
[ 1.,  1.,  2.,  2.],
[ 3.,  3.,  4.,  4.],
[ 3.,  3.,  4.,  4.]]]])

>>> m = nn.Upsample(scale_factor=2, mode='bilinear')  # align_corners=False
>>> m(input)
tensor([[[[ 1.0000,  1.2500,  1.7500,  2.0000],
[ 1.5000,  1.7500,  2.2500,  2.5000],
[ 2.5000,  2.7500,  3.2500,  3.5000],
[ 3.0000,  3.2500,  3.7500,  4.0000]]]])

>>> m = nn.Upsample(scale_factor=2, mode='bilinear', align_corners=True)
>>> m(input)
tensor([[[[ 1.0000,  1.3333,  1.6667,  2.0000],
[ 1.6667,  2.0000,  2.3333,  2.6667],
[ 2.3333,  2.6667,  3.0000,  3.3333],
[ 3.0000,  3.3333,  3.6667,  4.0000]]]])

>>> # Try scaling the same data in a larger tensor
>>>
>>> input_3x3 = torch.zeros(3, 3).view(1, 1, 3, 3)
>>> input_3x3[:, :, :2, :2].copy_(input)
tensor([[[[ 1.,  2.],
[ 3.,  4.]]]])
>>> input_3x3
tensor([[[[ 1.,  2.,  0.],
[ 3.,  4.,  0.],
[ 0.,  0.,  0.]]]])

>>> m = nn.Upsample(scale_factor=2, mode='bilinear')  # align_corners=False
>>> # Notice that values in top left corner are the same with the small input (except at boundary)
>>> m(input_3x3)
tensor([[[[ 1.0000,  1.2500,  1.7500,  1.5000,  0.5000,  0.0000],
[ 1.5000,  1.7500,  2.2500,  1.8750,  0.6250,  0.0000],
[ 2.5000,  2.7500,  3.2500,  2.6250,  0.8750,  0.0000],
[ 2.2500,  2.4375,  2.8125,  2.2500,  0.7500,  0.0000],
[ 0.7500,  0.8125,  0.9375,  0.7500,  0.2500,  0.0000],
[ 0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000]]]])

>>> m = nn.Upsample(scale_factor=2, mode='bilinear', align_corners=True)
>>> # Notice that values in top left corner are now changed
>>> m(input_3x3)
tensor([[[[ 1.0000,  1.4000,  1.8000,  1.6000,  0.8000,  0.0000],
[ 1.8000,  2.2000,  2.6000,  2.2400,  1.1200,  0.0000],
[ 2.6000,  3.0000,  3.4000,  2.8800,  1.4400,  0.0000],
[ 2.4000,  2.7200,  3.0400,  2.5600,  1.2800,  0.0000],
[ 1.2000,  1.3600,  1.5200,  1.2800,  0.6400,  0.0000],
[ 0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000]]]])


### UpsamplingNearest2d¶

class torch.nn.UpsamplingNearest2d(size=None, scale_factor=None)[source]

Applies a 2D nearest neighbor upsampling to an input signal composed of several input channels.

To specify the scale, it takes either the size or the scale_factor as it’s constructor argument.

When size is given, it is the output size of the image (h, w).

Parameters: size (tuple, optional) – a tuple of ints (H_out, W_out) output sizes scale_factor (int, optional) – the multiplier for the image height or width

Warning

This class is deprecated in favor of Upsample.

Shape:
• Input: $$(N, C, H_{in}, W_{in})$$

• Output: $$(N, C, H_{out}, W_{out})$$ where

\begin{align}\begin{aligned}H_{out} = \left\lfloor H_{in} \times \text{scale_factor} \right\rfloor\\W_{out} = \left\lfloor W_{in} \times \text{scale_factor} \right\rfloor\end{aligned}\end{align}

Examples:

>>> input = torch.arange(1, 5).view(1, 1, 2, 2)
>>> input
tensor([[[[ 1.,  2.],
[ 3.,  4.]]]])

>>> m = nn.UpsamplingNearest2d(scale_factor=2)
>>> m(input)
tensor([[[[ 1.,  1.,  2.,  2.],
[ 1.,  1.,  2.,  2.],
[ 3.,  3.,  4.,  4.],
[ 3.,  3.,  4.,  4.]]]])


### UpsamplingBilinear2d¶

class torch.nn.UpsamplingBilinear2d(size=None, scale_factor=None)[source]

Applies a 2D bilinear upsampling to an input signal composed of several input channels.

To specify the scale, it takes either the size or the scale_factor as it’s constructor argument.

When size is given, it is the output size of the image (h, w).

Parameters: size (tuple, optional) – a tuple of ints (H_out, W_out) output sizes scale_factor (int, optional) – the multiplier for the image height or width

Warning

This class is deprecated in favor of Upsample. It is equivalent to nn.Upsample(..., mode='bilinear', align_corners=True).

Shape:
• Input: $$(N, C, H_{in}, W_{in})$$

• Output: $$(N, C, H_{out}, W_{out})$$ where

\begin{align}\begin{aligned}H_{out} = \left\lfloor H_{in} \times \text{scale_factor} \right\rfloor\\W_{out} = \left\lfloor W_{in} \times \text{scale_factor} \right\rfloor\end{aligned}\end{align}

Examples:

>>> input = torch.arange(1, 5).view(1, 1, 2, 2)
>>> input
tensor([[[[ 1.,  2.],
[ 3.,  4.]]]])

>>> m = nn.UpsamplingBilinear2d(scale_factor=2)
>>> m(input)
tensor([[[[ 1.0000,  1.3333,  1.6667,  2.0000],
[ 1.6667,  2.0000,  2.3333,  2.6667],
[ 2.3333,  2.6667,  3.0000,  3.3333],
[ 3.0000,  3.3333,  3.6667,  4.0000]]]])


## DataParallel layers (multi-GPU, distributed)¶

### DataParallel¶

class torch.nn.DataParallel(module, device_ids=None, output_device=None, dim=0)[source]

Implements data parallelism at the module level.

This container parallelizes the application of the given module by splitting the input across the specified devices by chunking in the batch dimension. In the forward pass, the module is replicated on each device, and each replica handles a portion of the input. During the backwards pass, gradients from each replica are summed into the original module.

The batch size should be larger than the number of GPUs used.

Arbitrary positional and keyword inputs are allowed to be passed into DataParallel EXCEPT Tensors. All tensors will be scattered on dim specified (default 0). Primitive types will be broadcasted, but all other types will be a shallow copy and can be corrupted if written to in the model’s forward pass.

Warning

Forward and backward hooks defined on module and its submodules will be invoked len(device_ids) times, each with inputs located on a particular device. Particularly, the hooks are only guaranteed to be executed in correct order with respect to operations on corresponding devices. For example, it is not guaranteed that hooks set via register_forward_pre_hook() be executed before all len(device_ids) forward() calls, but that each such hook be executed before the corresponding forward() call of that device.

Note

There is a subtlety in using the pack sequence -> recurrent network -> unpack sequence pattern in a Module wrapped in DataParallel. See My recurrent network doesn’t work with data parallelism section in FAQ for details.

Parameters: module – module to be parallelized device_ids – CUDA devices (default: all devices) output_device – device location of output (default: device_ids[0])

Example:

>>> net = torch.nn.DataParallel(model, device_ids=[0, 1, 2])
>>> output = net(input_var)


### DistributedDataParallel¶

class torch.nn.parallel.DistributedDataParallel(module, device_ids=None, output_device=None, dim=0, broadcast_buffers=True)[source]

Implements distributed data parallelism at the module level.

This container parallelizes the application of the given module by splitting the input across the specified devices by chunking in the batch dimension. The module is replicated on each machine and each device, and each such replica handles a portion of the input. During the backwards pass, gradients from each node are averaged.

The batch size should be larger than the number of GPUs used locally. It should also be an integer multiple of the number of GPUs so that each chunk is the same size (so that each GPU processes the same number of samples).

See also: Basics and Use nn.DataParallel instead of multiprocessing. The same constraints on input as in torch.nn.DataParallel apply.

Creation of this class requires the distributed package to be already initialized in the process group mode (see torch.distributed.init_process_group()).

Warning

This module works only with the nccl and gloo backends.

Warning

Constructor, forward method, and differentiation of the output (or a function of the output of this module) is a distributed synchronization point. Take that into account in case different processes might be executing different code.

Warning

This module assumes all parameters are registered in the model by the time it is created. No parameters should be added nor removed later. Same applies to buffers.

Warning

This module assumes all buffers and gradients are dense.

Warning

This module doesn’t work with torch.autograd.grad() (i.e. it will only work if gradients are to be accumulated in .grad attributes of parameters).

Warning

If you plan on using this module with a nccl backend or a gloo backend (that uses Infiniband), together with a DataLoader that uses multiple workers, please change the multiprocessing start method to forkserver (Python 3 only) or spawn. Unfortunately Gloo (that uses Infiniband) and NCCL2 are not fork safe, and you will likely experience deadlocks if you don’t change this setting.

Note

Parameters are never broadcast between processes. The module performs an all-reduce step on gradients and assumes that they will be modified by the optimizer in all processes in the same way. Buffers (e.g. BatchNorm stats) are broadcast from the module in process of rank 0, to all other replicas in the system in every iteration.

Warning

Forward and backward hooks defined on module and its submodules won’t be invoked anymore, unless the hooks are initialized in the forward() method.

Parameters: module – module to be parallelized device_ids – CUDA devices (default: all devices) output_device – device location of output (default: device_ids[0]) broadcast_buffers – flag that enables syncing (broadcasting) buffers of the module at beginning of the forward function. (default: True)

Example:

>>> torch.distributed.init_process_group(world_size=4, init_method='...')
>>> net = torch.nn.DistributedDataParallel(model)


## Utilities¶

torch.nn.utils.clip_grad_norm_(parameters, max_norm, norm_type=2)[source]

Clips gradient norm of an iterable of parameters.

The norm is computed over all gradients together, as if they were concatenated into a single vector. Gradients are modified in-place.

Parameters: parameters (Iterable[Tensor]) – an iterable of Tensors that will have gradients normalized max_norm (float or int) – max norm of the gradients norm_type (float or int) – type of the used p-norm. Can be 'inf' for infinity norm. Total norm of the parameters (viewed as a single vector).

torch.nn.utils.clip_grad_value_(parameters, clip_value)[source]

Clips gradient of an iterable of parameters at specified value.

Gradients are modified in-place.

Parameters: parameters (Iterable[Tensor]) – an iterable of Tensors that will have gradients normalized clip_value (float or int) – maximum allowed value of the gradients The gradients are clipped in the range [-clip_value, clip_value]

### weight_norm¶

torch.nn.utils.weight_norm(module, name='weight', dim=0)[source]

Applies weight normalization to a parameter in the given module.

$\mathbf{w} = g \dfrac{\mathbf{v}}{\|\mathbf{v}\|}$

Weight normalization is a reparameterization that decouples the magnitude of a weight tensor from its direction. This replaces the parameter specified by name (e.g. “weight”) with two parameters: one specifying the magnitude (e.g. “weight_g”) and one specifying the direction (e.g. “weight_v”). Weight normalization is implemented via a hook that recomputes the weight tensor from the magnitude and direction before every forward() call.

By default, with dim=0, the norm is computed independently per output channel/plane. To compute a norm over the entire weight tensor, use dim=None.

Parameters: module (nn.Module) – containing module name (str, optional) – name of weight parameter dim (int, optional) – dimension over which to compute the norm The original module with the weight norm hook

Example:

>>> m = weight_norm(nn.Linear(20, 40), name='weight')
Linear (20 -> 40)
>>> m.weight_g.size()
torch.Size([40, 1])
>>> m.weight_v.size()
torch.Size([40, 20])


### remove_weight_norm¶

torch.nn.utils.remove_weight_norm(module, name='weight')[source]

Removes the weight normalization reparameterization from a module.

Parameters: module (nn.Module) – containing module name (str, optional) – name of weight parameter

Example

>>> m = weight_norm(nn.Linear(20, 40))
>>> remove_weight_norm(m)


### PackedSequence¶

torch.nn.utils.rnn.PackedSequence(cls, *args)[source]

Holds the data and list of batch_sizes of a packed sequence.

All RNN modules accept packed sequences as inputs.

Note

Instances of this class should never be created manually. They are meant to be instantiated by functions like pack_padded_sequence().

Batch sizes represent the number elements at each sequence step in the batch, not the varying sequence lengths passed to pack_padded_sequence(). For instance, given data abc and x the PackedSequence would contain data axbc with batch_sizes=[2,1,1].

Variables: data (Tensor) – Tensor containing packed sequence batch_sizes (Tensor) – Tensor of integers holding information about the batch size at each sequence step

torch.nn.utils.rnn.pack_padded_sequence(input, lengths, batch_first=False)[source]

Packs a Tensor containing padded sequences of variable length.

Input can be of size T x B x * where T is the length of the longest sequence (equal to lengths[0]), B is the batch size, and * is any number of dimensions (including 0). If batch_first is True B x T x * inputs are expected.

The sequences should be sorted by length in a decreasing order, i.e. input[:,0] should be the longest sequence, and input[:,B-1] the shortest one.

Note

This function accepts any input that has at least two dimensions. You can apply it to pack the labels, and use the output of the RNN with them to compute the loss directly. A Tensor can be retrieved from a PackedSequence object by accessing its .data attribute.

Parameters: input (Tensor) – padded batch of variable length sequences. lengths (Tensor) – list of sequences lengths of each batch element. batch_first (bool, optional) – if True, the input is expected in B x T x * format. a PackedSequence object

torch.nn.utils.rnn.pad_packed_sequence(sequence, batch_first=False, padding_value=0.0, total_length=None)[source]

Pads a packed batch of variable length sequences.

It is an inverse operation to pack_padded_sequence().

The returned Tensor’s data will be of size T x B x *, where T is the length of the longest sequence and B is the batch size. If batch_first is True, the data will be transposed into B x T x * format.

Batch elements will be ordered decreasingly by their length.

Note

total_length is useful to implement the pack sequence -> recurrent network -> unpack sequence pattern in a Module wrapped in DataParallel. See this FAQ section for details.

Parameters: sequence (PackedSequence) – batch to pad batch_first (bool, optional) – if True, the output will be in B x T x * format. padding_value (float, optional) – values for padded elements. total_length (int, optional) – if not None, the output will be padded to have length total_length. This method will throw ValueError if total_length is less than the max sequence length in sequence. Tuple of Tensor containing the padded sequence, and a Tensor containing the list of lengths of each sequence in the batch.

torch.nn.utils.rnn.pad_sequence(sequences, batch_first=False, padding_value=0)[source]

Pad a list of variable length Tensors with zero

pad_sequence stacks a list of Tensors along a new dimension, and padds them to equal length. For example, if the input is list of sequences with size L x * and if batch_first is False, and T x B x * otherwise. The list of sequences should be sorted in the order of decreasing length.

B is batch size. It’s equal to the number of elements in sequences. T is length of the longest sequence. L is length of the sequence. * is any number of trailing dimensions, including none.

Example

>>> from torch.nn.utils.rnn import pad_sequence
>>> a = torch.ones(25, 300)
>>> b = torch.ones(22, 300)
>>> c = torch.ones(15, 300)
>>> pad_sequence([a, b, c]).size()
torch.Size([25, 3, 300])


Note

This function returns a Tensor of size T x B x * or B x T x * where T is the
length of longest sequence.
Function assumes trailing dimensions and type of all the Tensors
in sequences are same.
Parameters: sequences (list[Tensor]) – list of variable length sequences. batch_first (bool, optional) – output will be in B x T x * if True, or in T x B x * otherwise padding_value (float, optional) – value for padded elements. Tensor of size T x B x * if batch_first is False Tensor of size B x T x * otherwise

### pack_sequence¶

torch.nn.utils.rnn.pack_sequence(sequences)[source]

Packs a list of variable length Tensors

sequences should be a list of Tensors of size L x *, where L is the length of a sequence and * is any number of trailing dimensions, including zero. They should be sorted in the order of decreasing length.

Example

>>> from torch.nn.utils.rnn import pack_sequence
>>> a = torch.tensor([1,2,3])
>>> b = torch.tensor([4,5])
>>> c = torch.tensor([6])
>>> pack_sequence([a, b, c]])
PackedSequence(data=tensor([ 1,  4,  6,  2,  5,  3]), batch_sizes=tensor([ 3,  2,  1]))

Parameters: sequences (list[Tensor]) – A list of sequences of decreasing length. a PackedSequence object

# torch.nn.functional¶

## Convolution functions¶

### conv1d¶

torch.nn.functional.conv1d(input, weight, bias=None, stride=1, padding=0, dilation=1, groups=1) → Tensor

Applies a 1D convolution over an input signal composed of several input planes.

See Conv1d for details and output shape.

Parameters: input – input tensor of shape $$minibatch \times in\_channels \times iW$$ weight – filters of shape $$out\_channels \times \frac{in\_channels}{groups} \times kW$$ bias – optional bias of shape ($$out\_channels$$). Default: None stride – the stride of the convolving kernel. Can be a single number or a one-element tuple (sW,). Default: 1 padding – implicit zero paddings on both sides of the input. Can be a single number or a one-element tuple (padW,). Default: 0 dilation – the spacing between kernel elements. Can be a single number or a one-element tuple (dW,). Default: 1 groups – split input into groups, $$in\_channels$$ should be divisible by the number of groups. Default: 1

Examples:

>>> filters = torch.randn(33, 16, 3)
>>> inputs = torch.randn(20, 16, 50)
>>> F.conv1d(inputs, filters)


### conv2d¶

torch.nn.functional.conv2d(input, weight, bias=None, stride=1, padding=0, dilation=1, groups=1) → Tensor

Applies a 2D convolution over an input image composed of several input planes.

See Conv2d for details and output shape.

Parameters: input – input tensor of shape ($$minibatch \times in\_channels \times iH \times iW$$) weight – filters of shape ($$out\_channels \times \frac{in\_channels}{groups} \times kH \times kW$$) bias – optional bias tensor of shape ($$out\_channels$$). Default: None stride – the stride of the convolving kernel. Can be a single number or a tuple (sH, sW). Default: 1 padding – implicit zero paddings on both sides of the input. Can be a single number or a tuple (padH, padW). Default: 0 dilation – the spacing between kernel elements. Can be a single number or a tuple (dH, dW). Default: 1 groups – split input into groups, $$in\_channels$$ should be divisible by the number of groups. Default: 1

Examples:

>>> # With square kernels and equal stride
>>> filters = torch.randn(8,4,3,3)
>>> inputs = torch.randn(1,4,5,5)
>>> F.conv2d(inputs, filters, padding=1)


### conv3d¶

torch.nn.functional.conv3d(input, weight, bias=None, stride=1, padding=0, dilation=1, groups=1) → Tensor

Applies a 3D convolution over an input image composed of several input planes.

See Conv3d for details and output shape.

Parameters: input – input tensor of shape ($$minibatch \times in\_channels \times iT \times iH \times iW$$) weight – filters of shape ($$out\_channels \times \frac{in\_channels}{groups} \times kT \times kH \times kW$$) bias – optional bias tensor of shape ($$out\_channels$$). Default: None stride – the stride of the convolving kernel. Can be a single number or a tuple (sT, sH, sW). Default: 1 padding – implicit zero paddings on both sides of the input. Can be a single number or a tuple (padT, padH, padW). Default: 0 dilation – the spacing between kernel elements. Can be a single number or a tuple (dT, dH, dW). Default: 1 groups – split input into groups, $$in\_channels$$ should be divisible by the number of groups. Default: 1

Examples:

>>> filters = torch.randn(33, 16, 3, 3, 3)
>>> inputs = torch.randn(20, 16, 50, 10, 20)
>>> F.conv3d(inputs, filters)


### conv_transpose1d¶

torch.nn.functional.conv_transpose1d(input, weight, bias=None, stride=1, padding=0, output_padding=0, groups=1, dilation=1) → Tensor

Applies a 1D transposed convolution operator over an input signal composed of several input planes, sometimes also called “deconvolution”.

See ConvTranspose1d for details and output shape.

Parameters: input – input tensor of shape ($$minibatch \times in\_channels \times iW$$) weight – filters of shape ($$in\_channels \times \frac{out\_channels}{groups} \times kW$$) bias – optional bias of shape ($$out\_channels$$). Default: None stride – the stride of the convolving kernel. Can be a single number or a tuple (sW,). Default: 1 padding – implicit zero paddings on both sides of the input. Can be a single number or a tuple (padW,). Default: 0 output_padding – implicit zero-paddings of $$0 \leq padding < stride$$ on both sides of the output. Can be a single number or a tuple (out_padW,). Default: 0 groups – split input into groups, $$in\_channels$$ should be divisible by the number of groups. Default: 1 dilation – the spacing between kernel elements. Can be a single number or a tuple (dW,). Default: 1

Examples:

>>> inputs = torch.randn(20, 16, 50)
>>> weights = torch.randn(16, 33, 5)
>>> F.conv_transpose1d(inputs, weights)


### conv_transpose2d¶

torch.nn.functional.conv_transpose2d(input, weight, bias=None, stride=1, padding=0, output_padding=0, groups=1, dilation=1) → Tensor

Applies a 2D transposed convolution operator over an input image composed of several input planes, sometimes also called “deconvolution”.

See ConvTranspose2d for details and output shape.

Parameters: input – input tensor of shape ($$minibatch \times in\_channels \times iH \times iW$$) weight – filters of shape ($$in\_channels \times \frac{out\_channels}{groups} \times kH \times kW$$) bias – optional bias of shape ($$out\_channels$$). Default: None stride – the stride of the convolving kernel. Can be a single number or a tuple (sH, sW). Default: 1 padding – implicit zero paddings on both sides of the input. Can be a single number or a tuple (padH, padW). Default: 0 output_padding – implicit zero-paddings of $$0 \leq padding < stride$$ on both sides of the output. Can be a single number or a tuple (out_padH, out_padW). Default: 0 groups – split input into groups, $$in\_channels$$ should be divisible by the number of groups. Default: 1 dilation – the spacing between kernel elements. Can be a single number or a tuple (dH, dW). Default: 1

Examples:

>>> # With square kernels and equal stride
>>> inputs = torch.randn(1, 4, 5, 5)
>>> weights = torch.randn(4, 8, 3, 3)
>>> F.conv_transpose2d(inputs, weights, padding=1)


### conv_transpose3d¶

torch.nn.functional.conv_transpose3d(input, weight, bias=None, stride=1, padding=0, output_padding=0, groups=1, dilation=1) → Tensor

Applies a 3D transposed convolution operator over an input image composed of several input planes, sometimes also called “deconvolution”

See ConvTranspose3d for details and output shape.

Parameters: input – input tensor of shape ($$minibatch \times in\_channels \times iT \times iH \times iW$$) weight – filters of shape ($$in\_channels \times \frac{out\_channels}{groups} \times kT \times kH \times kW$$) bias – optional bias of shape ($$out\_channels$$). Default: None stride – the stride of the convolving kernel. Can be a single number or a tuple (sT, sH, sW). Default: 1 padding – implicit zero paddings on both sides of the input. Can be a single number or a tuple (padT, padH, padW). Default: 0 output_padding – implicit zero-paddings of 0 leq padding < stride on both sides of the output. Can be a single number or a tuple (out_padT, out_padH, out_padW). Default: 0 groups – split input into groups, $$in\_channels$$ should be divisible by the number of groups. Default: 1 dilation – the spacing between kernel elements. Can be a single number or a tuple (dT, dH, dW). Default: 1

Examples:

>>> inputs = torch.randn(20, 16, 50, 10, 20)
>>> weights = torch.randn(16, 33, 3, 3, 3)
>>> F.conv_transpose3d(inputs, weights)


## Pooling functions¶

### avg_pool1d¶

torch.nn.functional.avg_pool1d(input, 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.

See AvgPool1d for details and output shape.

Parameters: input – input tensor of shape ($$minibatch \times in\_channels \times iW$$) kernel_size – the size of the window. Can be a single number or a tuple (kW,) stride – the stride of the window. Can be a single number or a tuple (sW,). Default: kernel_size padding – implicit zero paddings on both sides of the input. Can be a single number or a tuple (padW,). Default: 0 ceil_mode – when True, will use ceil instead of floor to compute the output shape. Default: False count_include_pad – when True, will include the zero-padding in the averaging calculation. Default: True
Example::
>>> # pool of square window of size=3, stride=2
>>> input = torch.tensor([[[1,2,3,4,5,6,7]]])
>>> F.avg_pool1d(input, kernel_size=3, stride=2)
tensor([[[ 2.,  4.,  6.]]])


### avg_pool2d¶

torch.nn.functional.avg_pool2d(input, kernel_size, stride=None, padding=0, ceil_mode=False, count_include_pad=False) → Tensor

Applies 2D average-pooling operation in $$kH \times kW$$ regions by step size $$sH \times sW$$ steps. The number of output features is equal to the number of input planes.

See AvgPool2d for details and output shape.

Parameters: input – input tensor ($$minibatch \times in\_channels \times iH \times iW$$) kernel_size – size of the pooling region. Can be a single number or a tuple ($$kH \times kW$$) stride – stride of the pooling operation. Can be a single number or a tuple (sH, sW). Default: kernel_size padding – implicit zero paddings on both sides of the input. Can be a single number or a tuple (padH, padW). Default: 0 ceil_mode – when True, will use ceil instead of floor in the formula to compute the output shape. Default: False count_include_pad – when True, will include the zero-padding in the averaging calculation. Default: False

Warning

Default value for count_include_pad was True in versions before 0.3, and will be changed back to True from 0.4.1 and forward.

### avg_pool3d¶

torch.nn.functional.avg_pool3d(input, kernel_size, stride=None, padding=0, ceil_mode=False, count_include_pad=False) → Tensor

Applies 3D average-pooling operation in $$kT \times kH \times kW$$ regions by step size $$sT \times sH \times sW$$ steps. The number of output features is equal to $$\lfloor\frac{\text{input planes}}{sT}\rfloor$$.

See AvgPool3d for details and output shape.

Parameters: input – input tensor ($$minibatch \times in\_channels \times iT \times iH \times iW$$) kernel_size – size of the pooling region. Can be a single number or a tuple ($$kT \times kH \times kW$$) stride – stride of the pooling operation. Can be a single number or a tuple (sT, sH, sW). Default: kernel_size padding – implicit zero paddings on both sides of the input. Can be a single number or a tuple (padT, padH, padW), Default: 0 ceil_mode – when True, will use ceil instead of floor in the formula to compute the output shape count_include_pad – when True, will include the zero-padding in the averaging calculation. Default: False

Warning

Default value for count_include_pad was True in versions before 0.3, and will be changed back to True from 0.4.1 and forward.

### max_pool1d¶

torch.nn.functional.max_pool1d(input, kernel_size, stride=None, padding=0, dilation=1, ceil_mode=False, return_indices=False)[source]

Applies a 1D max pooling over an input signal composed of several input planes.

See MaxPool1d for details.

### max_pool2d¶

torch.nn.functional.max_pool2d(input, kernel_size, stride=None, padding=0, dilation=1, ceil_mode=False, return_indices=False)[source]

Applies a 2D max pooling over an input signal composed of several input planes.

See MaxPool2d for details.

### max_pool3d¶

torch.nn.functional.max_pool3d(input, kernel_size, stride=None, padding=0, dilation=1, ceil_mode=False, return_indices=False)[source]

Applies a 3D max pooling over an input signal composed of several input planes.

See MaxPool3d for details.

### max_unpool1d¶

torch.nn.functional.max_unpool1d(input, indices, kernel_size, stride=None, padding=0, output_size=None)[source]

Computes a partial inverse of MaxPool1d.

See MaxUnpool1d for details.

### max_unpool2d¶

torch.nn.functional.max_unpool2d(input, indices, kernel_size, stride=None, padding=0, output_size=None)[source]

Computes a partial inverse of MaxPool2d.

See MaxUnpool2d for details.

### max_unpool3d¶

torch.nn.functional.max_unpool3d(input, indices, kernel_size, stride=None, padding=0, output_size=None)[source]

Computes a partial inverse of MaxPool3d.

See MaxUnpool3d for details.

### lp_pool1d¶

torch.nn.functional.lp_pool1d(input, norm_type, kernel_size, stride=None, ceil_mode=False)[source]

Applies a 1D power-average pooling over an input signal composed of several input planes.

See LPPool1d for details.

### lp_pool2d¶

torch.nn.functional.lp_pool2d(input, norm_type, kernel_size, stride=None, ceil_mode=False)[source]

Applies a 2D power-average pooling over an input signal composed of several input planes.

See LPPool2d for details.

torch.nn.functional.adaptive_max_pool1d(input, output_size, return_indices=False)[source]

Applies a 1D adaptive max pooling over an input signal composed of several input planes.

See AdaptiveMaxPool1d for details and output shape.

Parameters: output_size – the target output size (single integer) return_indices – whether to return pooling indices. Default: False

torch.nn.functional.adaptive_max_pool2d(input, output_size, return_indices=False)[source]

Applies a 2D adaptive max pooling over an input signal composed of several input planes.

See AdaptiveMaxPool2d for details and output shape.

Parameters: output_size – the target output size (single integer or double-integer tuple) return_indices – whether to return pooling indices. Default: False

torch.nn.functional.adaptive_max_pool3d(input, output_size, return_indices=False)[source]

Applies a 3D adaptive max pooling over an input signal composed of several input planes.

See AdaptiveMaxPool3d for details and output shape.

Parameters: output_size – the target output size (single integer or triple-integer tuple) return_indices – whether to return pooling indices. Default: False

torch.nn.functional.adaptive_avg_pool1d(input, output_size) → Tensor

Applies a 1D adaptive average pooling over an input signal composed of several input planes.

See AdaptiveAvgPool1d for details and output shape.

Parameters: output_size – the target output size (single integer)

torch.nn.functional.adaptive_avg_pool2d(input, output_size) → Tensor

Applies a 2D adaptive average pooling over an input signal composed of several input planes.

See AdaptiveAvgPool2d for details and output shape.

Parameters: output_size – the target output size (single integer or double-integer tuple)

torch.nn.functional.adaptive_avg_pool3d(input, output_size) → Tensor

Applies a 3D adaptive average pooling over an input signal composed of several input planes.

See AdaptiveAvgPool3d for details and output shape.

Parameters: output_size – the target output size (single integer or triple-integer tuple)

## Non-linear activation functions¶

### threshold¶

torch.nn.functional.threshold(input, threshold, value, inplace=False)[source]

Thresholds each element of the input Tensor.

See Threshold for more details.

torch.nn.functional.threshold_(input, threshold, value) → Tensor

In-place version of threshold().

### relu¶

torch.nn.functional.relu(input, inplace=False) → Tensor[source]

Applies the rectified linear unit function element-wise. See ReLU for more details.

torch.nn.functional.relu_(input) → Tensor

In-place version of relu().

### hardtanh¶

torch.nn.functional.hardtanh(input, min_val=-1., max_val=1., inplace=False) → Tensor[source]

Applies the HardTanh function element-wise. See Hardtanh for more details.

torch.nn.functional.hardtanh_(input, min_val=-1., max_val=1.) → Tensor

In-place version of hardtanh().

### relu6¶

torch.nn.functional.relu6(input, inplace=False) → Tensor[source]

Applies the element-wise function $$\text{ReLU6}(x) = \min(\max(0,x), 6)$$.

See ReLU6 for more details.

### elu¶

torch.nn.functional.elu(input, alpha=1.0, inplace=False)[source]

Applies element-wise, $$\text{ELU}(x) = \max(0,x) + \min(0, \alpha * (\exp(x) - 1))$$.

See ELU for more details.

torch.nn.functional.elu_(input, alpha=1.) → Tensor

In-place version of elu().

### selu¶

torch.nn.functional.selu(input, inplace=False) → Tensor[source]

Applies element-wise, $$\text{SELU}(x) = scale * (\max(0,x) + \min(0, \alpha * (\exp(x) - 1)))$$, with $$\alpha=1.6732632423543772848170429916717$$ and $$scale=1.0507009873554804934193349852946$$.

See SELU for more details.

### leaky_relu¶

torch.nn.functional.leaky_relu(input, negative_slope=0.01, inplace=False) → Tensor[source]

Applies element-wise, $$\text{LeakyReLU}(x) = \max(0, x) + \text{negative_slope} * \min(0, x)$$

See LeakyReLU for more details.

torch.nn.functional.leaky_relu_(input, negative_slope=0.01) → Tensor

In-place version of leaky_relu().

### prelu¶

torch.nn.functional.prelu(input, weight) → Tensor

Applies element-wise the function $$\text{PReLU}(x) = \max(0,x) + \text{weight} * \min(0,x)$$ where weight is a learnable parameter.

See PReLU for more details.

### rrelu¶

torch.nn.functional.rrelu(input, lower=1./8, upper=1./3, training=False, inplace=False) → Tensor[source]

Randomized leaky ReLU.

See RReLU for more details.

torch.nn.functional.rrelu_(input, lower=1./8, upper=1./3, training=False) → Tensor

In-place version of rrelu().

### glu¶

torch.nn.functional.glu(input, dim=-1) → Tensor[source]

The gated linear unit. Computes:

$H = A \times \sigma(B)$

where input is split in half along dim to form A and B.

Parameters: input (Tensor) – input tensor dim (int) – dimension on which to split the input

### logsigmoid¶

torch.nn.functional.logsigmoid(input) → Tensor

Applies element-wise $$\text{LogSigmoid}(x) = \log \left(\frac{1}{1 + \exp(-x_i)}\right)$$

See LogSigmoid for more details.

### hardshrink¶

torch.nn.functional.hardshrink(input, lambd=0.5) → Tensor

Applies the hard shrinkage function element-wise

See Hardshrink for more details.

### tanhshrink¶

torch.nn.functional.tanhshrink(input) → Tensor[source]

Applies element-wise, $$\text{Tanhshrink}(x) = x - \text{Tanh}(x)$$

See Tanhshrink for more details.

### softsign¶

torch.nn.functional.softsign(input) → Tensor[source]

Applies element-wise, the function $$\text{SoftSign}(x) = \frac{x}{1 + |x|}$$

See Softsign for more details.

### softplus¶

torch.nn.functional.softplus(input, beta=1, threshold=20) → Tensor

### softmin¶

torch.nn.functional.softmin(input, dim=None, _stacklevel=3)[source]

Applies a softmin function.

Note that $$\text{Softmin}(x) = \text{Softmax}(-x)$$. See softmax definition for mathematical formula.

See Softmin for more details.

Parameters: input (Tensor) – input dim (int) – A dimension along which softmin will be computed (so every slice along dim will sum to 1).

### softmax¶

torch.nn.functional.softmax(input, dim=None, _stacklevel=3)[source]

Applies a softmax function.

Softmax is defined as:

$$\text{Softmax}(x_{i}) = \frac{exp(x_i)}{\sum_j exp(x_j)}$$

It is applied to all slices along dim, and will re-scale them so that the elements lie in the range (0, 1) and sum to 1.

See Softmax for more details.

Parameters: input (Tensor) – input dim (int) – A dimension along which softmax will be computed.

Note

This function doesn’t work directly with NLLLoss, which expects the Log to be computed between the Softmax and itself. Use log_softmax instead (it’s faster and has better numerical properties).

### softshrink¶

torch.nn.functional.softshrink(input, lambd=0.5) → Tensor

Applies the soft shrinkage function elementwise

See Softshrink for more details.

### log_softmax¶

torch.nn.functional.log_softmax(input, dim=None, _stacklevel=3)[source]

Applies a softmax followed by a logarithm.

While mathematically equivalent to log(softmax(x)), doing these two operations separately is slower, and numerically unstable. This function uses an alternative formulation to compute the output and gradient correctly.

See LogSoftmax for more details.

Parameters: input (Tensor) – input dim (int) – A dimension along which log_softmax will be computed.

### tanh¶

torch.nn.functional.tanh(input) → Tensor[source]

Applies element-wise, $$\text{Tanh}(x) = \tanh(x) = \frac{\exp(x) - \exp(-x)}{\exp(x) + \exp(-x)}$$

See Tanh for more details.

### sigmoid¶

torch.nn.functional.sigmoid(input) → Tensor[source]

Applies the element-wise function $$\text{Sigmoid}(x) = \frac{1}{1 + \exp(-x)}$$

See Sigmoid for more details.

## Normalization functions¶

### batch_norm¶

torch.nn.functional.batch_norm(input, running_mean, running_var, weight=None, bias=None, training=False, momentum=0.1, eps=1e-05)[source]

Applies Batch Normalization for each channel across a batch of data.

See BatchNorm1d, BatchNorm2d, BatchNorm3d for details.

### instance_norm¶

torch.nn.functional.instance_norm(input, running_mean=None, running_var=None, weight=None, bias=None, use_input_stats=True, momentum=0.1, eps=1e-05)[source]

Applies Instance Normalization for each channel in each data sample in a batch.

### layer_norm¶

torch.nn.functional.layer_norm(input, normalized_shape, weight=None, bias=None, eps=1e-05)[source]

Applies Layer Normalization for last certain number of dimensions.

See LayerNorm for details.

### local_response_norm¶

torch.nn.functional.local_response_norm(input, size, alpha=0.0001, beta=0.75, k=1)[source]

Applies local response normalization over an input signal composed of several input planes, where channels occupy the second dimension. Applies normalization across channels.

See LocalResponseNorm for details.

### normalize¶

torch.nn.functional.normalize(input, p=2, dim=1, eps=1e-12)[source]

Performs $$L_p$$ normalization of inputs over specified dimension.

Does:

$v = \frac{v}{\max(\lVert v \rVert_p, \epsilon)}$

for each subtensor v over dimension dim of input. Each subtensor is flattened into a vector, i.e. $$\lVert v \rVert_p$$ is not a matrix norm.

With default arguments normalizes over the second dimension with Euclidean norm.

Parameters: input – input tensor of any shape p (float) – the exponent value in the norm formulation. Default: 2 dim (int) – the dimension to reduce. Default: 1 eps (float) – small value to avoid division by zero. Default: 1e-12

## Linear functions¶

### linear¶

torch.nn.functional.linear(input, weight, bias=None)[source]

Applies a linear transformation to the incoming data: $$y = xA^T + b$$.

Shape:
• Input: $$(N, *, in\_features)$$ where * means any number of additional dimensions
• Weight: $$(out\_features, in\_features)$$
• Bias: $$(out\_features)$$
• Output: $$(N, *, out\_features)$$

## Dropout functions¶

### dropout¶

torch.nn.functional.dropout(input, p=0.5, training=False, inplace=False)[source]

### alpha_dropout¶

torch.nn.functional.alpha_dropout(input, p=0.5, training=False)[source]

Applies alpha dropout to the input.

See AlphaDropout for details.

Parameters: p (float, optional) – the drop probability. Default: 0.5 training (bool, optional) – switch between training and evaluation mode. Default: False

### dropout2d¶

torch.nn.functional.dropout2d(input, p=0.5, training=False, inplace=False)[source]

### dropout3d¶

torch.nn.functional.dropout3d(input, p=0.5, training=False, inplace=False)[source]

## Distance functions¶

### pairwise_distance¶

torch.nn.functional.pairwise_distance(x1, x2, p=2, eps=1e-06, keepdim=False)[source]

See torch.nn.PairwiseDistance for details

### cosine_similarity¶

torch.nn.functional.cosine_similarity(x1, x2, dim=1, eps=1e-08)[source]

Returns cosine similarity between x1 and x2, computed along dim.

$\text{similarity} = \dfrac{x_1 \cdot x_2}{\max(\Vert x_1 \Vert _2 \cdot \Vert x_2 \Vert _2, \epsilon)}$
Parameters: x1 (Tensor) – First input. x2 (Tensor) – Second input (of size matching x1). dim (int, optional) – Dimension of vectors. Default: 1 eps (float, optional) – Small value to avoid division by zero. Default: 1e-8
Shape:
• Input: $$(\ast_1, D, \ast_2)$$ where D is at position dim.
• Output: $$(\ast_1, \ast_2)$$ where 1 is at position dim.

Example:

>>> input1 = torch.randn(100, 128)
>>> input2 = torch.randn(100, 128)
>>> output = F.cosine_similarity(input1, input2)
>>> print(output)


## Loss functions¶

### binary_cross_entropy¶

torch.nn.functional.binary_cross_entropy(input, target, weight=None, size_average=True, reduce=True)[source]

Function that measures the Binary Cross Entropy between the target and the output.

See BCELoss for details.

Parameters: input – Tensor of arbitrary shape target – Tensor of the same shape as input weight (Tensor, optional) – a manual rescaling weight if provided it’s repeated to match input tensor shape size_average (bool, optional) – By default, the losses are averaged over observations for each minibatch. However, if the field size_average is set to False, the losses are instead summed for each minibatch. Default: True reduce (bool, optional) – By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per input/target element instead and ignores size_average. Default: True

Examples:

>>> input = torch.randn((3, 2), requires_grad=True)
>>> target = torch.rand((3, 2), requires_grad=False)
>>> loss = F.binary_cross_entropy(F.sigmoid(input), target)
>>> loss.backward()


### poisson_nll_loss¶

torch.nn.functional.poisson_nll_loss(input, target, log_input=True, full=False, size_average=True, eps=1e-08, reduce=True)[source]

Poisson negative log likelihood loss.

See PoissonNLLLoss for details.

Parameters: input – expectation of underlying Poisson distribution. target – random sample $$target \sim \text{Poisson}(input)$$. log_input – if True the loss is computed as $$\exp(\text{input}) - \text{target} * \text{input}$$, if False then loss is $$\text{input} - \text{target} * \log(\text{input}+\text{eps})$$. Default: True full – whether to compute full loss, i. e. to add the Stirling approximation term. Default: False $$\text{target} * \log(\text{target}) - \text{target} + 0.5 * \log(2 * \pi * \text{target})$$. size_average – By default, the losses are averaged over observations for each minibatch. However, if the field size_average is set to False, the losses are instead summed for each minibatch. Default: True eps (float, optional) – Small value to avoid evaluation of $$\log(0)$$ when log_input=False. Default: 1e-8 reduce (bool, optional) – By default, the losses are averaged over observations for each minibatch, or summed, depending on size_average. When reduce is False, returns a loss per batch instead and ignores size_average. Default: True

### cosine_embedding_loss¶

torch.nn.functional.cosine_embedding_loss(input1, input2, target, margin=0, size_average=True, reduce=True) → Tensor[source]

See CosineEmbeddingLoss for details.

### cross_entropy¶

torch.nn.functional.cross_entropy(input, target, weight=None, size_average=True, ignore_index=-100, reduce=True)[source]

This criterion combines log_softmax and nll_loss in a single function.

See CrossEntropyLoss for details.

Parameters: input (Tensor) – $$(N, C)$$ where C = number of classes or $$(N, C, H, W)$$ in case of 2D Loss, or $$(N, C, d_1, d_2, ..., d_K)$$ where $$K > 1$$ in the case of K-dimensional loss. target (Tensor) – $$(N)$$ where each value is $$0 \leq \text{targets}[i] \leq C-1$$, or $$(N, d_1, d_2, ..., d_K)$$ where $$K \geq 1$$ for K-dimensional loss. weight (Tensor, optional) – a manual rescaling weight given to each class. If given, has to be a Tensor of size C size_average (bool, optional) – By default, the losses are averaged over observations for each minibatch. However, if the field size_average is set to False, the losses are instead summed for each minibatch. Ignored if reduce is False. Default: True ignore_index (int, optional) – Specifies a target value that is ignored and does not contribute to the input gradient. When size_average is True, the loss is averaged over non-ignored targets. Default: -100 reduce (bool, optional) – By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch instead and ignores size_average. Default: True

Examples:

>>> input = torch.randn(3, 5, requires_grad=True)
>>> target = torch.randint(5, (3,), dtype=torch.int64)
>>> loss = F.cross_entropy(input, target)
>>> loss.backward()


### hinge_embedding_loss¶

torch.nn.functional.hinge_embedding_loss(input, target, margin=1.0, size_average=True, reduce=True) → Tensor[source]

See HingeEmbeddingLoss for details.

### kl_div¶

torch.nn.functional.kl_div(input, target, size_average=True) → Tensor

The Kullback-Leibler divergence Loss.

See KLDivLoss for details.

Parameters: input – Tensor of arbitrary shape target – Tensor of the same shape as input size_average – if True the output is divided by the number of elements in input tensor. Default: True reduce (bool, optional) – By default, the losses are averaged over observations for each minibatch, or summed, depending on size_average. When reduce is False, returns a loss per input/target element instead and ignores size_average. Default: True

### l1_loss¶

torch.nn.functional.l1_loss(input, target, size_average=True, reduce=True) → Tensor[source]

Function that takes the mean element-wise absolute value difference.

See L1Loss for details.

### mse_loss¶

torch.nn.functional.mse_loss(input, target, size_average=True, reduce=True) → Tensor[source]

Measures the element-wise mean squared error.

See MSELoss for details.

### margin_ranking_loss¶

torch.nn.functional.margin_ranking_loss(input1, input2, target, margin=0, size_average=True, reduce=True) → Tensor[source]

See MarginRankingLoss for details.

### multilabel_margin_loss¶

torch.nn.functional.multilabel_margin_loss(input, target, size_average=True, reduce=True) → Tensor

See MultiLabelMarginLoss for details.

### multilabel_soft_margin_loss¶

torch.nn.functional.multilabel_soft_margin_loss(input, target, weight=None, size_average=True) → Tensor[source]

See MultiLabelSoftMarginLoss for details.

### multi_margin_loss¶

torch.nn.functional.multi_margin_loss(input, target, p=1, margin=1, weight=None, size_average=True, reduce=True) → Tensor[source]

See MultiMarginLoss for details.

### nll_loss¶

torch.nn.functional.nll_loss(input, target, weight=None, size_average=True, ignore_index=-100, reduce=True)[source]

The negative log likelihood loss.

See NLLLoss for details.

Parameters: input – $$(N, C)$$ where C = number of classes or $$(N, C, H, W)$$ in case of 2D Loss, or $$(N, C, d_1, d_2, ..., d_K)$$ where $$K > 1$$ in the case of K-dimensional loss. target – $$(N)$$ where each value is $$0 \leq \text{targets}[i] \leq C-1$$, or $$(N, d_1, d_2, ..., d_K)$$ where $$K \geq 1$$ for K-dimensional loss. weight (Tensor, optional) – a manual rescaling weight given to each class. If given, has to be a Tensor of size C size_average (bool, optional) – By default, the losses are averaged over observations for each minibatch. If size_average is False, the losses are summed for each minibatch. Default: True ignore_index (int, optional) – Specifies a target value that is ignored and does not contribute to the input gradient. When size_average is True, the loss is averaged over non-ignored targets. Default: -100

Example:

>>> # input is of size N x C = 3 x 5
>>> input = torch.randn(3, 5, requires_grad=True)
>>> # each element in target has to have 0 <= value < C
>>> target = torch.tensor([1, 0, 4])
>>> output = F.nll_loss(F.log_softmax(input), target)
>>> output.backward()


### binary_cross_entropy_with_logits¶

torch.nn.functional.binary_cross_entropy_with_logits(input, target, weight=None, size_average=True, reduce=True)[source]

Function that measures Binary Cross Entropy between target and output logits.

See BCEWithLogitsLoss for details.

Parameters: input – Tensor of arbitrary shape target – Tensor of the same shape as input weight (Tensor, optional) – a manual rescaling weight if provided it’s repeated to match input tensor shape size_average (bool, optional) – By default, the losses are averaged over observations for each minibatch. However, if the field size_average is set to False, the losses are instead summed for each minibatch. Default: True reduce (bool, optional) – By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per input/target element instead and ignores size_average. Default: True

Examples:

>>> input = torch.randn(3, requires_grad=True)
>>> target = torch.empty(3).random_(2)
>>> loss = F.binary_cross_entropy_with_logits(input, target)
>>> loss.backward()


### smooth_l1_loss¶

torch.nn.functional.smooth_l1_loss(input, target, size_average=True, reduce=True) → Tensor

Function that uses a squared term if the absolute element-wise error falls below 1 and an L1 term otherwise.

See SmoothL1Loss for details.

### soft_margin_loss¶

torch.nn.functional.soft_margin_loss(input, target, size_average=True, reduce=True) → Tensor

See SoftMarginLoss for details.

### triplet_margin_loss¶

torch.nn.functional.triplet_margin_loss(anchor, positive, negative, margin=1.0, p=2, eps=1e-06, swap=False, size_average=True, reduce=True)[source]

See TripletMarginLoss for details

## Vision functions¶

### pixel_shuffle¶

torch.nn.functional.pixel_shuffle(input, upscale_factor)[source]

Rearranges elements in a tensor of shape $$[*, C*r^2, H, W]$$ to a tensor of shape $$[C, H*r, W*r]$$.

See PixelShuffle for details.

Parameters: input (Tensor) – Input upscale_factor (int) – factor to increase spatial resolution by

Examples:

>>> ps = nn.PixelShuffle(3)
>>> input = torch.empty(1, 9, 4, 4)
>>> output = ps(input)
>>> print(output.size())
torch.Size([1, 1, 12, 12])


torch.nn.functional.pad(input, pad, mode='constant', value=0)[source]

Nd constant padding: The number of dimensions to pad is
$$\left\lfloor\frac{len(padding)}{2}\right\rfloor$$ and the dimensions that get padded begins with the last dimension and moves forward. See below for examples.
1D, 2D and 3D “reflect” / “replicate” padding:
for 1D:
3D input tensor with padding of the form (padLeft, padRight)
for 2D:
for 3D:

See torch.nn.ConstantPad2d, torch.nn.ReflectionPad2d, and torch.nn.ReplicationPad2d for concrete examples on how each of the padding modes works.

Parameters: input (Tensor) – Nd tensor pad (tuple) – m-elem tuple, where $$\frac{m}{2} \leq$$ input dimensions and $$m$$ is even. mode – ‘constant’, ‘reflect’ or ‘replicate’. Default: ‘constant’ value – fill value for ‘constant’ padding. Default: 0

Examples:

>>> t4d = torch.empty(3, 3, 4, 2)
>>> p1d = (1, 1) # pad last dim by 1 on each side
>>> out = F.pad(t4d, p1d, "constant", 0)  # effectively zero padding
>>> print(out.data.size())
torch.Size([3, 3, 4, 4])
>>> p2d = (1, 1, 2, 2) # pad last dim by (1, 1) and 2nd to last by (2, 2)
>>> out = F.pad(t4d, p2d, "constant", 0)
>>> print(out.data.size())
torch.Size([3, 3, 8, 4])
>>> t4d = torch.empty(3, 3, 4, 2)
>>> p3d = (0, 1, 2, 1, 3, 3) # pad by (0, 1), (2, 1), and (3, 3)
>>> out = F.pad(t4d, p3d, "constant", 0)
>>> print(out.data.size())
torch.Size([3, 9, 7, 3])


### upsample¶

torch.nn.functional.upsample(input, size=None, scale_factor=None, mode='nearest', align_corners=None)[source]

Upsamples the input to either the given size or the given scale_factor

The algorithm used for upsampling is determined by mode.

Currently temporal, spatial and volumetric upsampling are supported, i.e. expected inputs are 3-D, 4-D or 5-D in shape.

The input dimensions are interpreted in the form: mini-batch x channels x [optional depth] x [optional height] x width.

The modes available for upsampling are: nearest, linear (3D-only), bilinear (4D-only), trilinear (5D-only)

Parameters: input (Tensor) – the input tensor size (int or Tuple[int] or Tuple[int, int] or Tuple[int, int, int]) – output spatial size. scale_factor (int) – multiplier for spatial size. Has to be an integer. mode (string) – algorithm used for upsampling: ‘nearest’ | ‘linear’ | ‘bilinear’ | ‘trilinear’. Default: ‘nearest’ align_corners (bool, optional) – if True, the corner pixels of the input and output tensors are aligned, and thus preserving the values at those pixels. This only has effect when mode is linear, bilinear, or trilinear. Default: False

Warning

With align_corners = True, the linearly interpolating modes (linear, bilinear, and trilinear) don’t proportionally align the output and input pixels, and thus the output values can depend on the input size. This was the default behavior for these modes up to version 0.3.1. Since then, the default behavior is align_corners = False. See Upsample for concrete examples on how this affects the outputs.

### upsample_nearest¶

torch.nn.functional.upsample_nearest(input, size=None, scale_factor=None)[source]

Upsamples the input, using nearest neighbours’ pixel values.

Warning

This function is deprecated in favor of torch.nn.functional.upsample(). This is equivalent with nn.functional.upsample(..., mode='nearest').

Currently spatial and volumetric upsampling are supported (i.e. expected inputs are 4 or 5 dimensional).

Parameters: input (Tensor) – input size (int or Tuple[int, int] or Tuple[int, int, int]) – output spatia size. scale_factor (int) – multiplier for spatial size. Has to be an integer.

### upsample_bilinear¶

torch.nn.functional.upsample_bilinear(input, size=None, scale_factor=None)[source]

Upsamples the input, using bilinear upsampling.

Warning

This function is deprecated in favor of torch.nn.functional.upsample(). This is equivalent with nn.functional.upsample(..., mode='bilinear', align_corners=True).

Expected inputs are spatial (4 dimensional). Use upsample_trilinear fo volumetric (5 dimensional) inputs.

Parameters: input (Tensor) – input size (int or Tuple[int, int]) – output spatial size. scale_factor (int or Tuple[int, int]) – multiplier for spatial size

### grid_sample¶

torch.nn.functional.grid_sample(input, grid, mode='bilinear', padding_mode='zeros')[source]

Given an input and a flow-field grid, computes the output using input pixel locations from the grid.

Uses bilinear interpolation to sample the input pixels. Currently, only spatial (4 dimensional) and volumetric (5 dimensional) inputs are supported.

For each output location, grid has x, y input pixel locations which are used to compute output. In the case of 5D inputs, grid has x, y, z pixel locations.

Note

To avoid confusion in notation, let’s note that x corresponds to the width dimension IW, y corresponds to the height dimension IH and z corresponds to the depth dimension ID.

grid has values in the range of [-1, 1]. This is because the pixel locations are normalized by the input height and width.

For example, values: x: -1, y: -1 is the left-top pixel of the input, and values: x: 1, y: 1 is the right-bottom pixel of the input.

If grid has values outside the range of [-1, 1], those locations are handled as defined by padding_mode. Options are zeros or border, defining those locations to use 0 or image border values as contribution to the bilinear interpolation.

Note

This function is used in building Spatial Transformer Networks

Parameters: input (Tensor) – input batch (N x C x IH x IW) or (N x C x ID x IH x IW) grid (Tensor) – flow-field of size (N x OH x OW x 2) or (N x OD x OH x OW x 3) padding_mode (str) – padding mode for outside grid values ‘zeros’ | ‘border’. Default: ‘zeros’ output Tensor output (Tensor)

### affine_grid¶

torch.nn.functional.affine_grid(theta, size)[source]

Generates a 2d flow field, given a batch of affine matrices theta Generally used in conjunction with grid_sample() to implement Spatial Transformer Networks.

Parameters: theta (Tensor) – input batch of affine matrices ($$N \times 2 \times 3$$) size (torch.Size) – the target output image size ($$N \times C \times H \times W$$) Example: torch.Size((32, 3, 24, 24)) output Tensor of size ($$N \times H \times W \times 2$$) output (Tensor)

## DataParallel functions (multi-GPU, distributed)¶

### data_parallel¶

torch.nn.parallel.data_parallel(module, inputs, device_ids=None, output_device=None, dim=0, module_kwargs=None)[source]

Evaluates module(input) in parallel across the GPUs given in device_ids.

This is the functional version of the DataParallel module.

Parameters: module – the module to evaluate in parallel inputs – inputs to the module device_ids – GPU ids on which to replicate module output_device – GPU location of the output Use -1 to indicate the CPU. (default: device_ids[0]) a Tensor containing the result of module(input) located on output_device

# torch.nn.init¶

torch.nn.init.calculate_gain(nonlinearity, param=None)[source]

Return the recommended gain value for the given nonlinearity function. The values are as follows:

nonlinearity gain
Linear / Identity $$1$$
Conv{1,2,3}D $$1$$
Sigmoid $$1$$
Tanh $$\frac{5}{3}$$
ReLU $$\sqrt{2}$$
Leaky Relu $$\sqrt{\frac{2}{1 + \text{negative_slope}^2}}$$
Parameters: nonlinearity – the non-linear function (nn.functional name) param – optional parameter for the non-linear function

Examples

>>> gain = nn.init.calculate_gain('leaky_relu')

torch.nn.init.uniform_(tensor, a=0, b=1)[source]

Fills the input Tensor with values drawn from the uniform distribution $$\mathcal{U}(a, b)$$.

Parameters: tensor – an n-dimensional torch.Tensor a – the lower bound of the uniform distribution b – the upper bound of the uniform distribution

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.uniform_(w)

torch.nn.init.normal_(tensor, mean=0, std=1)[source]

Fills the input Tensor with values drawn from the normal distribution $$\mathcal{N}(\text{mean}, \text{std})$$.

Parameters: tensor – an n-dimensional torch.Tensor mean – the mean of the normal distribution std – the standard deviation of the normal distribution

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.normal_(w)

torch.nn.init.constant_(tensor, val)[source]

Fills the input Tensor with the value $$\text{val}$$.

Parameters: tensor – an n-dimensional torch.Tensor val – the value to fill the tensor with

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.constant_(w, 0.3)

torch.nn.init.eye_(tensor)[source]

Fills the 2-dimensional input Tensor with the identity matrix. Preserves the identity of the inputs in Linear layers, where as many inputs are preserved as possible.

Parameters: tensor – a 2-dimensional torch.Tensor

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.eye_(w)

torch.nn.init.dirac_(tensor)[source]

Fills the {3, 4, 5}-dimensional input Tensor with the Dirac delta function. Preserves the identity of the inputs in Convolutional layers, where as many input channels are preserved as possible.

Parameters: tensor – a {3, 4, 5}-dimensional torch.Tensor

Examples

>>> w = torch.empty(3, 16, 5, 5)
>>> nn.init.dirac_(w)

torch.nn.init.xavier_uniform_(tensor, gain=1)[source]

Fills the input Tensor with values according to the method described in “Understanding the difficulty of training deep feedforward neural networks” - Glorot, X. & Bengio, Y. (2010), using a uniform distribution. The resulting tensor will have values sampled from $$\mathcal{U}(-a, a)$$ where

$a = \text{gain} \times \sqrt{\frac{6}{\text{fan_in} + \text{fan_out}}}$

Also known as Glorot initialization.

Parameters: tensor – an n-dimensional torch.Tensor gain – an optional scaling factor

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.xavier_uniform_(w, gain=nn.init.calculate_gain('relu'))

torch.nn.init.xavier_normal_(tensor, gain=1)[source]

Fills the input Tensor with values according to the method described in “Understanding the difficulty of training deep feedforward neural networks” - Glorot, X. & Bengio, Y. (2010), using a normal distribution. The resulting tensor will have values sampled from $$\mathcal{N}(0, \text{std})$$ where

$\text{std} = \text{gain} \times \sqrt{\frac{2}{\text{fan_in} + \text{fan_out}}}$

Also known as Glorot initialization.

Parameters: tensor – an n-dimensional torch.Tensor gain – an optional scaling factor

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.xavier_normal_(w)

torch.nn.init.kaiming_uniform_(tensor, a=0, mode='fan_in', nonlinearity='leaky_relu')[source]

Fills the input Tensor with values according to the method described in “Delving deep into rectifiers: Surpassing human-level performance on ImageNet classification” - He, K. et al. (2015), using a uniform distribution. The resulting tensor will have values sampled from $$\mathcal{U}(-\text{bound}, \text{bound})$$ where

$\text{bound} = \sqrt{\frac{6}{(1 + a^2) \times \text{fan_in}}}$

Also known as He initialization.

Parameters: tensor – an n-dimensional torch.Tensor a – the negative slope of the rectifier used after this layer (0 for ReLU by default) mode – either ‘fan_in’ (default) or ‘fan_out’. Choosing fan_in preserves the magnitude of the variance of the weights in the forward pass. Choosing fan_out preserves the magnitudes in the backwards pass. nonlinearity – the non-linear function (nn.functional name), recommended to use only with ‘relu’ or ‘leaky_relu’ (default).

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.kaiming_uniform_(w, mode='fan_in', nonlinearity='relu')

torch.nn.init.kaiming_normal_(tensor, a=0, mode='fan_in', nonlinearity='leaky_relu')[source]

Fills the input Tensor with values according to the method described in “Delving deep into rectifiers: Surpassing human-level performance on ImageNet classification” - He, K. et al. (2015), using a normal distribution. The resulting tensor will have values sampled from $$\mathcal{N}(0, \text{std})$$ where

$\text{std} = \sqrt{\frac{2}{(1 + a^2) \times \text{fan_in}}}$

Also known as He initialization.

Parameters: tensor – an n-dimensional torch.Tensor a – the negative slope of the rectifier used after this layer (0 for ReLU by default) mode – either ‘fan_in’ (default) or ‘fan_out’. Choosing fan_in preserves the magnitude of the variance of the weights in the forward pass. Choosing fan_out preserves the magnitudes in the backwards pass. nonlinearity – the non-linear function (nn.functional name), recommended to use only with ‘relu’ or ‘leaky_relu’ (default).

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.kaiming_normal_(w, mode='fan_out', nonlinearity='relu')

torch.nn.init.orthogonal_(tensor, gain=1)[source]

Fills the input Tensor with a (semi) orthogonal matrix, as described in “Exact solutions to the nonlinear dynamics of learning in deep linear neural networks” - Saxe, A. et al. (2013). The input tensor must have at least 2 dimensions, and for tensors with more than 2 dimensions the trailing dimensions are flattened.

Parameters: tensor – an n-dimensional torch.Tensor, where $$n \geq 2$$ gain – optional scaling factor

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.orthogonal_(w)

torch.nn.init.sparse_(tensor, sparsity, std=0.01)[source]

Fills the 2D input Tensor as a sparse matrix, where the non-zero elements will be drawn from the normal distribution $$\mathcal{N}(0, 0.01)$$, as described in “Deep learning via Hessian-free optimization” - Martens, J. (2010).

Parameters: tensor – an n-dimensional torch.Tensor sparsity – The fraction of elements in each column to be set to zero std – the standard deviation of the normal distribution used to generate the non-zero values

Examples

>>> w = torch.empty(3, 5)
>>> nn.init.sparse_(w, sparsity=0.1)
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