nn.md

# torch.nn

## Parameters（参数）

```py
class torch.nn.Parameter
```


Parameters对象是一种会被视为模块参数（module parameter）的Tensor张量。

Parameters类是[`Tensor`](tensors.html#torch.Tensor "torch.Tensor") 的子类, 不过相对于它的父类，Parameters类有一个很重要的特性就是当其在 [`Module`](#torch.nn.Module "torch.nn.Module")类中被使用并被当做这个[`Module`](#torch.nn.Module "torch.nn.Module")类的模块属性的时候，那么这个Parameters对象会被自动地添加到这个[`Module`](#torch.nn.Module "torch.nn.Module")类的参数列表(list of parameters)之中，同时也就会被添加入此[`Module`](#torch.nn.Module "torch.nn.Module")类的 [`parameters()`](#torch.nn.Module.parameters "torch.nn.Module.parameters")方法所返回的参数迭代器中。而Parameters类的父类Tensor类也可以被用为构建模块的属性，但不会被加入参数列表。这样主要是因为，有时可能需要在模型中存储一些非模型参数的临时状态，比如RNN中的最后一个隐状态。而通过使用非[`Parameter`](#torch.nn.Parameter "torch.nn.Parameter")的Tensor类，可以将这些临时变量注册(register)为模型的属性的同时使其不被加入参数列表。

Parameters: 

*   **data** ([_Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – 参数张量(parameter tensor).
*   **requires_grad** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – 参数是否需要梯度， 默认为 `True`。更多细节请看 [如何将子图踢出反向传播过程](notes/autograd.html#excluding-subgraphs)。 



## Containers（容器）

### Module（模块）

```py
class torch.nn.Module
```

模块（Module）是所有神经网络模型的基类。

你创建模型的时候也应该继承这个类哦。

模块(Module)中还可以包含其他的模块，你可以将一个模块赋值成为另一个模块的属性，从而成为这个模块的一个子模块。而通过不断的赋值，你可以将不同的模块组织成一个树结构:

```py
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) # 当前的nn.Conv2d模块就被赋值成为Model模块的一个子模块，成为“树结构”的叶子
        self.conv2 = nn.Conv2d(20, 20, 5)

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

```

通过赋值这种方式添加的子模块将会被模型注册(register)，而后当调用模块的一些参数转换函数（[`to()`](#torch.nn.Module.to "torch.nn.Module.to")）的时候，子模块的参数也会一并转换。

```py
add_module(name, module)
```
向当前模块添加一个子模块。
此子模块可以作为当前模块的属性被访问到，而属性名就是add_module()函数中的name参数。

add_module()函数参数: 

*   **name** (_string_) – 子模块的名字. 函数调用完成后，可以通过访问当前模块的此字段来访问该子模块。
*   **parameter** ([_Module_](#torch.nn.Module "torch.nn.Module")) – 要添加到当前模块的子模块。



```py
apply(fn)
```


apply()函数的主要作用是将 `fn` 递归地应用于模块的所有子模块（`.children()`函数的返回值）以及模块自身。此函数的一个经典应用就是初始化模型的所有参数这一过程(同样参见于 torch-nn-init)。

| Parameters: | **fn** ([`Module`](#torch.nn.Module "torch.nn.Module") -> None) – 要应用于所有子模型的函数 |
| --- | --- |
| Returns: | self |
| --- | --- |
| Return type: | [Module](#torch.nn.Module "torch.nn.Module") |
| --- | --- |

例子:

```py
>>> 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) # 将init_weights()函数应用于模块的所有子模块
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)
)

```

```py
buffers(recurse=True)
```
返回模块的缓冲区的迭代器

| Parameters: | **recurse** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")) – 如果设置为True，产生的缓冲区迭代器会遍历模块自己与所有子模块，否则只会遍历模块的直连的成员。 |
| --- | --- |
| Yields: | _torch.Tensor_ – 模型缓冲区 |
| --- | --- |

举例:

```py
>>> for buf in model.buffers():
>>>     print(type(buf.data), buf.size())
<class 'torch.FloatTensor'> (20L,)
<class 'torch.FloatTensor'> (20L, 1L, 5L, 5L)

```

```py
children()
```

返回一个当前所有子模块的迭代器
Returns an iterator over immediate children modules.

| Yields: | _Module_ – 子模块 |
| --- | --- |

```py
cpu()
```

将模型的所有参数(parameter)和缓冲区(buffer)都转移到CPU内存中。

| Returns: | self |
| --- | --- |
| Return type: | [Module](#torch.nn.Module "torch.nn.Module") |
| --- | --- |

```py
cuda(device=None)
```

将模型的所有参数和缓冲区都转移到CUDA设备内存中。

因为cuda()函数同时会将处理模块中的所有参数并缓存这些参数的对象。所以如果想让模块在GPU上进行优化操作，一定要在构建优化器之前调用模块的cuda()函数。

| Parameters: | **device** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ _optional_) – 如果设备编号被指定，所有的参数都会被拷贝到编号指定设备上 |
| --- | --- |
| Returns: | self |
| --- | --- |
| Return type: | [Module](#torch.nn.Module "torch.nn.Module") |
| --- | --- |

```py
double()
```

将所有的浮点数类型的参数(parameters)和缓冲区(buffers)转换为`double`数据类型。

| Returns: | self |
| --- | --- |
| Return type: | [Module](#torch.nn.Module "torch.nn.Module") |
| --- | --- |

```py
dump_patches = False
```

这个字段可以为[`load_state_dict()`](#torch.nn.Module.load_state_dict "torch.nn.Module.load_state_dict")提供 BC 支持（BC support实在不懂是什么意思-.-）。 在 [`state_dict()`](#torch.nn.Module.state_dict "torch.nn.Module.state_dict")函数返回的状态字典（state dict）中， 有一个名为`_metadata`的属性中存储了这个state_dict的版本号。`_metadata`是一个遵从了状态字典（state dict）的命名规范的关键字字典， 要想了解这个`_metadata`在加载状态（loading state dict）的时候是怎么用的，可以看一下 `_load_from_state_dict`部分的文档。


如果新的参数/缓冲区被添加于/移除自这个模块之中时，这个版本号数字会随之发生变化。同时模块的`_load_from_state_dict`方法会比较版本号的信息并依据此状态词典（state dict）的变化做出一些适当的调整。

```py
eval()
```

将模块转换为测试模式。

这个函数只对特定的模块类型有效，如 [`Dropout`](#torch.nn.Dropout "torch.nn.Dropout")和`BatchNorm`等等。如果想了解这些特定模块在训练/测试模式下各自的运作细节，可以看一下这些特殊模块的文档部分。

```py
extra_repr()
```

为模块设置额外的展示信息(extra representation)。

如果想要打印展示(print)你的模块的一些定制的额外信息，那你应该在你的模块中复现这个函数。单行和多行的字符串都可以被接受。


```py
float()
```

将所有浮点数类型的参数(parameters)和缓冲区(buffers)转换为`float`数据类型。

| Returns: | self |
| --- | --- |
| Return type: | [Module](#torch.nn.Module "torch.nn.Module") |
| --- | --- |

```py
forward(*input)
```

定义了每次模块被调用之后所进行的计算过程。

应该被Module类的所有子类重写。

Note

尽管模块的前向操作都被定义在这个函数里面，但是当你要进行模块的前向操作的时候，还是要直接调用模块[`Module`](#torch.nn.Module "torch.nn.Module") 的实例函数，而不是直接调用这个forward()函数。这主要是因为前者会照顾到注册在此模块之上的钩子函数（the registered hooks）的运行，而后者则不会。

```py
half()
```

将所有的浮点数类型的参数(parameters)和缓冲区(buffers)转换为`half`数据类型。

| Returns: | self |
| --- | --- |
| Return type: | [Module](#torch.nn.Module "torch.nn.Module") |
| --- | --- |

```py
load_state_dict(state_dict, strict=True)
```

将[`state_dict`](#torch.nn.Module.state_dict "torch.nn.Module.state_dict")中的参数（parameters）和缓冲区（buffers）拷贝到模块和其子模块之中。如果`strict`被设置为`True`，那么[`state_dict`](#torch.nn.Module.state_dict "torch.nn.Module.state_dict")中的键值（keys）必须与模型的[`state_dict()`]函数所返回的键值（keys）信息保持完全的一致。

load_state_dict()函数参数： 

*   **state_dict** ([_dict_](https://docs.python.org/3/library/stdtypes.html#dict "(in Python v3.7)")) – 一个包含了参数和持久缓冲区的字典。
*   **strict** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – 是否严格要求 [`state_dict`](#torch.nn.Module.state_dict "torch.nn.Module.state_dict") 中的键值（keys）与模型 [`state_dict()`](#torch.nn.Module.state_dict "torch.nn.Module.state_dict") 函数返回的键值（keys）信息保持完全一致。 默认： `True`



```py
modules()
```

返回一个当前模块内所有模块（包括自身）的迭代器。

| Yields: | _Module_ – a module in the network |
| --- | --- |

Note

注意重复的模块只会被返回一次。比在下面这个例子中，`l`就只会被返回一次。

例子:

```py
>>> 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)

```

```py
named_buffers(prefix='', recurse=True)
```

返回一个模块缓冲区的迭代器，每次返回的元素是由缓冲区的名字和缓冲区自身组成的元组。

named_buffers()函数的参数: 

*   **prefix** ([_str_](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.7)")) – 要添加在所有缓冲区名字之前的前缀。
*   **recurse** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")) – 如果设置为True，那样迭代器中不光会返回这个模块自身直连成员的缓冲区，同时也会递归返回其子模块的缓冲区。否则，只返回这个模块直连成员的缓冲区。


| Yields: | _(string, torch.Tensor)_ – 包含了缓冲区的名字和缓冲区自身的元组 |
| --- | --- |

例子:

```py
>>> for name, buf in self.named_buffers():
>>>    if name in ['running_var']:
>>>        print(buf.size())

```

```py
named_children()
```

返回一个当前模型直连的子模块的迭代器，每次返回的元素是由子模块的名字和子模块自身组成的元组。


| Yields: | _(string, Module)_ – 包含了子模块的名字和子模块自身的元组 |
| --- | --- |

例子：

```py
>>> for name, module in model.named_children():
>>>     if name in ['conv4', 'conv5']:
>>>         print(module)

```

```py
named_modules(memo=None, prefix='')
```

返回一个当前模块内所有模块（包括自身）的迭代器，每次返回的元素是由模块的名字和模块自身组成的元组。


| Yields: | _(string, Module)_ – 模块名字和模块自身组成的元组 |
| --- | --- |

Note

重复的模块只会被返回一次。在下面的例子中，`l`只被返回了一次。

例子：

```py
>>> 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))

```

```py
named_parameters(prefix='', recurse=True)
```

返回一个当前模块内所有参数的迭代器，每次返回的元素是由参数的名字和参数自身组成的元组。

named_parameters()函数参数：

*   **prefix** ([_str_](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.7)")) – 要在所有参数名字前面添加的前缀。
*   **recurse** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")) – 如果设置为True，那样迭代器中不光会返回这个模块自身直连成员的参数，同时也会返回其子模块的参数。否则，只返回这个模块直连成员的参数。


| Yields: | _(string, Parameter)_ – 参数名字和参数自身组成的元组 |
| --- | --- |

例子:

```py
>>> for name, param in self.named_parameters():
>>>    if name in ['bias']:
>>>        print(param.size())

```

```py
parameters(recurse=True)
```

返回一个遍历模块所有参数的迭代器。
parameters()函数一个经典的应用就是实践中经常将此函数的返回值传入优化器。

| Parameters: | **recurse** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")) –  如果设置为True，那样迭代器中不光会返回这个模块自身直连成员的参数，同时也会递归返回其子模块的参数。否则，只返回这个模块直连成员的参数。 |
| --- | --- |
| Yields: | _Parameter_ – 模块参数 |
| --- | --- |

例子:

```py
>>> for param in model.parameters():
>>>     print(type(param.data), param.size())
<class 'torch.FloatTensor'> (20L,)
<class 'torch.FloatTensor'> (20L, 1L, 5L, 5L)

```

```py
register_backward_hook(hook)
```

在模块上注册一个挂载在反向操作之后的钩子函数。（挂载在backward之后这个点上的钩子函数）

对于每次输入，当模块关于此次输入的反向梯度的计算过程完成，该钩子函数都会被调用一次。此钩子函数需要遵从以下函数签名：


```py
hook(module, grad_input, grad_output) -> Tensor or None

```

如果模块的输入或输出是多重的（multiple inputs or outputs），那 `grad_input` 和 `grad_output` 应当是元组数据。 钩子函数不能对输入的参数`grad_input` 和 `grad_output`进行任何更改，但是可以选择性地根据输入的参数返回一个新的梯度回去，而这个新的梯度在后续的计算中会替换掉`grad_input`。

| Returns: | 一个句柄（handle），这个handle的特点就是通过调用`handle.remove()`函数就可以将这个添加于模块之上的钩子移除掉。|
| --- | --- |
| Return type: | `torch.utils.hooks.RemovableHandle` |
| --- | --- |

Warning

对于一些具有很多复杂操作的[`Module`](#torch.nn.Module "torch.nn.Module")，当前的hook实现版本还不能达到完全理想的效果。举个例子，有些错误的情况下，函数的输入参数`grad_input` 和 `grad_output`中可能只是真正的输入和输出变量的一个子集。对于此类的[`Module`](#torch.nn.Module "torch.nn.Module")，你应该使用[`torch.Tensor.register_hook()`]直接将钩子挂载到某个特定的输入输出的变量上，而不是当前的模块。

```py
register_buffer(name, tensor)
```

往模块上添加一个持久缓冲区。

这个函数的经常会被用于向模块添加不会被认为是模块参数（model parameter）的缓冲区。举个栗子，BatchNorm的`running_mean`就不是一个参数，但却属于持久状态。

所添加的缓冲区可以通过给定的名字(name参数)以访问模块的属性的方式进行访问。

register_buffer()函数的参数: 

*   **name** (_string_) – 要添加的缓冲区的名字。所添加的缓冲区可以通过此名字以访问模块的属性的方式进行访问。
*   **tensor** ([_Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – 需要注册到模块上的缓冲区。



例子:

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

```

```py
register_forward_hook(hook)
```

在模块上注册一个挂载在前向操作之后的钩子函数。（挂载在forward操作结束之后这个点）

此钩子函数在每次模块的 [`forward()`](#torch.nn.Module.forward "torch.nn.Module.forward")函数运行结束产生output之后就会被触发。此钩子函数需要遵从以下函数签名：

```py
hook(module, input, output) -> None

```

此钩子函数不能进行会修改 input 和 output 这两个参数的操作。

| Returns: | 一个句柄（handle），这个handle的特点就是通过调用`handle.remove()`函数就可以将这个添加于模块之上的钩子移除掉。 |
| --- | --- |
| Return type: | `torch.utils.hooks.RemovableHandle` |
| --- | --- |

```py
register_forward_pre_hook(hook)
```

在模块上注册一个挂载在前向操作之前的钩子函数。（挂载在forward操作开始之前这个点）


此钩子函数在每次模块的 [`forward()`](#torch.nn.Module.forward "torch.nn.Module.forward")函数运行开始之前会被触发。此钩子函数需要遵从以下函数签名：
The hook will be called every time before [`forward()`](#torch.nn.Module.forward "torch.nn.Module.forward") is invoked. It should have the following signature:

```py
hook(module, input) -> None

```

此钩子函数不能进行会修改 input 这个参数的操作。

| Returns: | 一个句柄（handle），这个handle的特点就是通过调用`handle.remove()`函数就可以将这个添加于模块之上的钩子移除掉。 |
| --- | --- |
| Return type: | `torch.utils.hooks.RemovableHandle` |
| --- | --- |

```py
register_parameter(name, param)
```

向模块添加一个参数（parameter）。

所添加的参数（parameter）可以通过给定的名字(name参数)以访问模块的属性的方式进行访问。

register_parameter()函数的参数： 

*   **name** (_string_) – 所添加的参数的名字. 所添加的参数（parameter）可以通过此名字以访问模块的属性的方式进行访问
*   **parameter** ([_Parameter_](#torch.nn.Parameter "torch.nn.Parameter")) – 要添加到模块之上的参数。



```py
state_dict(destination=None, prefix='', keep_vars=False)
```

返回一个包含了模块当前所有状态(state)的字典(dictionary)。

所有的参数和持久缓冲区都被囊括在其中。字典的键值就是响应的参数和缓冲区的名字(name)。


| Returns: | 一个包含了模块当前所有状态的字典 |
| --- | --- |
| Return type: | [dict](https://docs.python.org/3/library/stdtypes.html#dict "(in Python v3.7)") |
| --- | --- |

例子:

```py
>>> module.state_dict().keys()
['bias', 'weight']

```

```py
to(*args, **kwargs)
```

移动 并且/或者（and/or）转换所有的参数和缓冲区。

这个函数可以这样调用：

```py
to(device=None, dtype=None, non_blocking=False)
```

```py
to(dtype, non_blocking=False)
```

```py
to(tensor, non_blocking=False)
```

此函数的函数签名跟[`torch.Tensor.to()`](tensors.html#torch.Tensor.to "torch.Tensor.to")函数的函数签名很相似，只不过这个函数`dtype`参数只接受浮点数类型的dtype，如float， double， half（ floating point desired `dtype` s）。同时，这个方法只会将浮点数类型的参数和缓冲区（the floating point parameters and buffers）转化为`dtype`（如果输入参数中给定的话）的数据类型。而对于整数类型的参数和缓冲区（the integral parameters and buffers），即便输入参数中给定了`dtype`，也不会进行转换操作，而如果给定了 `device`参数，移动操作则会正常进行。当`non_blocking`参数被设置为True之后，此函数会尽可能地相对于 host 进行异步的 转换/移动 操作，比如，将存储在固定内存（pinned memory）上的CPU Tensors移动到CUDA设备上这一过程既是如此。

例子在下面。

Note

这个方法对模块的修改都是in-place操作。

to()函数的参数: 

*   **device** (`torch.device`) – 想要将这个模块中的参数和缓冲区转移到的设备。
*   **dtype** (`torch.dtype`) – 想要将这个模块中浮点数的参数和缓冲区转化为的浮点数数据类型。
*   **tensor** ([_torch.Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – 一个Tensor，如果被指定，其dtype和device信息，将分别起到上面两个参数的作用，也就是说，这个模块的浮点数的参数和缓冲区的数据类型将会被转化为这个Tensor的dtype类型，同时被转移到此Tensor所处的设备device上去。


| Returns: | self |
| --- | --- |
| Return type: | [Module](#torch.nn.Module "torch.nn.Module") |
| --- | --- |

例子:

```py
>>> linear = nn.Linear(2, 2)
>>> linear.weight
Parameter containing:
tensor([[ 0.1913, -0.3420],
 [-0.5113, -0.2325]])
>>> linear.to(torch.double)
Linear(in_features=2, out_features=2, bias=True)
>>> linear.weight
Parameter containing:
tensor([[ 0.1913, -0.3420],
 [-0.5113, -0.2325]], dtype=torch.float64)
>>> gpu1 = torch.device("cuda:1")
>>> linear.to(gpu1, dtype=torch.half, non_blocking=True)
Linear(in_features=2, out_features=2, bias=True)
>>> linear.weight
Parameter containing:
tensor([[ 0.1914, -0.3420],
 [-0.5112, -0.2324]], dtype=torch.float16, device='cuda:1')
>>> cpu = torch.device("cpu")
>>> linear.to(cpu)
Linear(in_features=2, out_features=2, bias=True)
>>> linear.weight
Parameter containing:
tensor([[ 0.1914, -0.3420],
 [-0.5112, -0.2324]], dtype=torch.float16)

```

```py
train(mode=True)
```

将模块转换成训练模式。

这个函数只对特定的模块类型有效，如 [`Dropout`](#torch.nn.Dropout "torch.nn.Dropout")和`BatchNorm`等等。如果想了解这些特定模块在训练/测试模式下各自的运作细节，可以看一下这些特殊模块的文档部分。

| Returns: | self |
| --- | --- |
| Return type: | [Module](#torch.nn.Module "torch.nn.Module") |
| --- | --- |

```py
type(dst_type)
```

将所有的参数和缓冲区转化为 `dst_type`的数据类型。

| Parameters: | **dst_type** ([_type_](https://docs.python.org/3/library/functions.html#type "(in Python v3.7)") _or_ _string_) – 要转化的数据类型 |
| --- | --- |
| Returns: | self |
| --- | --- |
| Return type: | [Module](#torch.nn.Module "torch.nn.Module") |
| --- | --- |

```py
zero_grad()
```

讲模块所有参数的梯度设置为0。

### Sequential

```py
class torch.nn.Sequential(*args)
```

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:

```py
# 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

```py
class torch.nn.ModuleList(modules=None)
```

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:

```py
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

```

```py
append(module)
```

Appends a given module to the end of the list.

| Parameters: | **module** ([_nn.Module_](#torch.nn.Module "torch.nn.Module")) – module to append |
| --- | --- |

```py
extend(modules)
```

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

| Parameters: | **modules** (_iterable_) – iterable of modules to append |
| --- | --- |

```py
insert(index, module)
```

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

Parameters: 

*   **index** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – index to insert.
*   **module** ([_nn.Module_](#torch.nn.Module "torch.nn.Module")) – module to insert



### ModuleDict

```py
class torch.nn.ModuleDict(modules=None)
```

Holds submodules in a dictionary.

ModuleDict can be indexed like a regular Python dictionary, but modules it contains are properly registered, and will be visible by all Module methods.

| Parameters: | **modules** (_iterable__,_ _optional_) – a mapping (dictionary) of (string: module) or an iterable of key/value pairs of type (string, module) |
| --- | --- |

Example:

```py
class MyModule(nn.Module):
    def __init__(self):
        super(MyModule, self).__init__()
        self.choices = nn.ModuleDict({
                'conv': nn.Conv2d(10, 10, 3),
                'pool': nn.MaxPool2d(3)
        })
        self.activations = nn.ModuleDict([
                ['lrelu', nn.LeakyReLU()],
                ['prelu', nn.PReLU()]
        ])

    def forward(self, x, choice, act):
        x = self.choices[choice](x)
        x = self.activations[act](x)
        return x

```

```py
clear()
```

Remove all items from the ModuleDict.

```py
items()
```

Return an iterable of the ModuleDict key/value pairs.

```py
keys()
```

Return an iterable of the ModuleDict keys.

```py
pop(key)
```

Remove key from the ModuleDict and return its module.

| Parameters: | **key** (_string_) – key to pop from the ModuleDict |
| --- | --- |

```py
update(modules)
```

Update the ModuleDict with the key/value pairs from a mapping or an iterable, overwriting existing keys.

| Parameters: | **modules** (_iterable_) – a mapping (dictionary) of (string: `Module``) or an iterable of key/value pairs of type (string, `Module``) |
| --- | --- |

```py
values()
```

Return an iterable of the ModuleDict values.

### ParameterList

```py
class torch.nn.ParameterList(parameters=None)
```

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:

```py
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

```

```py
append(parameter)
```

Appends a given parameter at the end of the list.

| Parameters: | **parameter** ([_nn.Parameter_](#torch.nn.Parameter "torch.nn.Parameter")) – parameter to append |
| --- | --- |

```py
extend(parameters)
```

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

| Parameters: | **parameters** (_iterable_) – iterable of parameters to append |
| --- | --- |

### ParameterDict

```py
class torch.nn.ParameterDict(parameters=None)
```

Holds parameters in a dictionary.

ParameterDict can be indexed like a regular Python dictionary, but parameters it contains are properly registered, and will be visible by all Module methods.

| Parameters: | **parameters** (_iterable__,_ _optional_) – a mapping (dictionary) of (string : [`Parameter`](#torch.nn.Parameter "torch.nn.Parameter")) or an iterable of key,value pairs of type (string, [`Parameter`](#torch.nn.Parameter "torch.nn.Parameter")) |
| --- | --- |

Example:

```py
class MyModule(nn.Module):
    def __init__(self):
        super(MyModule, self).__init__()
        self.params = nn.ParameterDict({
                'left': nn.Parameter(torch.randn(5, 10)),
                'right': nn.Parameter(torch.randn(5, 10))
        })

    def forward(self, x, choice):
        x = self.params[choice].mm(x)
        return x

```

```py
clear()
```

Remove all items from the ParameterDict.

```py
items()
```

Return an iterable of the ParameterDict key/value pairs.

```py
keys()
```

Return an iterable of the ParameterDict keys.

```py
pop(key)
```

Remove key from the ParameterDict and return its parameter.

| Parameters: | **key** (_string_) – key to pop from the ParameterDict |
| --- | --- |

```py
update(parameters)
```

Update the ParameterDict with the key/value pairs from a mapping or an iterable, overwriting existing keys.

| Parameters: | **parameters** (_iterable_) – a mapping (dictionary) of (string : [`Parameter`](#torch.nn.Parameter "torch.nn.Parameter")) or an iterable of key/value pairs of type (string, [`Parameter`](#torch.nn.Parameter "torch.nn.Parameter")) |
| --- | --- |

```py
values()
```

Return an iterable of the ParameterDict values.

## Convolution layers

### Conv1d

```py
class torch.nn.Conv1d(in_channels, out_channels, kernel_size, stride=1, padding=0, dilation=1, groups=1, bias=True)
```

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 ![](img/1dad4f3ff614c986028f7100e0205f6d.jpg) and output ![](img/a03de8b18f61a493174a56530fb03f1d.jpg) can be precisely described as:

![](img/806f7530da55bf294a636b8c7ed38bcb.jpg)

where ![](img/d5d3d32b4a35f91edb54c3c3f87d582e.jpg) is the valid [cross-correlation](https://en.wikipedia.org/wiki/Cross-correlation) operator, ![](img/9341d9048ac485106d2b2ee8de14876f.jpg) is a batch size, ![](img/6c8feca3b2da3d6cf371417edff4be4f.jpg) denotes a number of channels, ![](img/db4a9fef02111450bf98261889de550c.jpg) 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](https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md) 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,

    &gt; *   At groups=1, all inputs are convolved to all outputs.
    &gt; *   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.
    &gt; *   At groups= `in_channels`, each input channel is convolved with its own set of filters, of size ![](img/19131f9f53448ae579b613bc7bc90158.jpg)

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](https://en.wikipedia.org/wiki/Cross-correlation), and not a full [cross-correlation](https://en.wikipedia.org/wiki/Cross-correlation). It is up to the user to add proper padding.

Note

When `groups == in_channels` and `out_channels == K * in_channels`, where `K` is a positive integer, this operation is also termed in literature as depthwise convolution.

In other words, for an input of size ![](img/7db3e5e5d600c81e77756d5eee050505.jpg), a depthwise convolution with a depthwise multiplier `K`, can be constructed by arguments ![](img/eab8f2745761d762e48a59446243af90.jpg).

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting `torch.backends.cudnn.deterministic = True`. Please see the notes on [Reproducibility](notes/randomness.html) for background.

Parameters: 

*   **in_channels** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – Number of channels in the input image
*   **out_channels** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – Number of channels produced by the convolution
*   **kernel_size** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – Size of the convolving kernel
*   **stride** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – Stride of the convolution. Default: 1
*   **padding** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – Zero-padding added to both sides of the input. Default: 0
*   **dilation** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – Spacing between kernel elements. Default: 1
*   **groups** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ _optional_) – Number of blocked connections from input channels to output channels. Default: 1
*   **bias** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – If `True`, adds a learnable bias to the output. Default: `True`



```py
Shape:
```

*   Input: ![](img/7db3e5e5d600c81e77756d5eee050505.jpg)

*   Output: ![](img/3423094375906aa21d1b2e095e95c230.jpg) where

    ![](img/91d48a39a90c6b4ed37ac863c1a8ff7b.jpg)

| Variables: | 

*   **weight** ([_Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – the learnable weights of the module of shape (out_channels, in_channels, kernel_size). The values of these weights are sampled from ![](img/3d305f1c240ff844b6cb2c1c6660e0af.jpg) where ![](img/69aab1ce658aabc9a2d986ae8281e2ad.jpg)
*   **bias** ([_Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – the learnable bias of the module of shape (out_channels). If `bias` is `True`, then the values of these weights are sampled from ![](img/3d305f1c240ff844b6cb2c1c6660e0af.jpg) where ![](img/69aab1ce658aabc9a2d986ae8281e2ad.jpg)



Examples:

```py
>>> m = nn.Conv1d(16, 33, 3, stride=2)
>>> input = torch.randn(20, 16, 50)
>>> output = m(input)

```

### Conv2d

```py
class torch.nn.Conv2d(in_channels, out_channels, kernel_size, stride=1, padding=0, dilation=1, groups=1, bias=True)
```

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 ![](img/a6c3a4e9779c159b39576bee3400a00b.jpg) and output ![](img/4b354af142fb0f01680d390ef552829f.jpg) can be precisely described as:

![](img/a4928651cb959fa7871eaebdb489b083.jpg)

where ![](img/d5d3d32b4a35f91edb54c3c3f87d582e.jpg) is the valid 2D [cross-correlation](https://en.wikipedia.org/wiki/Cross-correlation) operator, ![](img/9341d9048ac485106d2b2ee8de14876f.jpg) is a batch size, ![](img/6c8feca3b2da3d6cf371417edff4be4f.jpg) denotes a number of channels, ![](img/9b7d9beafd65e2cf6493bdca741827a5.jpg) is a height of input planes in pixels, and ![](img/90490a34512e9bd1843ed4da713d0813.jpg) 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](https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md) 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,

    &gt; *   At groups=1, all inputs are convolved to all outputs.
    &gt; *   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.
    &gt; *   At groups= `in_channels`, each input channel is convolved with its own set of filters, of size: ![](img/19131f9f53448ae579b613bc7bc90158.jpg).

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](https://en.wikipedia.org/wiki/Cross-correlation), and not a full [cross-correlation](https://en.wikipedia.org/wiki/Cross-correlation). It is up to the user to add proper padding.

Note

When `groups == in_channels` and `out_channels == K * in_channels`, where `K` is a positive integer, this operation is also termed in literature as depthwise convolution.

In other words, for an input of size ![](img/0385ad868fed790d36381b9e8788c18b.jpg), a depthwise convolution with a depthwise multiplier `K`, can be constructed by arguments ![](img/8aee041e54a302b342d50912ce67f44b.jpg).

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting `torch.backends.cudnn.deterministic = True`. Please see the notes on [Reproducibility](notes/randomness.html) for background.

Parameters: 

*   **in_channels** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – Number of channels in the input image
*   **out_channels** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – Number of channels produced by the convolution
*   **kernel_size** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – Size of the convolving kernel
*   **stride** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – Stride of the convolution. Default: 1
*   **padding** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – Zero-padding added to both sides of the input. Default: 0
*   **dilation** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – Spacing between kernel elements. Default: 1
*   **groups** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ _optional_) – Number of blocked connections from input channels to output channels. Default: 1
*   **bias** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – If `True`, adds a learnable bias to the output. Default: `True`



```py
Shape:
```

*   Input: ![](img/0385ad868fed790d36381b9e8788c18b.jpg)

*   Output: ![](img/d3edfe8a9bbdd73ba5c4b566353777f0.jpg) where

    ![](img/a89a5326ab89279b92f4720f63b4eaae.jpg)

    ![](img/03f69d6e3dffc3254359e41f8b310667.jpg)

| Variables: | 

*   **weight** ([_Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – the learnable weights of the module of shape (out_channels, in_channels, kernel_size[0], kernel_size[1]). The values of these weights are sampled from ![](img/3d305f1c240ff844b6cb2c1c6660e0af.jpg) where ![](img/c12e2153347b696ebb784e5675cc566e.jpg)
*   **bias** ([_Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – the learnable bias of the module of shape (out_channels). If `bias` is `True`, then the values of these weights are sampled from ![](img/3d305f1c240ff844b6cb2c1c6660e0af.jpg) where ![](img/c12e2153347b696ebb784e5675cc566e.jpg)



Examples:

```py
>>> # 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

```py
class torch.nn.Conv3d(in_channels, out_channels, kernel_size, stride=1, padding=0, dilation=1, groups=1, bias=True)
```

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 ![](img/ca863d6b44a0246998de77c7c423ec32.jpg) and output ![](img/f05e8faaf90b4c16b23ca0165e8e09f4.jpg) can be precisely described as:

![](img/39831867c152a21de6e580bf01c0cb7f.jpg)

where ![](img/d5d3d32b4a35f91edb54c3c3f87d582e.jpg) is the valid 3D [cross-correlation](https://en.wikipedia.org/wiki/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](https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md) 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,

    &gt; *   At groups=1, all inputs are convolved to all outputs.
    &gt; *   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.
    &gt; *   At groups= `in_channels`, each input channel is convolved with its own set of filters, of size ![](img/648a514da1dace3deacf3f078287e157.jpg).

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](https://en.wikipedia.org/wiki/Cross-correlation), and not a full [cross-correlation](https://en.wikipedia.org/wiki/Cross-correlation). It is up to the user to add proper padding.

Note

When `groups == in_channels` and `out_channels == K * in_channels`, where `K` is a positive integer, this operation is also termed in literature as depthwise convolution.

> In other words, for an input of size ![](img/a8d71105bc4954eb54660bc5d37c23de.jpg), a depthwise convolution with a depthwise multiplier `K`, can be constructed by arguments ![](img/8aee041e54a302b342d50912ce67f44b.jpg).

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting `torch.backends.cudnn.deterministic = True`. Please see the notes on [Reproducibility](notes/randomness.html) for background.

Parameters: 

*   **in_channels** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – Number of channels in the input image
*   **out_channels** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – Number of channels produced by the convolution
*   **kernel_size** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – Size of the convolving kernel
*   **stride** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – Stride of the convolution. Default: 1
*   **padding** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – Zero-padding added to all three sides of the input. Default: 0
*   **dilation** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – Spacing between kernel elements. Default: 1
*   **groups** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ _optional_) – Number of blocked connections from input channels to output channels. Default: 1
*   **bias** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – If `True`, adds a learnable bias to the output. Default: `True`



```py
Shape:
```

*   Input: ![](img/a8d71105bc4954eb54660bc5d37c23de.jpg)

*   Output: ![](img/f05e8faaf90b4c16b23ca0165e8e09f4.jpg) where

    ![](img/bbc2662490bb72269672fe81af1fe003.jpg)

    ![](img/b7ca056f55603d0632bb03bdf9435d47.jpg)

    ![](img/d040a26cd9a91c4d230afd4c15d0e1e6.jpg)

| Variables: | 

*   **weight** ([_Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – the learnable weights of the module of shape (out_channels, in_channels, kernel_size[0], kernel_size[1], kernel_size[2]) The values of these weights are sampled from ![](img/3d305f1c240ff844b6cb2c1c6660e0af.jpg) where ![](img/378f5c5b47c36239b817ad23a612a9f7.jpg)
*   **bias** ([_Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – the learnable bias of the module of shape (out_channels). If `bias` is `True`, then the values of these weights are sampled from ![](img/3d305f1c240ff844b6cb2c1c6660e0af.jpg) where ![](img/378f5c5b47c36239b817ad23a612a9f7.jpg)



Examples:

```py
>>> # 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

```py
class torch.nn.ConvTranspose1d(in_channels, out_channels, kernel_size, stride=1, padding=0, output_padding=0, groups=1, bias=True, dilation=1)
```

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 `kernel_size - 1 - padding` number of points. See note below for details.

*   `output_padding` controls the additional size added to one side of the output shape. See note below for details.

*   `dilation` controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but this [link](https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md) 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,

    &gt; *   At groups=1, all inputs are convolved to all outputs.
    &gt; *   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.
    &gt; *   At groups= `in_channels`, each input channel is convolved with its own set of filters (of size ![](img/648a514da1dace3deacf3f078287e157.jpg)).

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](https://en.wikipedia.org/wiki/Cross-correlation), and not a full [cross-correlation](https://en.wikipedia.org/wiki/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`](#torch.nn.Conv1d "torch.nn.Conv1d") and a [`ConvTranspose1d`](#torch.nn.ConvTranspose1d "torch.nn.ConvTranspose1d") are initialized with same parameters, they are inverses of each other in regard to the input and output shapes. However, when `stride &gt; 1`, [`Conv1d`](#torch.nn.Conv1d "torch.nn.Conv1d") maps multiple input shapes to the same output shape. `output_padding` is provided to resolve this ambiguity by effectively increasing the calculated output shape on one side. Note that `output_padding` is only used to find output shape, but does not actually add zero-padding to output.

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting `torch.backends.cudnn.deterministic = True`. Please see the notes on [Reproducibility](notes/randomness.html) for background.

Parameters: 

*   **in_channels** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – Number of channels in the input image
*   **out_channels** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – Number of channels produced by the convolution
*   **kernel_size** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – Size of the convolving kernel
*   **stride** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – Stride of the convolution. Default: 1
*   **padding** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – `kernel_size - 1 - padding` zero-padding will be added to both sides of the input. Default: 0
*   **output_padding** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – Additional size added to one side of the output shape. Default: 0
*   **groups** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ _optional_) – Number of blocked connections from input channels to output channels. Default: 1
*   **bias** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – If `True`, adds a learnable bias to the output. Default: `True`
*   **dilation** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – Spacing between kernel elements. Default: 1



```py
Shape:
```

*   Input: ![](img/7db3e5e5d600c81e77756d5eee050505.jpg)

*   Output: ![](img/3423094375906aa21d1b2e095e95c230.jpg) where

    ![](img/c37a7e44707d3c08522f44ab4e4d6841.jpg)

| Variables: | 

*   **weight** ([_Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – the learnable weights of the module of shape (in_channels, out_channels, kernel_size[0], kernel_size[1]). The values of these weights are sampled from ![](img/3d305f1c240ff844b6cb2c1c6660e0af.jpg) where ![](img/69aab1ce658aabc9a2d986ae8281e2ad.jpg)
*   **bias** ([_Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – the learnable bias of the module of shape (out_channels). If `bias` is `True`, then the values of these weights are sampled from ![](img/3d305f1c240ff844b6cb2c1c6660e0af.jpg) where ![](img/69aab1ce658aabc9a2d986ae8281e2ad.jpg)



### ConvTranspose2d

```py
class torch.nn.ConvTranspose2d(in_channels, out_channels, kernel_size, stride=1, padding=0, output_padding=0, groups=1, bias=True, dilation=1)
```

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 `kernel_size - 1 - padding` number of points. See note below for details.

*   `output_padding` controls the additional size added to one side of the output shape. See note below for details.

*   `dilation` controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but this [link](https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md) 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,

    &gt; *   At groups=1, all inputs are convolved to all outputs.
    &gt; *   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.
    &gt; *   At groups= `in_channels`, each input channel is convolved with its own set of filters (of size ![](img/648a514da1dace3deacf3f078287e157.jpg)).

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](https://en.wikipedia.org/wiki/Cross-correlation), and not a full [cross-correlation](https://en.wikipedia.org/wiki/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`](#torch.nn.Conv2d "torch.nn.Conv2d") and a [`ConvTranspose2d`](#torch.nn.ConvTranspose2d "torch.nn.ConvTranspose2d") are initialized with same parameters, they are inverses of each other in regard to the input and output shapes. However, when `stride &gt; 1`, [`Conv2d`](#torch.nn.Conv2d "torch.nn.Conv2d") maps multiple input shapes to the same output shape. `output_padding` is provided to resolve this ambiguity by effectively increasing the calculated output shape on one side. Note that `output_padding` is only used to find output shape, but does not actually add zero-padding to output.

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting `torch.backends.cudnn.deterministic = True`. Please see the notes on [Reproducibility](notes/randomness.html) for background.

Parameters: 

*   **in_channels** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – Number of channels in the input image
*   **out_channels** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – Number of channels produced by the convolution
*   **kernel_size** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – Size of the convolving kernel
*   **stride** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – Stride of the convolution. Default: 1
*   **padding** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – `kernel_size - 1 - padding` zero-padding will be added to both sides of each dimension in the input. Default: 0
*   **output_padding** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – Additional size added to one side of each dimension in the output shape. Default: 0
*   **groups** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ _optional_) – Number of blocked connections from input channels to output channels. Default: 1
*   **bias** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – If `True`, adds a learnable bias to the output. Default: `True`
*   **dilation** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – Spacing between kernel elements. Default: 1



```py
Shape:
```

*   Input: ![](img/0385ad868fed790d36381b9e8788c18b.jpg)
*   Output: ![](img/d3edfe8a9bbdd73ba5c4b566353777f0.jpg) where

![](img/a2616e3fb8e8e919b799c2e62921c374.jpg)

![](img/dee6540c49e827b0ececaf0154154b54.jpg)

| Variables: | 

*   **weight** ([_Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – the learnable weights of the module of shape (in_channels, out_channels, kernel_size[0], kernel_size[1]) The values of these weights are sampled from ![](img/3d305f1c240ff844b6cb2c1c6660e0af.jpg) where ![](img/c12e2153347b696ebb784e5675cc566e.jpg)
*   **bias** ([_Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – the learnable bias of the module of shape (out_channels) If `bias` is `True`, then the values of these weights are sampled from ![](img/3d305f1c240ff844b6cb2c1c6660e0af.jpg) where ![](img/c12e2153347b696ebb784e5675cc566e.jpg)



Examples:

```py
>>> # 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

```py
class torch.nn.ConvTranspose3d(in_channels, out_channels, kernel_size, stride=1, padding=0, output_padding=0, groups=1, bias=True, dilation=1)
```

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 `kernel_size - 1 - padding` number of points. See note below for details.

*   `output_padding` controls the additional size added to one side of the output shape. See note below for details.

*   `dilation` controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but this [link](https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md) 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,

    &gt; *   At groups=1, all inputs are convolved to all outputs.
    &gt; *   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.
    &gt; *   At groups= `in_channels`, each input channel is convolved with its own set of filters (of size ![](img/648a514da1dace3deacf3f078287e157.jpg)).

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](https://en.wikipedia.org/wiki/Cross-correlation), and not a full [cross-correlation](https://en.wikipedia.org/wiki/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`](#torch.nn.Conv3d "torch.nn.Conv3d") and a [`ConvTranspose3d`](#torch.nn.ConvTranspose3d "torch.nn.ConvTranspose3d") are initialized with same parameters, they are inverses of each other in regard to the input and output shapes. However, when `stride &gt; 1`, [`Conv3d`](#torch.nn.Conv3d "torch.nn.Conv3d") maps multiple input shapes to the same output shape. `output_padding` is provided to resolve this ambiguity by effectively increasing the calculated output shape on one side. Note that `output_padding` is only used to find output shape, but does not actually add zero-padding to output.

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting `torch.backends.cudnn.deterministic = True`. Please see the notes on [Reproducibility](notes/randomness.html) for background.

Parameters: 

*   **in_channels** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – Number of channels in the input image
*   **out_channels** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – Number of channels produced by the convolution
*   **kernel_size** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – Size of the convolving kernel
*   **stride** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – Stride of the convolution. Default: 1
*   **padding** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – `kernel_size - 1 - padding` zero-padding will be added to both sides of each dimension in the input. Default: 0
*   **output_padding** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – Additional size added to one side of each dimension in the output shape. Default: 0
*   **groups** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ _optional_) – Number of blocked connections from input channels to output channels. Default: 1
*   **bias** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – If `True`, adds a learnable bias to the output. Default: `True`
*   **dilation** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – Spacing between kernel elements. Default: 1



```py
Shape:
```

*   Input: ![](img/a8d71105bc4954eb54660bc5d37c23de.jpg)
*   Output: ![](img/f05e8faaf90b4c16b23ca0165e8e09f4.jpg) where

![](img/35234de680c85870881b7f5d9e8de589.jpg)

![](img/044bc4ee93fc4a1725b5b5dc5840b408.jpg)

![](img/133b249f21b73617ee100c4c072eee15.jpg)

| Variables: | 

*   **weight** ([_Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – the learnable weights of the module of shape (in_channels, out_channels, kernel_size[0], kernel_size[1], kernel_size[2]) The values of these weights are sampled from ![](img/3d305f1c240ff844b6cb2c1c6660e0af.jpg) where ![](img/378f5c5b47c36239b817ad23a612a9f7.jpg)
*   **bias** ([_Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – the learnable bias of the module of shape (out_channels) If `bias` is `True`, then the values of these weights are sampled from ![](img/3d305f1c240ff844b6cb2c1c6660e0af.jpg) where ![](img/378f5c5b47c36239b817ad23a612a9f7.jpg)



Examples:

```py
>>> # With square kernels and equal stride
>>> m = nn.ConvTranspose3d(16, 33, 3, stride=2)
>>> # non-square kernels and unequal stride and with padding
>>> m = nn.ConvTranspose3d(16, 33, (3, 5, 2), stride=(2, 1, 1), padding=(0, 4, 2))
>>> input = torch.randn(20, 16, 10, 50, 100)
>>> output = m(input)

```

### Unfold

```py
class torch.nn.Unfold(kernel_size, dilation=1, padding=0, stride=1)
```

Extracts sliding local blocks from a batched input tensor.

Consider an batched `input` tensor of shape ![](img/2468b226c29a7e754a9c20f0214fa85f.jpg), where ![](img/9341d9048ac485106d2b2ee8de14876f.jpg) is the batch dimension, ![](img/6c8feca3b2da3d6cf371417edff4be4f.jpg) is the channel dimension, and ![](img/28ec51e742166ea3400be6e7343bbfa5.jpg) represent arbitrary spatial dimensions. This operation flattens each sliding `kernel_size`-sized block within the spatial dimensions of `input` into a column (i.e., last dimension) of a 3-D `output` tensor of shape ![](img/4e1cad10fa9480fa82adbe59a5ae81fa.jpg), where ![](img/a8846766f2e1b47021f1520993773ccb.jpg) is the total number of values with in each block (a block has ![](img/8c7a54ca7193bc3a6c5ace8c3b07d24c.jpg) spatial locations each containing a ![](img/6c8feca3b2da3d6cf371417edff4be4f.jpg)-channeled vector), and ![](img/db4a9fef02111450bf98261889de550c.jpg) is the total number of such blocks:

![](img/1d2c6a9103e2b33f725602aebf90364e.jpg)

where ![](img/42a2dca8a9cb6104321cf29ae30fd56a.jpg) is formed by the spatial dimensions of `input` (![](img/28ec51e742166ea3400be6e7343bbfa5.jpg) above), and ![](img/9566974d45a96737f7e0ecf302d877b8.jpg) is over all spatial dimensions.

Therefore, indexing `output` at the last dimension (column dimension) gives all values within a certain block.

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

*   `stride` controls the stride for the sliding blocks.
*   `padding` controls the amount of implicit zero-paddings on both sides for `padding` number of points for each dimension before reshaping.
*   `dilation` controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but this [link](https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md) has a nice visualization of what `dilation` does.

Parameters: 

*   **kernel_size** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – the size of the sliding blocks
*   **stride** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – the stride of the sliding blocks in the input spatial dimensions. Default: 1
*   **padding** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – implicit zero padding to be added on both sides of input. Default: 0
*   **dilation** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – a parameter that controls the stride of elements within the neighborhood. Default: 1



*   If `kernel_size`, `dilation`, `padding` or `stride` is an int or a tuple of length 1, their values will be replicated across all spatial dimensions.
*   For the case of two input spatial dimensions this operation is sometimes called `im2col`.

Note

[`Fold`](#torch.nn.Fold "torch.nn.Fold") calculates each combined value in the resulting large tensor by summing all values from all containing blocks. [`Unfold`](#torch.nn.Unfold "torch.nn.Unfold") extracts the values in the local blocks by copying from the large tensor. So, if the blocks overlap, they are not inverses of each other.

Warning

Currently, only 4-D input tensors (batched image-like tensors) are supported.

```py
Shape:
```

*   Input: ![](img/2468b226c29a7e754a9c20f0214fa85f.jpg)
*   Output: ![](img/4e1cad10fa9480fa82adbe59a5ae81fa.jpg) as described above

Examples:

```py
>>> unfold = nn.Unfold(kernel_size=(2, 3))
>>> input = torch.randn(2, 5, 3, 4)
>>> output = unfold(input)
>>> # each patch contains 30 values (2x3=6 vectors, each of 5 channels)
>>> # 4 blocks (2x3 kernels) in total in the 3x4 input
>>> output.size()
torch.Size([2, 30, 4])

>>> # Convolution is equivalent with Unfold + Matrix Multiplication + Fold (or view to output shape)
>>> inp = torch.randn(1, 3, 10, 12)
>>> w = torch.randn(2, 3, 4, 5)
>>> inp_unf = torch.nn.functional.unfold(inp, (4, 5))
>>> out_unf = inp_unf.transpose(1, 2).matmul(w.view(w.size(0), -1).t()).transpose(1, 2)
>>> out = torch.nn.functional.fold(out_unf, (7, 8), (1, 1))
>>> # or equivalently (and avoiding a copy),
>>> # out = out_unf.view(1, 2, 7, 8)
>>> (torch.nn.functional.conv2d(inp, w) - out).abs().max()
tensor(1.9073e-06)

```

### Fold

```py
class torch.nn.Fold(output_size, kernel_size, dilation=1, padding=0, stride=1)
```

Combines an array of sliding local blocks into a large containing tensor.

Consider a batched `input` tensor containing sliding local blocks, e.g., patches of images, of shape ![](img/9e56ff5e3827b936da5cfa3a5258b12e.jpg), where ![](img/9341d9048ac485106d2b2ee8de14876f.jpg) is batch dimension, ![](img/a8846766f2e1b47021f1520993773ccb.jpg) is the number of values with in a block (a block has ![](img/8c7a54ca7193bc3a6c5ace8c3b07d24c.jpg) spatial locations each containing a ![](img/6c8feca3b2da3d6cf371417edff4be4f.jpg)-channeled vector), and ![](img/db4a9fef02111450bf98261889de550c.jpg) is the total number of blocks. (This is exacly the same specification as the output shape of [`Unfold`](#torch.nn.Unfold "torch.nn.Unfold").) This operation combines these local blocks into the large `output` tensor of shape ![](img/c2176aae9e099eeee07cc00c4dc7b7e7.jpg) by summing the overlapping values. Similar to [`Unfold`](#torch.nn.Unfold "torch.nn.Unfold"), the arguments must satisfy

![](img/465bba7070e80a7e5964f46f7f5ed8bb.jpg)

where ![](img/9566974d45a96737f7e0ecf302d877b8.jpg) is over all spatial dimensions.

*   `output_size` describes the spatial shape of the large containing tensor of the sliding local blocks. It is useful to resolve the ambiguity when multiple input shapes map to same number of sliding blocks, e.g., with `stride &gt; 0`.

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

*   `stride` controls the stride for the sliding blocks.
*   `padding` controls the amount of implicit zero-paddings on both sides for `padding` number of points for each dimension before reshaping.
*   `dilation` controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but this [link](https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md) has a nice visualization of what `dilation` does.

Parameters: 

*   **output_size** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – the shape of the spatial dimensions of the output (i.e., `input.sizes()[2:]`)
*   **kernel_size** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – the size of the sliding blocks
*   **stride** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – the stride of the sliding blocks in the input spatial dimensions. Default: 1
*   **padding** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – implicit zero padding to be added on both sides of input. Default: 0
*   **dilation** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – a parameter that controls the stride of elements within the neighborhood. Default: 1



*   If `output_size`, `kernel_size`, `dilation`, `padding` or `stride` is an int or a tuple of length 1 then their values will be replicated across all spatial dimensions.
*   For the case of two output spatial dimensions this operation is sometimes called `col2im`.

Note

[`Fold`](#torch.nn.Fold "torch.nn.Fold") calculates each combined value in the resulting large tensor by summing all values from all containing blocks. [`Unfold`](#torch.nn.Unfold "torch.nn.Unfold") extracts the values in the local blocks by copying from the large tensor. So, if the blocks overlap, they are not inverses of each other.

Warning

Currently, only 4-D output tensors (batched image-like tensors) are supported.

```py
Shape:
```

*   Input: ![](img/4e1cad10fa9480fa82adbe59a5ae81fa.jpg)
*   Output: ![](img/c2176aae9e099eeee07cc00c4dc7b7e7.jpg) as described above

Examples:

```py
>>> fold = nn.Fold(output_size=(4, 5), kernel_size=(2, 2))
>>> input = torch.randn(1, 3 * 2 * 2, 1)
>>> output = fold(input)
>>> output.size()

```

## Pooling layers

### MaxPool1d

```py
class torch.nn.MaxPool1d(kernel_size, stride=None, padding=0, dilation=1, return_indices=False, ceil_mode=False)
```

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 ![](img/5816e96aa78b7425cf792435bba8bc29.jpg) and output ![](img/d131773750846713475c600aa8cd917a.jpg) can be precisely described as:

![](img/9e414c5b7df992e54f3227bb130be349.jpg)

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](https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md) 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 for [`torch.nn.MaxUnpool1d`](#torch.nn.MaxUnpool1d "torch.nn.MaxUnpool1d") later
*   **ceil_mode** – when True, will use `ceil` instead of `floor` to compute the output shape



```py
Shape:
```

*   Input: ![](img/3ceb415a2a1558bab9998c277f780ec3.jpg)

*   Output: ![](img/d131773750846713475c600aa8cd917a.jpg), where

    ![](img/ff16cce6b4741640e8adc0a271cd4592.jpg)

Examples:

```py
>>> # pool of size=3, stride=2
>>> m = nn.MaxPool1d(3, stride=2)
>>> input = torch.randn(20, 16, 50)
>>> output = m(input)

```

### MaxPool2d

```py
class torch.nn.MaxPool2d(kernel_size, stride=None, padding=0, dilation=1, return_indices=False, ceil_mode=False)
```

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 ![](img/23f8772594b27bd387be708fe9c085e1.jpg), output ![](img/a0ef05f779873fc4dcbf020b1ea14754.jpg) and `kernel_size` ![](img/6384e001ad4c0989683deb86f6ffbd2f.jpg) can be precisely described as:

![](img/caa8cbcbb8bbbbc6b0e47f9daa80ab12.jpg)

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](https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md) 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 for [`torch.nn.MaxUnpool2d`](#torch.nn.MaxUnpool2d "torch.nn.MaxUnpool2d") later
*   **ceil_mode** – when True, will use `ceil` instead of `floor` to compute the output shape



```py
Shape:
```

*   Input: ![](img/ff71b16eb10237262566c6907acaaf1f.jpg)

*   Output: ![](img/a0ef05f779873fc4dcbf020b1ea14754.jpg), where

    ![](img/991d42318f90dcb68b26938c542b8457.jpg)

    ![](img/1e35edf42ee6921adb435b5ca638d406.jpg)

Examples:

```py
>>> # 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

```py
class torch.nn.MaxPool3d(kernel_size, stride=None, padding=0, dilation=1, return_indices=False, ceil_mode=False)
```

Applies a 3D max pooling over an input signal composed of several input planes. This is not a test

In the simplest case, the output value of the layer with input size ![](img/f5a45f7b445db562b21cfcb525637aab.jpg), output ![](img/41ca4c8d4c65c979d2d643c6f62ea280.jpg) and `kernel_size` ![](img/f5dcdebf9a81b9d15227749ae7535eb7.jpg) can be precisely described as:

![](img/f0f7a770dcfb802e7fc0f8995cfad3d7.jpg)

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](https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md) 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 for [`torch.nn.MaxUnpool3d`](#torch.nn.MaxUnpool3d "torch.nn.MaxUnpool3d") later
*   **ceil_mode** – when True, will use `ceil` instead of `floor` to compute the output shape



```py
Shape:
```

*   Input: ![](img/c187d190013d0785320e3412fe8cd669.jpg)

*   Output: ![](img/41ca4c8d4c65c979d2d643c6f62ea280.jpg), where

    ![](img/0e49f319aa911192458f7b02321eff3a.jpg)

    ![](img/b8fbd329439d7eba62abdf0df19f464d.jpg)

    ![](img/eb1d0c30d1cf681f38e8391bd7d03dff.jpg)

Examples:

```py
>>> # 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

```py
class torch.nn.MaxUnpool1d(kernel_size, stride=None, padding=0)
```

Computes a partial inverse of [`MaxPool1d`](#torch.nn.MaxPool1d "torch.nn.MaxPool1d").

[`MaxPool1d`](#torch.nn.MaxPool1d "torch.nn.MaxPool1d") is not fully invertible, since the non-maximal values are lost.

[`MaxUnpool1d`](#torch.nn.MaxUnpool1d "torch.nn.MaxUnpool1d") takes in as input the output of [`MaxPool1d`](#torch.nn.MaxPool1d "torch.nn.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`](#torch.nn.MaxPool1d "torch.nn.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_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – Size of the max pooling window.
*   **stride** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – Stride of the max pooling window. It is set to `kernel_size` by default.
*   **padding** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – Padding that was added to the input



```py
Inputs:
```

*   `input`: the input Tensor to invert
*   `indices`: the indices given out by [`MaxPool1d`](#torch.nn.MaxPool1d "torch.nn.MaxPool1d")
*   `output_size` (optional): the targeted output size

```py
Shape:
```

*   Input: ![](img/ccc1792005f1eb97a439118aeba930e9.jpg)

*   Output: ![](img/1b0403b4ee318895368afc8fa37b9407.jpg), where

    ![](img/9618fc866026e724d16c5481dd67dc4c.jpg)

    or as given by `output_size` in the call operator

Example:

```py
>>> 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

```py
class torch.nn.MaxUnpool2d(kernel_size, stride=None, padding=0)
```

Computes a partial inverse of [`MaxPool2d`](#torch.nn.MaxPool2d "torch.nn.MaxPool2d").

[`MaxPool2d`](#torch.nn.MaxPool2d "torch.nn.MaxPool2d") is not fully invertible, since the non-maximal values are lost.

[`MaxUnpool2d`](#torch.nn.MaxUnpool2d "torch.nn.MaxUnpool2d") takes in as input the output of [`MaxPool2d`](#torch.nn.MaxPool2d "torch.nn.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`](#torch.nn.MaxPool2d "torch.nn.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_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – Size of the max pooling window.
*   **stride** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – Stride of the max pooling window. It is set to `kernel_size` by default.
*   **padding** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – Padding that was added to the input



```py
Inputs:
```

*   `input`: the input Tensor to invert
*   `indices`: the indices given out by [`MaxPool2d`](#torch.nn.MaxPool2d "torch.nn.MaxPool2d")
*   `output_size` (optional): the targeted output size

```py
Shape:
```

*   Input: ![](img/ff71b16eb10237262566c6907acaaf1f.jpg)

*   Output: ![](img/a0ef05f779873fc4dcbf020b1ea14754.jpg), where

    ![](img/f6dd707e18ccbf75f607d05338443e87.jpg)

    ![](img/ac5d54ef9922f9e0dbe2dc916bf9d80b.jpg)

    or as given by `output_size` in the call operator

Example:

```py
>>> 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

```py
class torch.nn.MaxUnpool3d(kernel_size, stride=None, padding=0)
```

Computes a partial inverse of [`MaxPool3d`](#torch.nn.MaxPool3d "torch.nn.MaxPool3d").

[`MaxPool3d`](#torch.nn.MaxPool3d "torch.nn.MaxPool3d") is not fully invertible, since the non-maximal values are lost. [`MaxUnpool3d`](#torch.nn.MaxUnpool3d "torch.nn.MaxUnpool3d") takes in as input the output of [`MaxPool3d`](#torch.nn.MaxPool3d "torch.nn.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`](#torch.nn.MaxPool3d "torch.nn.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_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – Size of the max pooling window.
*   **stride** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – Stride of the max pooling window. It is set to `kernel_size` by default.
*   **padding** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – Padding that was added to the input



```py
Inputs:
```

*   `input`: the input Tensor to invert
*   `indices`: the indices given out by [`MaxPool3d`](#torch.nn.MaxPool3d "torch.nn.MaxPool3d")
*   `output_size` (optional): the targeted output size

```py
Shape:
```

*   Input: ![](img/c187d190013d0785320e3412fe8cd669.jpg)

*   Output: ![](img/41ca4c8d4c65c979d2d643c6f62ea280.jpg), where

    ![](img/190cbccb4ab554a9b19bfc3df956f982.jpg)

    ![](img/785a4e892f32eee65446b4e269fc452b.jpg)

    ![](img/e666e9d78ffab5d03b4cf1adf1a6e331.jpg)

    or as given by `output_size` in the call operator

Example:

```py
>>> # 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

```py
class torch.nn.AvgPool1d(kernel_size, stride=None, padding=0, ceil_mode=False, count_include_pad=True)
```

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 ![](img/5816e96aa78b7425cf792435bba8bc29.jpg), output ![](img/d131773750846713475c600aa8cd917a.jpg) and `kernel_size` ![](img/a1c2f8d5b1226e67bdb44b12a6ddf18b.jpg) can be precisely described as:

![](img/5df0036df168f4a16d4437d91968f640.jpg)

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



```py
Shape:
```

*   Input: ![](img/3ceb415a2a1558bab9998c277f780ec3.jpg)

*   Output: ![](img/d131773750846713475c600aa8cd917a.jpg), where

    ![](img/ad61a9298a545292682229fef2f1a910.jpg)

Examples:

```py
>>> # 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

```py
class torch.nn.AvgPool2d(kernel_size, stride=None, padding=0, ceil_mode=False, count_include_pad=True)
```

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 ![](img/23f8772594b27bd387be708fe9c085e1.jpg), output ![](img/a0ef05f779873fc4dcbf020b1ea14754.jpg) and `kernel_size` ![](img/6384e001ad4c0989683deb86f6ffbd2f.jpg) can be precisely described as:

![](img/b7a0e1d0a42a3626724c14d89a10a44f.jpg)

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



```py
Shape:
```

*   Input: ![](img/ff71b16eb10237262566c6907acaaf1f.jpg)

*   Output: ![](img/a0ef05f779873fc4dcbf020b1ea14754.jpg), where

    ![](img/8b8b2b1a77c4f104a936efb1708366ef.jpg)

    ![](img/2792347200dabe493ae8baee428f9bf8.jpg)

Examples:

```py
>>> # 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

```py
class torch.nn.AvgPool3d(kernel_size, stride=None, padding=0, ceil_mode=False, count_include_pad=True)
```

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 ![](img/f5a45f7b445db562b21cfcb525637aab.jpg), output ![](img/41ca4c8d4c65c979d2d643c6f62ea280.jpg) and `kernel_size` ![](img/f5dcdebf9a81b9d15227749ae7535eb7.jpg) can be precisely described as:

![](img/79acedd31cd18baac8d97ab96a7092e0.jpg)

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



```py
Shape:
```

*   Input: ![](img/c187d190013d0785320e3412fe8cd669.jpg)

*   Output: ![](img/41ca4c8d4c65c979d2d643c6f62ea280.jpg), where

    ![](img/443035401ce7a1144122a862f34493cf.jpg)

    ![](img/8488a299a75cb56e138e1dc5a24a10db.jpg)

    ![](img/c799c115b670c02d039f828fe1afa443.jpg)

Examples:

```py
>>> # 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

```py
class torch.nn.FractionalMaxPool2d(kernel_size, output_size=None, output_ratio=None, return_indices=False, _random_samples=None)
```

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](http://arxiv.org/abs/1412.6071) by Ben Graham

The max-pooling operation is applied in ![](img/52ec12db6613ee8a0f6f41143ab2e8a2.jpg) 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

```py
>>> # 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

```py
class torch.nn.LPPool1d(norm_type, kernel_size, stride=None, ceil_mode=False)
```

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

On each window, the function computed is:

![](img/e4451f809255881ee286970ddf3fb377.jpg)

*   At p = infinity, one gets Max Pooling
*   At p = 1, one gets Sum Pooling (which is proportional to Average Pooling)

Note

If the sum to the power of `p` is zero, the gradient of this function is not defined. This implementation will set the gradient to zero in this case.

Parameters: 

*   **kernel_size** – a single int, the size of the window
*   **stride** – a single int, the stride of the window. Default value is `kernel_size`
*   **ceil_mode** – when True, will use `ceil` instead of `floor` to compute the output shape



```py
Shape:
```

*   Input: ![](img/3ceb415a2a1558bab9998c277f780ec3.jpg)

*   Output: ![](img/d131773750846713475c600aa8cd917a.jpg), where

    ![](img/5d246e9891509c48081bc89191e64418.jpg)

```py
Examples::
```

```py
>>> # 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

```py
class torch.nn.LPPool2d(norm_type, kernel_size, stride=None, ceil_mode=False)
```

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

On each window, the function computed is:

![](img/e4451f809255881ee286970ddf3fb377.jpg)

*   At p = ![](img/b0c1b8fa38555e0b1ca3265b84bb3974.jpg), one gets Max Pooling
*   At p = 1, one gets Sum Pooling (which is proportional to average pooling)

The parameters `kernel_size`, `stride` can either be:

> *   a single `int` – in which case the same value is used for the height and width dimension
> *   a `tuple` of two ints – in which case, the first `int` is used for the height dimension, and the second `int` for the width dimension

Note

If the sum to the power of `p` is zero, the gradient of this function is not defined. This implementation will set the gradient to zero in this case.

Parameters: 

*   **kernel_size** – the size of the window
*   **stride** – the stride of the window. Default value is `kernel_size`
*   **ceil_mode** – when True, will use `ceil` instead of `floor` to compute the output shape



```py
Shape:
```

*   Input: ![](img/ff71b16eb10237262566c6907acaaf1f.jpg)

*   Output: ![](img/a0ef05f779873fc4dcbf020b1ea14754.jpg), where

    ![](img/44bfdaa5e6b603085c2da3eddb558556.jpg)

    ![](img/d59b07475dea090e5f7110600d8f8bdc.jpg)

Examples:

```py
>>> # 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)

```

### AdaptiveMaxPool1d

```py
class torch.nn.AdaptiveMaxPool1d(output_size, return_indices=False)
```

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

```py
>>> # target output size of 5
>>> m = nn.AdaptiveMaxPool1d(5)
>>> input = torch.randn(1, 64, 8)
>>> output = m(input)

```

### AdaptiveMaxPool2d

```py
class torch.nn.AdaptiveMaxPool2d(output_size, return_indices=False)
```

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

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

```

### AdaptiveMaxPool3d

```py
class torch.nn.AdaptiveMaxPool3d(output_size, return_indices=False)
```

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

```py
>>> # target output size of 5x7x9
>>> m = nn.AdaptiveMaxPool3d((5,7,9))
>>> input = torch.randn(1, 64, 8, 9, 10)
>>> output = m(input)
>>> # target output size of 7x7x7 (cube)
>>> m = nn.AdaptiveMaxPool3d(7)
>>> input = torch.randn(1, 64, 10, 9, 8)
>>> output = m(input)
>>> # target output size of 7x9x8
>>> m = nn.AdaptiveMaxPool3d((7, None, None))
>>> input = torch.randn(1, 64, 10, 9, 8)
>>> output = m(input)

```

### AdaptiveAvgPool1d

```py
class torch.nn.AdaptiveAvgPool1d(output_size)
```

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

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

```

### AdaptiveAvgPool2d

```py
class torch.nn.AdaptiveAvgPool2d(output_size)
```

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

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

```

### AdaptiveAvgPool3d

```py
class torch.nn.AdaptiveAvgPool3d(output_size)
```

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

```py
>>> # target output size of 5x7x9
>>> m = nn.AdaptiveAvgPool3d((5,7,9))
>>> input = torch.randn(1, 64, 8, 9, 10)
>>> output = m(input)
>>> # target output size of 7x7x7 (cube)
>>> m = nn.AdaptiveAvgPool3d(7)
>>> input = torch.randn(1, 64, 10, 9, 8)
>>> output = m(input)
>>> # target output size of 7x9x8
>>> m = nn.AdaptiveMaxPool3d((7, None, None))
>>> input = torch.randn(1, 64, 10, 9, 8)
>>> output = m(input)

```

## Padding layers

### ReflectionPad1d

```py
class torch.nn.ReflectionPad1d(padding)
```

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

For `N`-dimensional padding, use [`torch.nn.functional.pad()`](#torch.nn.functional.pad "torch.nn.functional.pad").

| Parameters: | **padding** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – the size of the padding. If is `int`, uses the same padding in all boundaries. If a 2-`tuple`, uses (![](img/08b2cac9ee37dde4cec3d372ebbfa0bd.jpg), ![](img/9f56071a00e2baa50d7fa9bde997852d.jpg)) |
| --- | --- |

```py
Shape:
```

*   Input: ![](img/964aa6df63e83f4468aa090441f01972.jpg)
*   Output: ![](img/ac2661719f40fc422e2b1590a1e7b4a4.jpg) where ![](img/e2294a717e6d12035072d23c45273863.jpg)

Examples:

```py
>>> m = nn.ReflectionPad1d(2)
>>> input = torch.arange(8, dtype=torch.float).reshape(1, 2, 4)
>>> input
tensor([[[0., 1., 2., 3.],
 [4., 5., 6., 7.]]])
>>> m(input)
tensor([[[2., 1., 0., 1., 2., 3., 2., 1.],
 [6., 5., 4., 5., 6., 7., 6., 5.]]])
>>> m(input)
tensor([[[2., 1., 0., 1., 2., 3., 2., 1.],
 [6., 5., 4., 5., 6., 7., 6., 5.]]])
>>> # using different paddings for different sides
>>> m = nn.ReflectionPad1d((3, 1))
>>> m(input)
tensor([[[3., 2., 1., 0., 1., 2., 3., 2.],
 [7., 6., 5., 4., 5., 6., 7., 6.]]])

```

### ReflectionPad2d

```py
class torch.nn.ReflectionPad2d(padding)
```

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

For `N`-dimensional padding, use [`torch.nn.functional.pad()`](#torch.nn.functional.pad "torch.nn.functional.pad").

| Parameters: | **padding** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – the size of the padding. If is `int`, uses the same padding in all boundaries. If a 4-`tuple`, uses (![](img/08b2cac9ee37dde4cec3d372ebbfa0bd.jpg), ![](img/9f56071a00e2baa50d7fa9bde997852d.jpg), ![](img/65f6ce26141c225acd502a7bef164f66.jpg), ![](img/9a98061e27ba6ed06e846767b9c77c3a.jpg)) |
| --- | --- |

```py
Shape:
```

*   Input: ![](img/ff71b16eb10237262566c6907acaaf1f.jpg)

*   Output: ![](img/a0ef05f779873fc4dcbf020b1ea14754.jpg) where

    ![](img/75aa7c4a6c84e0ccb8aa91592cf6a077.jpg) ![](img/e2294a717e6d12035072d23c45273863.jpg)

Examples:

```py
>>> m = nn.ReflectionPad2d(2)
>>> input = torch.arange(9, dtype=torch.float).reshape(1, 1, 3, 3)
>>> input
tensor([[[[0., 1., 2.],
 [3., 4., 5.],
 [6., 7., 8.]]]])
>>> m(input)
tensor([[[[8., 7., 6., 7., 8., 7., 6.],
 [5., 4., 3., 4., 5., 4., 3.],
 [2., 1., 0., 1., 2., 1., 0.],
 [5., 4., 3., 4., 5., 4., 3.],
 [8., 7., 6., 7., 8., 7., 6.],
 [5., 4., 3., 4., 5., 4., 3.],
 [2., 1., 0., 1., 2., 1., 0.]]]])
>>> # using different paddings for different sides
>>> m = nn.ReflectionPad2d((1, 1, 2, 0))
>>> m(input)
tensor([[[[7., 6., 7., 8., 7.],
 [4., 3., 4., 5., 4.],
 [1., 0., 1., 2., 1.],
 [4., 3., 4., 5., 4.],
 [7., 6., 7., 8., 7.]]]])

```

### ReplicationPad1d

```py
class torch.nn.ReplicationPad1d(padding)
```

Pads the input tensor using replication of the input boundary.

For `N`-dimensional padding, use [`torch.nn.functional.pad()`](#torch.nn.functional.pad "torch.nn.functional.pad").

| Parameters: | **padding** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – the size of the padding. If is `int`, uses the same padding in all boundaries. If a 2-`tuple`, uses (![](img/08b2cac9ee37dde4cec3d372ebbfa0bd.jpg), ![](img/9f56071a00e2baa50d7fa9bde997852d.jpg)) |
| --- | --- |

```py
Shape:
```

*   Input: ![](img/964aa6df63e83f4468aa090441f01972.jpg)
*   Output: ![](img/ac2661719f40fc422e2b1590a1e7b4a4.jpg) where ![](img/e2294a717e6d12035072d23c45273863.jpg)

Examples:

```py
>>> m = nn.ReplicationPad1d(2)
>>> input = torch.arange(8, dtype=torch.float).reshape(1, 2, 4)
>>> input
tensor([[[0., 1., 2., 3.],
 [4., 5., 6., 7.]]])
>>> m(input)
tensor([[[0., 0., 0., 1., 2., 3., 3., 3.],
 [4., 4., 4., 5., 6., 7., 7., 7.]]])
>>> # using different paddings for different sides
>>> m = nn.ReplicationPad1d((3, 1))
>>> m(input)
tensor([[[0., 0., 0., 0., 1., 2., 3., 3.],
 [4., 4., 4., 4., 5., 6., 7., 7.]]])

```

### ReplicationPad2d

```py
class torch.nn.ReplicationPad2d(padding)
```

Pads the input tensor using replication of the input boundary.

For `N`-dimensional padding, use [`torch.nn.functional.pad()`](#torch.nn.functional.pad "torch.nn.functional.pad").

| Parameters: | **padding** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – the size of the padding. If is `int`, uses the same padding in all boundaries. If a 4-`tuple`, uses (![](img/08b2cac9ee37dde4cec3d372ebbfa0bd.jpg), ![](img/9f56071a00e2baa50d7fa9bde997852d.jpg), ![](img/65f6ce26141c225acd502a7bef164f66.jpg), ![](img/9a98061e27ba6ed06e846767b9c77c3a.jpg)) |
| --- | --- |

```py
Shape:
```

*   Input: ![](img/ff71b16eb10237262566c6907acaaf1f.jpg)
*   Output: ![](img/a0ef05f779873fc4dcbf020b1ea14754.jpg) where ![](img/75aa7c4a6c84e0ccb8aa91592cf6a077.jpg) ![](img/e2294a717e6d12035072d23c45273863.jpg)

Examples:

```py
>>> m = nn.ReplicationPad2d(2)
>>> input = torch.arange(9, dtype=torch.float).reshape(1, 1, 3, 3)
>>> input
tensor([[[[0., 1., 2.],
 [3., 4., 5.],
 [6., 7., 8.]]]])
>>> m(input)
tensor([[[[0., 0., 0., 1., 2., 2., 2.],
 [0., 0., 0., 1., 2., 2., 2.],
 [0., 0., 0., 1., 2., 2., 2.],
 [3., 3., 3., 4., 5., 5., 5.],
 [6., 6., 6., 7., 8., 8., 8.],
 [6., 6., 6., 7., 8., 8., 8.],
 [6., 6., 6., 7., 8., 8., 8.]]]])
>>> # using different paddings for different sides
>>> m = nn.ReplicationPad2d((1, 1, 2, 0))
>>> m(input)
tensor([[[[0., 0., 1., 2., 2.],
 [0., 0., 1., 2., 2.],
 [0., 0., 1., 2., 2.],
 [3., 3., 4., 5., 5.],
 [6., 6., 7., 8., 8.]]]])

```

### ReplicationPad3d

```py
class torch.nn.ReplicationPad3d(padding)
```

Pads the input tensor using replication of the input boundary.

For `N`-dimensional padding, use [`torch.nn.functional.pad()`](#torch.nn.functional.pad "torch.nn.functional.pad").

| Parameters: | **padding** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – the size of the padding. If is `int`, uses the same padding in all boundaries. If a 6-`tuple`, uses (![](img/08b2cac9ee37dde4cec3d372ebbfa0bd.jpg), ![](img/9f56071a00e2baa50d7fa9bde997852d.jpg), ![](img/65f6ce26141c225acd502a7bef164f66.jpg), ![](img/9a98061e27ba6ed06e846767b9c77c3a.jpg), ![](img/bffb266183e8fa640240e16a45076c34.jpg), ![](img/9138ac0ee6f6e96dfe795ead91ec0003.jpg)) |
| --- | --- |

```py
Shape:
```

*   Input: ![](img/c187d190013d0785320e3412fe8cd669.jpg)
*   Output: ![](img/41ca4c8d4c65c979d2d643c6f62ea280.jpg) where ![](img/006114d9c80210ede5da92f2f3a44bb7.jpg) ![](img/75aa7c4a6c84e0ccb8aa91592cf6a077.jpg) ![](img/e2294a717e6d12035072d23c45273863.jpg)

Examples:

```py
>>> m = nn.ReplicationPad3d(3)
>>> input = torch.randn(16, 3, 8, 320, 480)
>>> output = m(input)
>>> # using different paddings for different sides
>>> m = nn.ReplicationPad3d((3, 3, 6, 6, 1, 1))
>>> output = m(input)

```

### ZeroPad2d

```py
class torch.nn.ZeroPad2d(padding)
```

Pads the input tensor boundaries with zero.

For `N`-dimensional padding, use [`torch.nn.functional.pad()`](#torch.nn.functional.pad "torch.nn.functional.pad").

| Parameters: | **padding** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – the size of the padding. If is `int`, uses the same padding in all boundaries. If a 4-`tuple`, uses (![](img/08b2cac9ee37dde4cec3d372ebbfa0bd.jpg), ![](img/9f56071a00e2baa50d7fa9bde997852d.jpg), ![](img/65f6ce26141c225acd502a7bef164f66.jpg), ![](img/9a98061e27ba6ed06e846767b9c77c3a.jpg)) |
| --- | --- |

```py
Shape:
```

*   Input: ![](img/ff71b16eb10237262566c6907acaaf1f.jpg)
*   Output: ![](img/a0ef05f779873fc4dcbf020b1ea14754.jpg) where ![](img/75aa7c4a6c84e0ccb8aa91592cf6a077.jpg) ![](img/e2294a717e6d12035072d23c45273863.jpg)

Examples:

```py
>>> m = nn.ZeroPad2d(2)
>>> input = torch.randn(1, 1, 3, 3)
>>> input
tensor([[[[-0.1678, -0.4418,  1.9466],
 [ 0.9604, -0.4219, -0.5241],
 [-0.9162, -0.5436, -0.6446]]]])
>>> m(input)
tensor([[[[ 0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000],
 [ 0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000],
 [ 0.0000,  0.0000, -0.1678, -0.4418,  1.9466,  0.0000,  0.0000],
 [ 0.0000,  0.0000,  0.9604, -0.4219, -0.5241,  0.0000,  0.0000],
 [ 0.0000,  0.0000, -0.9162, -0.5436, -0.6446,  0.0000,  0.0000],
 [ 0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000],
 [ 0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000]]]])
>>> # using different paddings for different sides
>>> m = nn.ZeroPad2d((1, 1, 2, 0))
>>> m(input)
tensor([[[[ 0.0000,  0.0000,  0.0000,  0.0000,  0.0000],
 [ 0.0000,  0.0000,  0.0000,  0.0000,  0.0000],
 [ 0.0000, -0.1678, -0.4418,  1.9466,  0.0000],
 [ 0.0000,  0.9604, -0.4219, -0.5241,  0.0000],
 [ 0.0000, -0.9162, -0.5436, -0.6446,  0.0000]]]])

```

### ConstantPad1d

```py
class torch.nn.ConstantPad1d(padding, value)
```

Pads the input tensor boundaries with a constant value.

For `N`-dimensional padding, use [`torch.nn.functional.pad()`](#torch.nn.functional.pad "torch.nn.functional.pad").

| Parameters: | **padding** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – the size of the padding. If is `int`, uses the same padding in both boundaries. If a 2-`tuple`, uses (![](img/08b2cac9ee37dde4cec3d372ebbfa0bd.jpg), ![](img/9f56071a00e2baa50d7fa9bde997852d.jpg)) |
| --- | --- |

```py
Shape:
```

*   Input: ![](img/964aa6df63e83f4468aa090441f01972.jpg)
*   Output: ![](img/ac2661719f40fc422e2b1590a1e7b4a4.jpg) where ![](img/e2294a717e6d12035072d23c45273863.jpg)

Examples:

```py
>>> m = nn.ConstantPad1d(2, 3.5)
>>> input = torch.randn(1, 2, 4)
>>> input
tensor([[[-1.0491, -0.7152, -0.0749,  0.8530],
 [-1.3287,  1.8966,  0.1466, -0.2771]]])
>>> m(input)
tensor([[[ 3.5000,  3.5000, -1.0491, -0.7152, -0.0749,  0.8530,  3.5000,
 3.5000],
 [ 3.5000,  3.5000, -1.3287,  1.8966,  0.1466, -0.2771,  3.5000,
 3.5000]]])
>>> m = nn.ConstantPad1d(2, 3.5)
>>> input = torch.randn(1, 2, 3)
>>> input
tensor([[[ 1.6616,  1.4523, -1.1255],
 [-3.6372,  0.1182, -1.8652]]])
>>> m(input)
tensor([[[ 3.5000,  3.5000,  1.6616,  1.4523, -1.1255,  3.5000,  3.5000],
 [ 3.5000,  3.5000, -3.6372,  0.1182, -1.8652,  3.5000,  3.5000]]])
>>> # using different paddings for different sides
>>> m = nn.ConstantPad1d((3, 1), 3.5)
>>> m(input)
tensor([[[ 3.5000,  3.5000,  3.5000,  1.6616,  1.4523, -1.1255,  3.5000],
 [ 3.5000,  3.5000,  3.5000, -3.6372,  0.1182, -1.8652,  3.5000]]])

```

### ConstantPad2d

```py
class torch.nn.ConstantPad2d(padding, value)
```

Pads the input tensor boundaries with a constant value.

For `N`-dimensional padding, use [`torch.nn.functional.pad()`](#torch.nn.functional.pad "torch.nn.functional.pad").

| Parameters: | **padding** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – the size of the padding. If is `int`, uses the same padding in all boundaries. If a 4-`tuple`, uses (![](img/08b2cac9ee37dde4cec3d372ebbfa0bd.jpg), ![](img/9f56071a00e2baa50d7fa9bde997852d.jpg), ![](img/65f6ce26141c225acd502a7bef164f66.jpg), ![](img/9a98061e27ba6ed06e846767b9c77c3a.jpg)) |
| --- | --- |

```py
Shape:
```

*   Input: ![](img/ff71b16eb10237262566c6907acaaf1f.jpg)
*   Output: ![](img/a0ef05f779873fc4dcbf020b1ea14754.jpg) where ![](img/75aa7c4a6c84e0ccb8aa91592cf6a077.jpg) ![](img/e2294a717e6d12035072d23c45273863.jpg)

Examples:

```py
>>> m = nn.ConstantPad2d(2, 3.5)
>>> input = torch.randn(1, 2, 2)
>>> input
tensor([[[ 1.6585,  0.4320],
 [-0.8701, -0.4649]]])
>>> m(input)
tensor([[[ 3.5000,  3.5000,  3.5000,  3.5000,  3.5000,  3.5000],
 [ 3.5000,  3.5000,  3.5000,  3.5000,  3.5000,  3.5000],
 [ 3.5000,  3.5000,  1.6585,  0.4320,  3.5000,  3.5000],
 [ 3.5000,  3.5000, -0.8701, -0.4649,  3.5000,  3.5000],
 [ 3.5000,  3.5000,  3.5000,  3.5000,  3.5000,  3.5000],
 [ 3.5000,  3.5000,  3.5000,  3.5000,  3.5000,  3.5000]]])
>>> m(input)
tensor([[[ 3.5000,  3.5000,  3.5000,  3.5000,  3.5000,  3.5000],
 [ 3.5000,  3.5000,  3.5000,  3.5000,  3.5000,  3.5000],
 [ 3.5000,  3.5000,  1.6585,  0.4320,  3.5000,  3.5000],
 [ 3.5000,  3.5000, -0.8701, -0.4649,  3.5000,  3.5000],
 [ 3.5000,  3.5000,  3.5000,  3.5000,  3.5000,  3.5000],
 [ 3.5000,  3.5000,  3.5000,  3.5000,  3.5000,  3.5000]]])
>>> # using different paddings for different sides
>>> m = nn.ConstantPad2d((3, 0, 2, 1), 3.5)
>>> m(input)
tensor([[[ 3.5000,  3.5000,  3.5000,  3.5000,  3.5000],
 [ 3.5000,  3.5000,  3.5000,  3.5000,  3.5000],
 [ 3.5000,  3.5000,  3.5000,  1.6585,  0.4320],
 [ 3.5000,  3.5000,  3.5000, -0.8701, -0.4649],
 [ 3.5000,  3.5000,  3.5000,  3.5000,  3.5000]]])

```

### ConstantPad3d

```py
class torch.nn.ConstantPad3d(padding, value)
```

Pads the input tensor boundaries with a constant value.

For `N`-dimensional padding, use [`torch.nn.functional.pad()`](#torch.nn.functional.pad "torch.nn.functional.pad").

| Parameters: | **padding** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ [_tuple_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")) – the size of the padding. If is `int`, uses the same padding in all boundaries. If a 6-`tuple`, uses (![](img/08b2cac9ee37dde4cec3d372ebbfa0bd.jpg), ![](img/9f56071a00e2baa50d7fa9bde997852d.jpg), ![](img/65f6ce26141c225acd502a7bef164f66.jpg), ![](img/9a98061e27ba6ed06e846767b9c77c3a.jpg), ![](img/bffb266183e8fa640240e16a45076c34.jpg), ![](img/9138ac0ee6f6e96dfe795ead91ec0003.jpg)) |
| --- | --- |

```py
Shape:
```

*   Input: ![](img/c187d190013d0785320e3412fe8cd669.jpg)
*   Output: ![](img/41ca4c8d4c65c979d2d643c6f62ea280.jpg) where ![](img/006114d9c80210ede5da92f2f3a44bb7.jpg) ![](img/75aa7c4a6c84e0ccb8aa91592cf6a077.jpg) ![](img/e2294a717e6d12035072d23c45273863.jpg)

Examples:

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

```

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

### ELU

```py
class torch.nn.ELU(alpha=1.0, inplace=False)
```

Applies the element-wise function:

![](img/1285687f031aec0751f4e0481f97b6b0.jpg)

Parameters: 

*   **alpha** – the ![](img/82005cc2e0087e2a52c7e43df4a19a00.jpg) value for the ELU formulation. Default: 1.0
*   **inplace** – can optionally do the operation in-place. Default: `False`



```py
Shape:
```

*   Input: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg) where `*` means, any number of additional dimensions
*   Output: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg), same shape as the input

![https://pytorch.org/docs/stable/_images//ELU.png](img/5d789140032850b13d5c00493bf62412.jpg)

Examples:

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

```

### Hardshrink

```py
class torch.nn.Hardshrink(lambd=0.5)
```

Applies the hard shrinkage function element-wise:

![](img/f934a1a7fa1553c38403f2e010708ed9.jpg)

| Parameters: | **lambd** – the ![](img/5e8df2ba7e47a784c714d176ed8bbb7a.jpg) value for the Hardshrink formulation. Default: 0.5 |
| --- | --- |

```py
Shape:
```

*   Input: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg) where `*` means, any number of additional dimensions
*   Output: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg), same shape as the input

![https://pytorch.org/docs/stable/_images//Hardshrink.png](img/45889773f687ed0d33a3ef9b66b0da32.jpg)

Examples:

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

```

### Hardtanh

```py
class torch.nn.Hardtanh(min_val=-1.0, max_val=1.0, inplace=False, min_value=None, max_value=None)
```

Applies the HardTanh function element-wise

HardTanh is defined as:

![](img/988cd664634d88b1e654ea5e8fe27d9a.jpg)

The range of the linear region ![](img/f30fa7744d61427a11bf0e75b1557a16.jpg) can be adjusted using `min_val` and `max_val`.

![https://pytorch.org/docs/stable/_images//Hardtanh.png](img/b22ab176e5aca7ca2b17e84fe525620e.jpg)

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`.

```py
Shape:
```

*   Input: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg) where `*` means, any number of additional dimensions
*   Output: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg), same shape as the input

Examples:

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

```

### LeakyReLU

```py
class torch.nn.LeakyReLU(negative_slope=0.01, inplace=False)
```

Applies the element-wise function:

![](img/92ce1c3da3211f30ef5273403da71c7a.jpg)

or

![](img/377c237cda65f4c68e3138efcc2bfef4.jpg)

Parameters: 

*   **negative_slope** – Controls the angle of the negative slope. Default: 1e-2
*   **inplace** – can optionally do the operation in-place. Default: `False`



```py
Shape:
```

*   Input: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg) where `*` means, any number of additional dimensions
*   Output: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg), same shape as the input

![https://pytorch.org/docs/stable/_images//LeakyReLU.png](img/7df3c1e498d7d00e9e32ce7716e15fc3.jpg)

Examples:

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

```

### LogSigmoid

```py
class torch.nn.LogSigmoid
```

Applies the element-wise function:

```py
Shape:
```

*   Input: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg) where `*` means, any number of additional dimensions
*   Output: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg), same shape as the input

![https://pytorch.org/docs/stable/_images//LogSigmoid.png](img/f03b653b702dcd536fbb404c6461b399.jpg)

Examples:

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

```

### PReLU

```py
class torch.nn.PReLU(num_parameters=1, init=0.25)
```

Applies the element-wise function:

![](img/96fb709d31ba330ca192080e660d4cf1.jpg)

or

![](img/f460dc15bedfa96b8a320033b3f4fd6f.jpg)

Here ![](img/070b1af5eca3a5c5d72884b536090f17.jpg) is a learnable parameter. When called without arguments, `nn.PReLU()` uses a single parameter ![](img/070b1af5eca3a5c5d72884b536090f17.jpg) across all input channels. If called with `nn.PReLU(nChannels)`, a separate ![](img/070b1af5eca3a5c5d72884b536090f17.jpg) is used for each input channel.

Note

weight decay should not be used when learning ![](img/070b1af5eca3a5c5d72884b536090f17.jpg) for good performance.

Note

Channel dim is the 2nd dim of input. When input has dims &lt; 2, then there is no channel dim and the number of channels = 1.

Parameters: 

*   **num_parameters** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – number of ![](img/070b1af5eca3a5c5d72884b536090f17.jpg) to learn. Although it takes an int as input, there is only two values are legitimate: 1, or the number of channels at input. Default: 1
*   **init** ([_float_](https://docs.python.org/3/library/functions.html#float "(in Python v3.7)")) – the initial value of ![](img/070b1af5eca3a5c5d72884b536090f17.jpg). Default: 0.25



```py
Shape:
```

*   Input: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg) where `*` means, any number of additional dimensions
*   Output: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg), same shape as the input

| Variables: | **weight** ([_Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – the learnable weights of shape (attr:`num_parameters`). The attr:`dtype` is default to |
| --- | --- |

![https://pytorch.org/docs/stable/_images//PReLU.png](img/59baba7257ac05b747455a25a3457baf.jpg)

Examples:

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

```

### ReLU

```py
class torch.nn.ReLU(inplace=False)
```

Applies the rectified linear unit function element-wise ![](img/f859c48107afb47986b3297459048c80.jpg)

![https://pytorch.org/docs/stable/_images//ReLU.png](img/6bfe295d2f51e4e33648ffb4273723a6.jpg)

| Parameters: | **inplace** – can optionally do the operation in-place. Default: `False` |
| --- | --- |

```py
Shape:
```

*   Input: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg) where `*` means, any number of additional dimensions
*   Output: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg), same shape as the input

Examples:

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

```

### ReLU6

```py
class torch.nn.ReLU6(inplace=False)
```

Applies the element-wise function:

![](img/38c45c0cb00fa6f9a372816012b26b01.jpg)

| Parameters: | **inplace** – can optionally do the operation in-place. Default: `False` |
| --- | --- |

```py
Shape:
```

*   Input: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg) where `*` means, any number of additional dimensions
*   Output: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg), same shape as the input

![https://pytorch.org/docs/stable/_images//ReLU6.png](img/3a82f9216f0db7d59f6c0f1c169156b0.jpg)

Examples:

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

```

### RReLU

```py
class torch.nn.RReLU(lower=0.125, upper=0.3333333333333333, inplace=False)
```

Applies the randomized leaky rectified liner unit function, element-wise, as described in the paper:

[Empirical Evaluation of Rectified Activations in Convolutional Network](https://arxiv.org/abs/1505.00853).

The function is defined as:

![](img/69aa6828f2f0bcd0ee1e173223ff4640.jpg)

where ![](img/070b1af5eca3a5c5d72884b536090f17.jpg) is randomly sampled from uniform distribution ![](img/7323b93ed925c9e5b0ce10c8a6c99daf.jpg).

> See: [https://arxiv.org/pdf/1505.00853.pdf](https://arxiv.org/pdf/1505.00853.pdf)

Parameters: 

*   **lower** – lower bound of the uniform distribution. Default: ![](img/444fc0427eb64f0bd2c9c16edf680d4f.jpg)
*   **upper** – upper bound of the uniform distribution. Default: ![](img/a90c89c913a1fe1e9462d60d8668936b.jpg)
*   **inplace** – can optionally do the operation in-place. Default: `False`



```py
Shape:
```

*   Input: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg) where `*` means, any number of additional dimensions
*   Output: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg), same shape as the input

Examples:

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

```

### SELU

```py
class torch.nn.SELU(inplace=False)
```

Applied element-wise, as:

![](img/c6753a504d14886a424af779f5906dc5.jpg)

with ![](img/e97a0b3de4bafa3464e17a8d8f66fd9d.jpg) and ![](img/aa01199f9b814d719de1e728e4a44ac3.jpg).

![https://pytorch.org/docs/stable/_images//SELU.png](img/10123138310ae40f4a78f55cefe37008.jpg)

More details can be found in the paper [Self-Normalizing Neural Networks](https://arxiv.org/abs/1706.02515) .

| Parameters: | **inplace** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – can optionally do the operation in-place. Default: `False` |
| --- | --- |

```py
Shape:
```

*   Input: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg) where `*` means, any number of additional dimensions
*   Output: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg), same shape as the input

Examples:

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

```

### CELU

```py
class torch.nn.CELU(alpha=1.0, inplace=False)
```

Applies the element-wise function:

![](img/86d69b42683362b7781f1a5809c0d0d1.jpg)

More details can be found in the paper [Continuously Differentiable Exponential Linear Units](https://arxiv.org/abs/1704.07483) .

Parameters: 

*   **alpha** – the ![](img/82005cc2e0087e2a52c7e43df4a19a00.jpg) value for the CELU formulation. Default: 1.0
*   **inplace** – can optionally do the operation in-place. Default: `False`



```py
Shape:
```

*   Input: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg) where `*` means, any number of additional dimensions
*   Output: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg), same shape as the input

![https://pytorch.org/docs/stable/_images//CELU.png](img/8d5fd8f893fb491c170f9a38af6edef9.jpg)

Examples:

```py
>>> m = nn.CELU()
>>> input = torch.randn(2)
>>> output = m(input)

```

### Sigmoid

```py
class torch.nn.Sigmoid
```

Applies the element-wise function:

![](img/8bf3a718397550598124548beb8c6b23.jpg)

```py
Shape:
```

*   Input: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg) where `*` means, any number of additional dimensions
*   Output: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg), same shape as the input

![https://pytorch.org/docs/stable/_images//Sigmoid.png](img/961caeb46e669eb70392afd515f9bde7.jpg)

Examples:

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

```

### Softplus

```py
class torch.nn.Softplus(beta=1, threshold=20)
```

Applies the element-wise function:

![](img/a0855ca512a1ba09192648efd45082ad.jpg)

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 ![](img/50705df736e9a7919e768cf8c4e4f794.jpg) value for the Softplus formulation. Default: 1
*   **threshold** – values above this revert to a linear function. Default: 20



```py
Shape:
```

*   Input: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg) where `*` means, any number of additional dimensions
*   Output: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg), same shape as the input

![https://pytorch.org/docs/stable/_images//Softplus.png](img/af06304134e1f56d7abc15570fa5adb9.jpg)

Examples:

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

```

### Softshrink

```py
class torch.nn.Softshrink(lambd=0.5)
```

Applies the soft shrinkage function elementwise:

![](img/5baf58b3007cf434725f41bf2dfae2ce.jpg)

| Parameters: | **lambd** – the ![](img/5e8df2ba7e47a784c714d176ed8bbb7a.jpg) value for the Softshrink formulation. Default: 0.5 |
| --- | --- |

```py
Shape:
```

*   Input: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg) where `*` means, any number of additional dimensions
*   Output: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg), same shape as the input

![https://pytorch.org/docs/stable/_images//Softshrink.png](img/cec198ab680657d41c1d2ac2176e5664.jpg)

Examples:

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

```

### Softsign

```py
class torch.nn.Softsign
```

Applies the element-wise function:

![](img/39ba3e3786920ceb12bc26b08b00de1c.jpg)

```py
Shape:
```

*   Input: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg) where `*` means, any number of additional dimensions
*   Output: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg), same shape as the input

![https://pytorch.org/docs/stable/_images//Softsign.png](img/b92a09469ce9fc0abfbe8c9af4228391.jpg)

Examples:

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

```

### Tanh

```py
class torch.nn.Tanh
```

Applies the element-wise function:

![](img/e3f58d9a8cbc89b247dd8de1c28bf7ce.jpg)

```py
Shape:
```

*   Input: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg) where `*` means, any number of additional dimensions
*   Output: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg), same shape as the input

![https://pytorch.org/docs/stable/_images//Tanh.png](img/5605304fc1fec06669e17cc872d47580.jpg)

Examples:

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

```

### Tanhshrink

```py
class torch.nn.Tanhshrink
```

Applies the element-wise function:

![](img/136fda10bacf7ae9068ca487ba861805.jpg)

```py
Shape:
```

*   Input: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg) where `*` means, any number of additional dimensions
*   Output: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg), same shape as the input

![https://pytorch.org/docs/stable/_images//Tanhshrink.png](img/8aea39259742ccdb14701a8f3c351b56.jpg)

Examples:

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

```

### Threshold

```py
class torch.nn.Threshold(threshold, value, inplace=False)
```

Thresholds each element of the input Tensor

Threshold is defined as:

![](img/3b32031caba73686c02a117e8e307c6f.jpg)

Parameters: 

*   **threshold** – The value to threshold at
*   **value** – The value to replace with
*   **inplace** – can optionally do the operation in-place. Default: `False`



```py
Shape:
```

*   Input: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg) where `*` means, any number of additional dimensions
*   Output: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg), same shape as the input

Examples:

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

```

## Non-linear activations (other)

### Softmin

```py
class torch.nn.Softmin(dim=None)
```

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

![](img/440f43280457a9287bbddf28553f8f70.jpg)

```py
Shape:
```

*   Input: any shape
*   Output: same as input

| Parameters: | **dim** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – A dimension along which Softmin will be computed (so every slice along dim will sum to 1). |
| --- | --- |
| Returns: | a Tensor of the same dimension and shape as the input, with values in the range [0, 1] |
| --- | --- |

Examples:

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

```

### Softmax

```py
class torch.nn.Softmax(dim=None)
```

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:

![](img/cbfd37534eccdda606d4f8494c31d2c0.jpg)

```py
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] |
| --- | --- |
| Parameters: | **dim** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – 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:

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

```

### Softmax2d

```py
class torch.nn.Softmax2d
```

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 ![](img/b16a2a186bda385e5f0016f5fe5a5c36.jpg)

```py
Shape:
```

*   Input: ![](img/23f8772594b27bd387be708fe9c085e1.jpg)
*   Output: ![](img/23f8772594b27bd387be708fe9c085e1.jpg) (same shape as input)

| Returns: | a Tensor of the same dimension and shape as the input with values in the range [0, 1] |
| --- | --- |

Examples:

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

```

### LogSoftmax

```py
class torch.nn.LogSoftmax(dim=None)
```

Applies the ![](img/db163ba416e1349a426e6a137e082ae2.jpg) function to an n-dimensional input Tensor. The LogSoftmax formulation can be simplified as:

![](img/397c4cfa2f291306d481811192d2d5d9.jpg)

```py
Shape:
```

*   Input: any shape
*   Output: same as input

| Parameters: | **dim** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – A dimension along which Softmax will be computed (so every slice along dim will sum to 1). |
| --- | --- |
| Returns: | a Tensor of the same dimension and shape as the input with values in the range [-inf, 0) |
| --- | --- |

Examples:

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

```

### AdaptiveLogSoftmaxWithLoss

```py
class torch.nn.AdaptiveLogSoftmaxWithLoss(in_features, n_classes, cutoffs, div_value=4.0, head_bias=False)
```

Efficient softmax approximation as described in [Efficient softmax approximation for GPUs](https://arxiv.org/abs/1609.04309) by Edouard Grave, Armand Joulin, Moustapha Cissé, David Grangier, and Hervé Jégou.

Adaptive softmax is an approximate strategy for training models with large output spaces. It is most effective when the label distribution is highly imbalanced, for example in natural language modelling, where the word frequency distribution approximately follows the [Zipf’s law](https://en.wikipedia.org/wiki/Zipf%27s_law).

Adaptive softmax partitions the labels into several clusters, according to their frequency. These clusters may contain different number of targets each. Additionally, clusters containing less frequent labels assign lower dimensional embeddings to those labels, which speeds up the computation. For each minibatch, only clusters for which at least one target is present are evaluated.

The idea is that the clusters which are accessed frequently (like the first one, containing most frequent labels), should also be cheap to compute – that is, contain a small number of assigned labels.

We highly recommend taking a look at the original paper for more details.

*   `cutoffs` should be an ordered Sequence of integers sorted in the increasing order. It controls number of clusters and the partitioning of targets into clusters. For example setting `cutoffs = [10, 100, 1000]` means that first `10` targets will be assigned to the ‘head’ of the adaptive softmax, targets `11, 12, …, 100` will be assigned to the first cluster, and targets `101, 102, …, 1000` will be assigned to the second cluster, while targets `1001, 1002, …, n_classes - 1` will be assigned to the last, third cluster
*   `div_value` is used to compute the size of each additional cluster, which is given as ![](img/32071c42affaaf731df4e3398b16de10.jpg), where ![](img/5df73ea97de3a7712b50ce2fecfea1a7.jpg) is the cluster index (with clusters for less frequent words having larger indices, and indices starting from ![](img/a3ea24a1f2a3549d3e5b0cacf3ecb7c7.jpg)).
*   `head_bias` if set to True, adds a bias term to the ‘head’ of the adaptive softmax. See paper for details. Set to False in the official implementation.

Warning

Labels passed as inputs to this module should be sorted accoridng to their frequency. This means that the most frequent label should be represented by the index `0`, and the least frequent label should be represented by the index `n_classes - 1`.

Note

This module returns a `NamedTuple` with `output` and `loss` fields. See further documentation for details.

Note

To compute log-probabilities for all classes, the `log_prob` method can be used.

Parameters: 

*   **in_features** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – Number of features in the input tensor
*   **n_classes** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – Number of classes in the dataset.
*   **cutoffs** (_Sequence_) – Cutoffs used to assign targets to their buckets.
*   **div_value** ([_float_](https://docs.python.org/3/library/functions.html#float "(in Python v3.7)")_,_ _optional_) – value used as an exponent to compute sizes of the clusters. Default: 4.0


| Returns: | 

*   **output** is a Tensor of size `N` containing computed target log probabilities for each example
*   **loss** is a Scalar representing the computed negative log likelihood loss


| Return type: | `NamedTuple` with `output` and `loss` fields |
| --- | --- |

```py
Shape:
```

*   input: ![](img/768be7688f5f58f4766106ddb821b007.jpg)
*   target: ![](img/2a3e2b832e04fe8d66596083b23da518.jpg) where each value satisfies ![](img/fe1e80e9faca308456bc49d4e79013e0.jpg)
*   output: ![](img/2a3e2b832e04fe8d66596083b23da518.jpg)
*   loss: `Scalar`

```py
log_prob(input)
```

Computes log probabilities for all ![](img/b285cfddea560d447d391e9d7ba660ba.jpg)

| Parameters: | **input** ([_Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – a minibatch of examples |
| --- | --- |
| Returns: | log-probabilities of for each class ![](img/32624581da7de65d68eb11d4201f9bef.jpg) in range ![](img/4e4201057f969a42a8d2de89e5f7c728.jpg), where ![](img/b285cfddea560d447d391e9d7ba660ba.jpg) is a parameter passed to `AdaptiveLogSoftmaxWithLoss` constructor. |
| --- | --- |

```py
Shape:
```

*   Input: ![](img/768be7688f5f58f4766106ddb821b007.jpg)
*   Output: ![](img/f3bcbc1689556ad810d1c658d44bd970.jpg)

```py
predict(input)
```

This is equivalent to `self.log_pob(input).argmax(dim=1)`, but is more efficient in some cases.

| Parameters: | **input** ([_Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – a minibatch of examples |
| --- | --- |
| Returns: | a class with the highest probability for each example |
| --- | --- |
| Return type: | output ([Tensor](tensors.html#torch.Tensor "torch.Tensor")) |
| --- | --- |

```py
Shape:
```

*   Input: ![](img/768be7688f5f58f4766106ddb821b007.jpg)
*   Output: ![](img/2a3e2b832e04fe8d66596083b23da518.jpg)

## Normalization layers

### BatchNorm1d

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

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](https://arxiv.org/abs/1502.03167) .

![](img/beea63da4eceb7d4c8971e826bafbb1a.jpg)

The mean and standard-deviation are calculated per-dimension over the mini-batches and ![](img/cdab9437b701fd21fb3294cfba7c4bc2.jpg) and ![](img/50705df736e9a7919e768cf8c4e4f794.jpg) are learnable parameter vectors of size `C` (where `C` is the input size). By default, the elements of ![](img/cdab9437b701fd21fb3294cfba7c4bc2.jpg) are sampled from ![](img/7ad9c99a642c915c6d560cbca6352454.jpg) and the elements of ![](img/50705df736e9a7919e768cf8c4e4f794.jpg) are set to 0.

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

If `track_running_stats` is set 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 ![](img/05beed2a6202dfed2f2c4d1ddf9f445f.jpg), where ![](img/9d834e987d38585c39d150fe8f46bc74.jpg) is the estimated statistic and ![](img/22c5ed7653e3fae804006a00210327fc.jpg) 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** – ![](img/6c8feca3b2da3d6cf371417edff4be4f.jpg) from an expected input of size ![](img/5816e96aa78b7425cf792435bba8bc29.jpg) or ![](img/db4a9fef02111450bf98261889de550c.jpg) from input of size ![](img/b6d0ccc6531c5d648e750c417c5cc72d.jpg)
*   **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. Can be set to `None` for cumulative moving average (i.e. simple average). 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`



```py
Shape:
```

*   Input: ![](img/9b9aebaa467ad07dca05b5086bd21ca2.jpg) or ![](img/5816e96aa78b7425cf792435bba8bc29.jpg)
*   Output: ![](img/9b9aebaa467ad07dca05b5086bd21ca2.jpg) or ![](img/5816e96aa78b7425cf792435bba8bc29.jpg) (same shape as input)

Examples:

```py
>>> # 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

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

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](https://arxiv.org/abs/1502.03167) .

![](img/63ee6938c8dea3b7cc66a2a245b15cfc.jpg)

The mean and standard-deviation are calculated per-dimension over the mini-batches and ![](img/cdab9437b701fd21fb3294cfba7c4bc2.jpg) and ![](img/50705df736e9a7919e768cf8c4e4f794.jpg) are learnable parameter vectors of size `C` (where `C` is the input size). By default, the elements of ![](img/cdab9437b701fd21fb3294cfba7c4bc2.jpg) are sampled from ![](img/7ad9c99a642c915c6d560cbca6352454.jpg) and the elements of ![](img/50705df736e9a7919e768cf8c4e4f794.jpg) are set to 0.

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

If `track_running_stats` is set 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 ![](img/05beed2a6202dfed2f2c4d1ddf9f445f.jpg), where ![](img/9d834e987d38585c39d150fe8f46bc74.jpg) is the estimated statistic and ![](img/22c5ed7653e3fae804006a00210327fc.jpg) 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** – ![](img/6c8feca3b2da3d6cf371417edff4be4f.jpg) from an expected input of size ![](img/23f8772594b27bd387be708fe9c085e1.jpg)
*   **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. Can be set to `None` for cumulative moving average (i.e. simple average). 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`



```py
Shape:
```

*   Input: ![](img/23f8772594b27bd387be708fe9c085e1.jpg)
*   Output: ![](img/23f8772594b27bd387be708fe9c085e1.jpg) (same shape as input)

Examples:

```py
>>> # 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

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

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](https://arxiv.org/abs/1502.03167) .

![](img/63ee6938c8dea3b7cc66a2a245b15cfc.jpg)

The mean and standard-deviation are calculated per-dimension over the mini-batches and ![](img/cdab9437b701fd21fb3294cfba7c4bc2.jpg) and ![](img/50705df736e9a7919e768cf8c4e4f794.jpg) are learnable parameter vectors of size `C` (where `C` is the input size). By default, the elements of ![](img/cdab9437b701fd21fb3294cfba7c4bc2.jpg) are sampled from ![](img/7ad9c99a642c915c6d560cbca6352454.jpg) and the elements of ![](img/50705df736e9a7919e768cf8c4e4f794.jpg) are set to 0.

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

If `track_running_stats` is set 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 ![](img/05beed2a6202dfed2f2c4d1ddf9f445f.jpg), where ![](img/9d834e987d38585c39d150fe8f46bc74.jpg) is the estimated statistic and ![](img/22c5ed7653e3fae804006a00210327fc.jpg) 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** – ![](img/6c8feca3b2da3d6cf371417edff4be4f.jpg) from an expected input of size ![](img/f5a45f7b445db562b21cfcb525637aab.jpg)
*   **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. Can be set to `None` for cumulative moving average (i.e. simple average). 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`



```py
Shape:
```

*   Input: ![](img/f5a45f7b445db562b21cfcb525637aab.jpg)
*   Output: ![](img/f5a45f7b445db562b21cfcb525637aab.jpg) (same shape as input)

Examples:

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

```

### GroupNorm

```py
class torch.nn.GroupNorm(num_groups, num_channels, eps=1e-05, affine=True)
```

Applies Group Normalization over a mini-batch of inputs as described in the paper [Group Normalization](https://arxiv.org/abs/1803.08494) .

![](img/2fee766f06767b7b87b3531029d92e1d.jpg)

The input channels are separated into `num_groups` groups, each containing `num_channels / num_groups` channels. The mean and standard-deviation are calculated separately over the each group. ![](img/cdab9437b701fd21fb3294cfba7c4bc2.jpg) and ![](img/50705df736e9a7919e768cf8c4e4f794.jpg) are learnable per-channel affine transform parameter vectorss of size `num_channels` if `affine` is `True`.

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

Parameters: 

*   **num_groups** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – number of groups to separate the channels into
*   **num_channels** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – number of channels expected in input
*   **eps** – a value added to the denominator for numerical stability. Default: 1e-5
*   **affine** – a boolean value that when set to `True`, this module has learnable per-channel affine parameters initialized to ones (for weights) and zeros (for biases). Default: `True`.



```py
Shape:
```

*   Input: ![](img/f5be296779e9f325e5c8f0c2284bc073.jpg)
*   Output: ![](img/f5be296779e9f325e5c8f0c2284bc073.jpg) (same shape as input)

Examples:

```py
>>> input = torch.randn(20, 6, 10, 10)
>>> # Separate 6 channels into 3 groups
>>> m = nn.GroupNorm(3, 6)
>>> # Separate 6 channels into 6 groups (equivalent with InstanceNorm)
>>> m = nn.GroupNorm(6, 6)
>>> # Put all 6 channels into a single group (equivalent with LayerNorm)
>>> m = nn.GroupNorm(1, 6)
>>> # Activating the module
>>> output = m(input)

```

### InstanceNorm1d

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

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](https://arxiv.org/abs/1607.08022) .

![](img/63ee6938c8dea3b7cc66a2a245b15cfc.jpg)

The mean and standard-deviation are calculated per-dimension separately for each object in a mini-batch. ![](img/cdab9437b701fd21fb3294cfba7c4bc2.jpg) and ![](img/50705df736e9a7919e768cf8c4e4f794.jpg) 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 ![](img/05beed2a6202dfed2f2c4d1ddf9f445f.jpg), where ![](img/9d834e987d38585c39d150fe8f46bc74.jpg) is the estimated statistic and ![](img/22c5ed7653e3fae804006a00210327fc.jpg) is the new observed value.

Note

[`InstanceNorm1d`](#torch.nn.InstanceNorm1d "torch.nn.InstanceNorm1d") and [`LayerNorm`](#torch.nn.LayerNorm "torch.nn.LayerNorm") are very similar, but have some subtle differences. [`InstanceNorm1d`](#torch.nn.InstanceNorm1d "torch.nn.InstanceNorm1d") is applied on each channel of channeled data like multidimensional time series, but [`LayerNorm`](#torch.nn.LayerNorm "torch.nn.LayerNorm") is usually applied on entire sample and often in NLP tasks. Additionaly, [`LayerNorm`](#torch.nn.LayerNorm "torch.nn.LayerNorm") applies elementwise affine transform, while [`InstanceNorm1d`](#torch.nn.InstanceNorm1d "torch.nn.InstanceNorm1d") usually don’t apply affine transform.

Parameters: 

*   **num_features** – ![](img/6c8feca3b2da3d6cf371417edff4be4f.jpg) from an expected input of size ![](img/5816e96aa78b7425cf792435bba8bc29.jpg) or ![](img/db4a9fef02111450bf98261889de550c.jpg) from input of size ![](img/b6d0ccc6531c5d648e750c417c5cc72d.jpg)
*   **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, initialized the same way as done for batch normalization. Default: `False`.
*   **track_running_stats** – a boolean value that when set to `True`, this module tracks the running mean and variance, and when set to `False`, this module does not track such statistics and always uses batch statistics in both training and eval modes. Default: `False`



```py
Shape:
```

*   Input: ![](img/5816e96aa78b7425cf792435bba8bc29.jpg)
*   Output: ![](img/5816e96aa78b7425cf792435bba8bc29.jpg) (same shape as input)

Examples:

```py
>>> # 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

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

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](https://arxiv.org/abs/1607.08022) .

![](img/63ee6938c8dea3b7cc66a2a245b15cfc.jpg)

The mean and standard-deviation are calculated per-dimension separately for each object in a mini-batch. ![](img/cdab9437b701fd21fb3294cfba7c4bc2.jpg) and ![](img/50705df736e9a7919e768cf8c4e4f794.jpg) 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 ![](img/05beed2a6202dfed2f2c4d1ddf9f445f.jpg), where ![](img/9d834e987d38585c39d150fe8f46bc74.jpg) is the estimated statistic and ![](img/22c5ed7653e3fae804006a00210327fc.jpg) is the new observed value.

Note

[`InstanceNorm2d`](#torch.nn.InstanceNorm2d "torch.nn.InstanceNorm2d") and [`LayerNorm`](#torch.nn.LayerNorm "torch.nn.LayerNorm") are very similar, but have some subtle differences. [`InstanceNorm2d`](#torch.nn.InstanceNorm2d "torch.nn.InstanceNorm2d") is applied on each channel of channeled data like RGB images, but [`LayerNorm`](#torch.nn.LayerNorm "torch.nn.LayerNorm") is usually applied on entire sample and often in NLP tasks. Additionaly, [`LayerNorm`](#torch.nn.LayerNorm "torch.nn.LayerNorm") applies elementwise affine transform, while [`InstanceNorm2d`](#torch.nn.InstanceNorm2d "torch.nn.InstanceNorm2d") usually don’t apply affine transform.

Parameters: 

*   **num_features** – ![](img/6c8feca3b2da3d6cf371417edff4be4f.jpg) from an expected input of size ![](img/23f8772594b27bd387be708fe9c085e1.jpg)
*   **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, initialized the same way as done for batch normalization. Default: `False`.
*   **track_running_stats** – a boolean value that when set to `True`, this module tracks the running mean and variance, and when set to `False`, this module does not track such statistics and always uses batch statistics in both training and eval modes. Default: `False`



```py
Shape:
```

*   Input: ![](img/23f8772594b27bd387be708fe9c085e1.jpg)
*   Output: ![](img/23f8772594b27bd387be708fe9c085e1.jpg) (same shape as input)

Examples:

```py
>>> # 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

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

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](https://arxiv.org/abs/1607.08022) .

![](img/63ee6938c8dea3b7cc66a2a245b15cfc.jpg)

The mean and standard-deviation are calculated per-dimension separately for each object in a mini-batch. ![](img/cdab9437b701fd21fb3294cfba7c4bc2.jpg) and ![](img/50705df736e9a7919e768cf8c4e4f794.jpg) 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 ![](img/05beed2a6202dfed2f2c4d1ddf9f445f.jpg), where ![](img/9d834e987d38585c39d150fe8f46bc74.jpg) is the estimated statistic and ![](img/22c5ed7653e3fae804006a00210327fc.jpg) is the new observed value.

Note

[`InstanceNorm3d`](#torch.nn.InstanceNorm3d "torch.nn.InstanceNorm3d") and [`LayerNorm`](#torch.nn.LayerNorm "torch.nn.LayerNorm") are very similar, but have some subtle differences. [`InstanceNorm3d`](#torch.nn.InstanceNorm3d "torch.nn.InstanceNorm3d") is applied on each channel of channeled data like 3D models with RGB color, but [`LayerNorm`](#torch.nn.LayerNorm "torch.nn.LayerNorm") is usually applied on entire sample and often in NLP tasks. Additionaly, [`LayerNorm`](#torch.nn.LayerNorm "torch.nn.LayerNorm") applies elementwise affine transform, while [`InstanceNorm3d`](#torch.nn.InstanceNorm3d "torch.nn.InstanceNorm3d") usually don’t apply affine transform.

Parameters: 

*   **num_features** – ![](img/6c8feca3b2da3d6cf371417edff4be4f.jpg) from an expected input of size ![](img/f5a45f7b445db562b21cfcb525637aab.jpg)
*   **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, initialized the same way as done for batch normalization. Default: `False`.
*   **track_running_stats** – a boolean value that when set to `True`, this module tracks the running mean and variance, and when set to `False`, this module does not track such statistics and always uses batch statistics in both training and eval modes. Default: `False`



```py
Shape:
```

*   Input: ![](img/f5a45f7b445db562b21cfcb525637aab.jpg)
*   Output: ![](img/f5a45f7b445db562b21cfcb525637aab.jpg) (same shape as input)

Examples:

```py
>>> # 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

```py
class torch.nn.LayerNorm(normalized_shape, eps=1e-05, elementwise_affine=True)
```

Applies Layer Normalization over a mini-batch of inputs as described in the paper [Layer Normalization](https://arxiv.org/abs/1607.06450) .

![](img/2fee766f06767b7b87b3531029d92e1d.jpg)

The mean and standard-deviation are calculated separately over the last certain number dimensions which have to be of the shape specified by `normalized_shape`. ![](img/cdab9437b701fd21fb3294cfba7c4bc2.jpg) and ![](img/50705df736e9a7919e768cf8c4e4f794.jpg) 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_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_list_](https://docs.python.org/3/library/stdtypes.html#list "(in Python v3.7)") _or_ _torch.Size_) –

    input shape from an expected input of size

    ![](img/7058ab5ae52adb329c22fa5456ad910f.jpg)

    If a single integer is used, it is treated as a singleton list, and this module will normalize over the last dimension which is expected to be of that specific size.

*   **eps** – a value added to the denominator for numerical stability. Default: 1e-5
*   **elementwise_affine** – a boolean value that when set to `True`, this module has learnable per-element affine parameters initialized to ones (for weights) and zeros (for biases). Default: `True`.



```py
Shape:
```

*   Input: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg)
*   Output: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg) (same shape as input)

Examples:

```py
>>> 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

```py
class torch.nn.LocalResponseNorm(size, alpha=0.0001, beta=0.75, k=1.0)
```

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

![](img/5522547c6e594dc7c5ffe998f57ad26b.jpg)

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



```py
Shape:
```

*   Input: ![](img/0113f670591e6e2a1a50722e1affdce5.jpg)
*   Output: ![](img/0113f670591e6e2a1a50722e1affdce5.jpg) (same shape as input)

Examples:

```py
>>> 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

```py
class torch.nn.RNN(*args, **kwargs)
```

Applies a multi-layer Elman RNN with ![](img/73b754b4f63e76c0f0327be51d4b263c.jpg) or ![](img/86a6387f3ec09e33de3faaa24f784bca.jpg) non-linearity to an input sequence.

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

![](img/1d1bd72124738a26685d33ce01c89beb.jpg)

where ![](img/a048a5bfcc0242b6427d15ed11ef7e23.jpg) is the hidden state at time `t`, ![](img/22c5ed7653e3fae804006a00210327fc.jpg) is the input at time `t`, and ![](img/722edd552cee200694a3bfccd4f755df.jpg) is the hidden state of the previous layer at time `t-1` or the initial hidden state at time `0`. If `nonlinearity` is `‘relu’`, then `ReLU` is used instead of `tanh`.

Parameters: 

*   **input_size** – The number of expected features in the input `x`
*   **hidden_size** – The number of features in the hidden state `h`
*   **num_layers** – Number of recurrent layers. E.g., setting `num_layers=2` would mean stacking two RNNs together to form a `stacked RNN`, with the second RNN taking in outputs of the first RNN and computing the final results. Default: 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)`. Default: `False`
*   **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`



```py
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()`](#torch.nn.utils.rnn.pack_padded_sequence "torch.nn.utils.rnn.pack_padded_sequence") or [`torch.nn.utils.rnn.pack_sequence()`](#torch.nn.utils.rnn.pack_sequence "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. Defaults to zero if not provided. If the RNN is bidirectional, num_directions should be 2, else it should be 1.

```py
Outputs: output, h_n
```

*   **output** of shape `(seq_len, batch, num_directions * hidden_size)`: tensor containing the output features (`h_k`) from the last layer of the RNN, for each `k`. If a [`torch.nn.utils.rnn.PackedSequence`](#torch.nn.utils.rnn.PackedSequence "torch.nn.utils.rnn.PackedSequence") has been given as the input, the output will also be a packed sequence.

    For the unpacked case, the directions can be separated using `output.view(seq_len, batch, num_directions, hidden_size)`, with forward and backward being direction `0` and `1` respectively. Similarly, the directions can be separated in the packed case.

*   **h_n** (num_layers * num_directions, batch, hidden_size): tensor containing the hidden state for `k = seq_len`.

    Like _output_, the layers can be separated using `h_n.view(num_layers, num_directions, batch, hidden_size)`.

| 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)`



Note

All the weights and biases are initialized from ![](img/3d305f1c240ff844b6cb2c1c6660e0af.jpg) where ![](img/cb80fd45c1b2dc2b84b2e80eb48d111e.jpg)

Note

If the following conditions are satisfied: 1) cudnn is enabled, 2) input data is on the GPU 3) input data has dtype `torch.float16` 4) V100 GPU is used, 5) input data is not in `PackedSequence` format persistent algorithm can be selected to improve performance.

Examples:

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

```

### LSTM

```py
class torch.nn.LSTM(*args, **kwargs)
```

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:

![](img/e45b4c4446dc36020077ab726cee248f.jpg)

where ![](img/a048a5bfcc0242b6427d15ed11ef7e23.jpg) is the hidden state at time `t`, ![](img/a96fd1792ebb964c44e6a4802fe73a45.jpg) is the cell state at time `t`, ![](img/22c5ed7653e3fae804006a00210327fc.jpg) is the input at time `t`, ![](img/722edd552cee200694a3bfccd4f755df.jpg) is the hidden state of the layer at time `t-1` or the initial hidden state at time `0`, and ![](img/0c33b098890c73bacbf2dbe5476b8ea0.jpg), ![](img/39e0c3cfa9742216d02b21de5ed57650.jpg), ![](img/2fe3fba6f09d597fd2b3cd6a1e0b4547.jpg), ![](img/8b4c3e8be7da971e832789294ddd61d4.jpg) are the input, forget, cell, and output gates, respectively. ![](img/2469b2bd2a1ab19ebfcee223dcb52bb1.jpg) is the sigmoid function.

In a multilayer LSTM, the input ![](img/3aef28832238eb9de1c3d226cc4f026e.jpg) of the ![](img/4c55f62a52ee5572ab96494e9e0a2876.jpg) -th layer (![](img/c2c7ccc0042019ca7a1bb7d536da8a87.jpg)) is the hidden state ![](img/aa2a9f5361143e6f3a32d54920079b52.jpg) of the previous layer multiplied by dropout ![](img/5e5fffda0db50ff1fedeef29921cdf85.jpg) where each ![](img/5b70351b42153bea8ab63d8e783cc0ac.jpg) is a Bernoulli random variable which is ![](img/28256dd5af833c877d63bfabfaa7b301.jpg) with probability `dropout`.

Parameters: 

*   **input_size** – The number of expected features in the input `x`
*   **hidden_size** – The number of features in the hidden state `h`
*   **num_layers** – Number of recurrent layers. E.g., setting `num_layers=2` would mean stacking two LSTMs together to form a `stacked LSTM`, with the second LSTM taking in outputs of the first LSTM and computing the final results. Default: 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). Default: `False`
*   **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`



```py
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()`](#torch.nn.utils.rnn.pack_padded_sequence "torch.nn.utils.rnn.pack_padded_sequence") or [`torch.nn.utils.rnn.pack_sequence()`](#torch.nn.utils.rnn.pack_sequence "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. If the RNN is bidirectional, num_directions should be 2, else it should be 1.

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

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

```py
Outputs: output, (h_n, c_n)
```

*   **output** of shape `(seq_len, batch, num_directions * hidden_size)`: tensor containing the output features `(h_t)` from the last layer of the LSTM, for each t. If a [`torch.nn.utils.rnn.PackedSequence`](#torch.nn.utils.rnn.PackedSequence "torch.nn.utils.rnn.PackedSequence") has been given as the input, the output will also be a packed sequence.

    For the unpacked case, the directions can be separated using `output.view(seq_len, batch, num_directions, hidden_size)`, with forward and backward being direction `0` and `1` respectively. Similarly, the directions can be separated in the packed case.

*   **h_n** of shape `(num_layers * num_directions, batch, hidden_size)`: tensor containing the hidden state for `t = seq_len`.

    Like _output_, the layers can be separated using `h_n.view(num_layers, num_directions, batch, hidden_size)` and similarly for _c_n_.

*   **c_n** (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 ![](img/3daedae8ea4977a42453935c04c06ad0.jpg) layer `(W_ii&#124;W_if&#124;W_ig&#124;W_io)`, of shape `(4*hidden_size x input_size)`
*   **weight_hh_l[k]** – the learnable hidden-hidden weights of the ![](img/3daedae8ea4977a42453935c04c06ad0.jpg) layer `(W_hi&#124;W_hf&#124;W_hg&#124;W_ho)`, of shape `(4*hidden_size x hidden_size)`
*   **bias_ih_l[k]** – the learnable input-hidden bias of the ![](img/3daedae8ea4977a42453935c04c06ad0.jpg) layer `(b_ii&#124;b_if&#124;b_ig&#124;b_io)`, of shape `(4*hidden_size)`
*   **bias_hh_l[k]** – the learnable hidden-hidden bias of the ![](img/3daedae8ea4977a42453935c04c06ad0.jpg) layer `(b_hi&#124;b_hf&#124;b_hg&#124;b_ho)`, of shape `(4*hidden_size)`



Note

All the weights and biases are initialized from ![](img/3d305f1c240ff844b6cb2c1c6660e0af.jpg) where ![](img/cb80fd45c1b2dc2b84b2e80eb48d111e.jpg)

Note

If the following conditions are satisfied: 1) cudnn is enabled, 2) input data is on the GPU 3) input data has dtype `torch.float16` 4) V100 GPU is used, 5) input data is not in `PackedSequence` format persistent algorithm can be selected to improve performance.

Examples:

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

```

### GRU

```py
class torch.nn.GRU(*args, **kwargs)
```

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:

![](img/76771dd2e48bad7097dc9524356200ef.jpg)

where ![](img/a048a5bfcc0242b6427d15ed11ef7e23.jpg) is the hidden state at time `t`, ![](img/22c5ed7653e3fae804006a00210327fc.jpg) is the input at time `t`, ![](img/722edd552cee200694a3bfccd4f755df.jpg) is the hidden state of the layer at time `t-1` or the initial hidden state at time `0`, and ![](img/33becaceee3dd4f30f106b6a8605226f.jpg), ![](img/98ba4bd98c899c9f15a00fe76fe782b2.jpg), ![](img/4d63033e7717e68b17fc937ffcbcde4b.jpg) are the reset, update, and new gates, respectively. ![](img/2469b2bd2a1ab19ebfcee223dcb52bb1.jpg) is the sigmoid function.

In a multilayer GRU, the input ![](img/3aef28832238eb9de1c3d226cc4f026e.jpg) of the ![](img/4c55f62a52ee5572ab96494e9e0a2876.jpg) -th layer (![](img/c2c7ccc0042019ca7a1bb7d536da8a87.jpg)) is the hidden state ![](img/aa2a9f5361143e6f3a32d54920079b52.jpg) of the previous layer multiplied by dropout ![](img/5e5fffda0db50ff1fedeef29921cdf85.jpg) where each ![](img/5b70351b42153bea8ab63d8e783cc0ac.jpg) is a Bernoulli random variable which is ![](img/28256dd5af833c877d63bfabfaa7b301.jpg) with probability `dropout`.

Parameters: 

*   **input_size** – The number of expected features in the input `x`
*   **hidden_size** – The number of features in the hidden state `h`
*   **num_layers** – Number of recurrent layers. E.g., setting `num_layers=2` would mean stacking two GRUs together to form a `stacked GRU`, with the second GRU taking in outputs of the first GRU and computing the final results. Default: 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). Default: `False`
*   **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`



```py
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()`](#torch.nn.utils.rnn.pack_padded_sequence "torch.nn.utils.rnn.pack_padded_sequence") for details.
*   **h_0** of shape `(num_layers * num_directions, batch, hidden_size)`: tensor containing the initial hidden state for each element in the batch. Defaults to zero if not provided. If the RNN is bidirectional, num_directions should be 2, else it should be 1.

```py
Outputs: output, h_n
```

*   **output** of shape `(seq_len, batch, num_directions * hidden_size)`: tensor containing the output features h_t from the last layer of the GRU, for each t. If a [`torch.nn.utils.rnn.PackedSequence`](#torch.nn.utils.rnn.PackedSequence "torch.nn.utils.rnn.PackedSequence") has been given as the input, the output will also be a packed sequence. For the unpacked case, the directions can be separated using `output.view(seq_len, batch, num_directions, hidden_size)`, with forward and backward being direction `0` and `1` respectively.

    Similarly, the directions can be separated in the packed case.

*   **h_n** of shape `(num_layers * num_directions, batch, hidden_size)`: tensor containing the hidden state for `t = seq_len`

    Like _output_, the layers can be separated using `h_n.view(num_layers, num_directions, batch, hidden_size)`.

| Variables: | 

*   **weight_ih_l[k]** – the learnable input-hidden weights of the ![](img/3daedae8ea4977a42453935c04c06ad0.jpg) layer (W_ir&#124;W_iz&#124;W_in), of shape `(3*hidden_size x input_size)`
*   **weight_hh_l[k]** – the learnable hidden-hidden weights of the ![](img/3daedae8ea4977a42453935c04c06ad0.jpg) layer (W_hr&#124;W_hz&#124;W_hn), of shape `(3*hidden_size x hidden_size)`
*   **bias_ih_l[k]** – the learnable input-hidden bias of the ![](img/3daedae8ea4977a42453935c04c06ad0.jpg) layer (b_ir&#124;b_iz&#124;b_in), of shape `(3*hidden_size)`
*   **bias_hh_l[k]** – the learnable hidden-hidden bias of the ![](img/3daedae8ea4977a42453935c04c06ad0.jpg) layer (b_hr&#124;b_hz&#124;b_hn), of shape `(3*hidden_size)`



Note

All the weights and biases are initialized from ![](img/3d305f1c240ff844b6cb2c1c6660e0af.jpg) where ![](img/cb80fd45c1b2dc2b84b2e80eb48d111e.jpg)

Note

If the following conditions are satisfied: 1) cudnn is enabled, 2) input data is on the GPU 3) input data has dtype `torch.float16` 4) V100 GPU is used, 5) input data is not in `PackedSequence` format persistent algorithm can be selected to improve performance.

Examples:

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

```

### RNNCell

```py
class torch.nn.RNNCell(input_size, hidden_size, bias=True, nonlinearity='tanh')
```

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

![](img/e748fe354d996221dbfa5f8e3412451e.jpg)

If `nonlinearity` is `‘relu’`, then ReLU is used in place of tanh.

Parameters: 

*   **input_size** – The number of expected features in the input `x`
*   **hidden_size** – The number of features in the hidden state `h`
*   **bias** – If `False`, then the layer does not use bias weights `b_ih` and `b_hh`. Default: `True`
*   **nonlinearity** – The non-linearity to use. Can be either ‘tanh’ or ‘relu’. Default: ‘tanh’



```py
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.

```py
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 `(hidden_size x input_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)`



Note

All the weights and biases are initialized from ![](img/3d305f1c240ff844b6cb2c1c6660e0af.jpg) where ![](img/cb80fd45c1b2dc2b84b2e80eb48d111e.jpg)

Examples:

```py
>>> 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

```py
class torch.nn.LSTMCell(input_size, hidden_size, bias=True)
```

A long short-term memory (LSTM) cell.

![](img/fb4d6ec81b25bb8201fbedd23b71b45f.jpg)

where ![](img/2469b2bd2a1ab19ebfcee223dcb52bb1.jpg) 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`



```py
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.

```py
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)`



Note

All the weights and biases are initialized from ![](img/3d305f1c240ff844b6cb2c1c6660e0af.jpg) where ![](img/cb80fd45c1b2dc2b84b2e80eb48d111e.jpg)

Examples:

```py
>>> 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

```py
class torch.nn.GRUCell(input_size, hidden_size, bias=True)
```

A gated recurrent unit (GRU) cell

![](img/a557e5b089bda248c2e25791d88d4b2a.jpg)

where ![](img/2469b2bd2a1ab19ebfcee223dcb52bb1.jpg) 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`



```py
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.

```py
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)`



Note

All the weights and biases are initialized from ![](img/3d305f1c240ff844b6cb2c1c6660e0af.jpg) where ![](img/cb80fd45c1b2dc2b84b2e80eb48d111e.jpg)

Examples:

```py
>>> 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

```py
class torch.nn.Linear(in_features, out_features, bias=True)
```

Applies a linear transformation to the incoming data: ![](img/8c4834b7cb4b9c7a795bf354412e8dd3.jpg)

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`



```py
Shape:
```

*   Input: ![](img/37251f14c8c7345b66309c1ce6181e4d.jpg) where ![](img/28ec51e742166ea3400be6e7343bbfa5.jpg) means any number of additional dimensions
*   Output: ![](img/052531b4914630967eb9a6ed4f143697.jpg) where all but the last dimension are the same shape as the input.

| Variables: | 

*   **weight** – the learnable weights of the module of shape ![](img/7bdd499093e2167451c56eb5c4480786.jpg). The values are initialized from ![](img/3d305f1c240ff844b6cb2c1c6660e0af.jpg), where ![](img/9d1dd979275f32a1bcc00f4e3885e68c.jpg)
*   **bias** – the learnable bias of the module of shape ![](img/27eac2d9aa3b57eabe07fcce145717d2.jpg). If `bias` is `True`, the values are initialized from ![](img/3d305f1c240ff844b6cb2c1c6660e0af.jpg) where ![](img/9d1dd979275f32a1bcc00f4e3885e68c.jpg)



Examples:

```py
>>> m = nn.Linear(20, 30)
>>> input = torch.randn(128, 20)
>>> output = m(input)
>>> print(output.size())
torch.Size([128, 30])

```

### Bilinear

```py
class torch.nn.Bilinear(in1_features, in2_features, out_features, bias=True)
```

Applies a bilinear transformation to the incoming data: ![](img/a0d89d1240ed669c322d042acea66b2c.jpg)

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`



```py
Shape:
```

*   Input: ![](img/9cf39fb88b1a94018532514fcb3e125c.jpg), ![](img/5b3219dff177846f3a5aebdb36ae5d30.jpg) where ![](img/28ec51e742166ea3400be6e7343bbfa5.jpg) means any number of additional dimensions. All but the last dimension of the inputs should be the same.
*   Output: ![](img/052531b4914630967eb9a6ed4f143697.jpg) where all but the last dimension are the same shape as the input.

| Variables: | 

*   **weight** – the learnable weights of the module of shape ![](img/3f2a47921a3568c8f0f8c45847fd2ad3.jpg). The values are initialized from ![](img/3d305f1c240ff844b6cb2c1c6660e0af.jpg), where ![](img/76606e23079bb41cbaeb5fa9ddc71c86.jpg)
*   **bias** – the learnable bias of the module of shape ![](img/27eac2d9aa3b57eabe07fcce145717d2.jpg) If `bias` is `True`, the values are initialized from ![](img/3d305f1c240ff844b6cb2c1c6660e0af.jpg), where ![](img/76606e23079bb41cbaeb5fa9ddc71c86.jpg)



Examples:

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

```

## Dropout layers

### Dropout

```py
class torch.nn.Dropout(p=0.5, inplace=False)
```

During training, randomly zeroes some of the elements of the input tensor with probability `p` using samples from a Bernoulli distribution. Each channel will be zeroed out independently on every forward call.

This has proven to be an effective technique for regularization and preventing the co-adaptation of neurons as described in the paper [Improving neural networks by preventing co-adaptation of feature detectors](https://arxiv.org/abs/1207.0580) .

Furthermore, the outputs are scaled by a factor of ![](img/37052da8591fea742432c58ac3a4dc59.jpg) 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`



```py
Shape:
```

*   Input: `Any`. Input can be of any shape
*   Output: `Same`. Output is of the same shape as input

Examples:

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

```

### Dropout2d

```py
class torch.nn.Dropout2d(p=0.5, inplace=False)
```

Randomly zero out entire channels (a channel is a 2D feature map, e.g., the ![](img/d8fdd0e28cfb03738fc5227885ee035a.jpg)-th channel of the ![](img/31df9c730e19ca29b59dce64b99d98c1.jpg)-th sample in the batched input is a 2D tensor ![](img/5bc8fbe2fea3359e55846184c5eb123a.jpg)) of the input tensor). Each channel will be zeroed out independently on every forward call. with probability `p` using samples from a Bernoulli distribution.

Usually the input comes from `nn.Conv2d` modules.

As described in the paper [Efficient Object Localization Using Convolutional Networks](http://arxiv.org/abs/1411.4280) , 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_](https://docs.python.org/3/library/functions.html#float "(in Python v3.7)")_,_ _optional_) – probability of an element to be zero-ed.
*   **inplace** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – If set to `True`, will do this operation in-place



```py
Shape:
```

*   Input: ![](img/23f8772594b27bd387be708fe9c085e1.jpg)
*   Output: ![](img/23f8772594b27bd387be708fe9c085e1.jpg) (same shape as input)

Examples:

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

```

### Dropout3d

```py
class torch.nn.Dropout3d(p=0.5, inplace=False)
```

Randomly zero out entire channels (a channel is a 3D feature map, e.g., the ![](img/d8fdd0e28cfb03738fc5227885ee035a.jpg)-th channel of the ![](img/31df9c730e19ca29b59dce64b99d98c1.jpg)-th sample in the batched input is a 3D tensor ![](img/5bc8fbe2fea3359e55846184c5eb123a.jpg)) of the input tensor). Each channel will be zeroed out independently on every forward call. with probability `p` using samples from a Bernoulli distribution.

Usually the input comes from `nn.Conv3d` modules.

As described in the paper [Efficient Object Localization Using Convolutional Networks](http://arxiv.org/abs/1411.4280) , 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_](https://docs.python.org/3/library/functions.html#float "(in Python v3.7)")_,_ _optional_) – probability of an element to be zeroed.
*   **inplace** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – If set to `True`, will do this operation in-place



```py
Shape:
```

*   Input: ![](img/f5a45f7b445db562b21cfcb525637aab.jpg)
*   Output: ![](img/f5a45f7b445db562b21cfcb525637aab.jpg) (same shape as input)

Examples:

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

```

### AlphaDropout

```py
class torch.nn.AlphaDropout(p=0.5, inplace=False)
```

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](https://arxiv.org/abs/1706.02515) .

Parameters: 

*   **p** ([_float_](https://docs.python.org/3/library/functions.html#float "(in Python v3.7)")) – probability of an element to be dropped. Default: 0.5
*   **inplace** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – If set to `True`, will do this operation in-place



```py
Shape:
```

*   Input: `Any`. Input can be of any shape
*   Output: `Same`. Output is of the same shape as input

Examples:

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

```

## Sparse layers

### Embedding

```py
class torch.nn.Embedding(num_embeddings, embedding_dim, padding_idx=None, max_norm=None, norm_type=2.0, scale_grad_by_freq=False, sparse=False, _weight=None)
```

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_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – size of the dictionary of embeddings
*   **embedding_dim** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – the size of each embedding vector
*   **padding_idx** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ _optional_) – If given, pads the output with the embedding vector at `padding_idx` (initialized to zeros) whenever it encounters the index.
*   **max_norm** ([_float_](https://docs.python.org/3/library/functions.html#float "(in Python v3.7)")_,_ _optional_) – If given, each embedding vector with norm larger than `max_norm` is renormalized to have norm `max_norm`.
*   **norm_type** ([_float_](https://docs.python.org/3/library/functions.html#float "(in Python v3.7)")_,_ _optional_) – The p of the p-norm to compute for the `max_norm` option. Default `2`.
*   **scale_grad_by_freq** (_boolean__,_ _optional_) – If given, this will scale gradients by the inverse of frequency of the words in the mini-batch. Default `False`.
*   **sparse** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – If `True`, gradient w.r.t. `weight` matrix will be a sparse tensor. See Notes for more details regarding sparse gradients.


| Variables: | **weight** ([_Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – the learnable weights of the module of shape (num_embeddings, embedding_dim) initialized from ![](img/dd84ddbf2f8040d87fb315eeeba51f6d.jpg) |
| --- | --- |

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`](#torch.nn.Embedding "torch.nn.Embedding") is always zero.

Examples:

```py
>>> # 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]]])

```

```py
classmethod from_pretrained(embeddings, freeze=True, sparse=False)
```

Creates Embedding instance from given 2-dimensional FloatTensor.

Parameters: 

*   **embeddings** ([_Tensor_](tensors.html#torch.Tensor "torch.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`
*   **sparse** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – if `True`, gradient w.r.t. weight matrix will be a sparse tensor. See Notes for more details regarding sparse gradients.



Examples:

```py
>>> # 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

```py
class torch.nn.EmbeddingBag(num_embeddings, embedding_dim, max_norm=None, norm_type=2.0, scale_grad_by_freq=False, mode='mean', sparse=False)
```

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

For bags of constant length, this class

> *   with `mode="sum"` is equivalent to [`Embedding`](#torch.nn.Embedding "torch.nn.Embedding") followed by `torch.sum(dim=1)`,
> *   with `mode="mean"` is equivalent to [`Embedding`](#torch.nn.Embedding "torch.nn.Embedding") followed by `torch.mean(dim=1)`,
> *   with `mode="max"` is equivalent to [`Embedding`](#torch.nn.Embedding "torch.nn.Embedding") followed by `torch.max(dim=1)`.

However, [`EmbeddingBag`](#torch.nn.EmbeddingBag "torch.nn.EmbeddingBag") is much more time and memory efficient than using a chain of these operations.

Parameters: 

*   **num_embeddings** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – size of the dictionary of embeddings
*   **embedding_dim** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – the size of each embedding vector
*   **max_norm** ([_float_](https://docs.python.org/3/library/functions.html#float "(in Python v3.7)")_,_ _optional_) – If given, each embedding vector with norm larger than `max_norm` is renormalized to have norm `max_norm`.
*   **norm_type** ([_float_](https://docs.python.org/3/library/functions.html#float "(in Python v3.7)")_,_ _optional_) – The p of the p-norm to compute for the `max_norm` option. Default `2`.
*   **scale_grad_by_freq** (_boolean__,_ _optional_) – if given, this will scale gradients by the inverse of frequency of the words in the mini-batch. Default `False`. Note: this option is not supported when `mode="max"`.
*   **mode** (_string__,_ _optional_) – `"sum"`, `"mean"` or `"max"`. Specifies the way to reduce the bag. Default: `"mean"`
*   **sparse** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – if `True`, gradient w.r.t. `weight` matrix will be a sparse tensor. See Notes for more details regarding sparse gradients. Note: this option is not supported when `mode="max"`.


| Variables: | **weight** ([_Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – the learnable weights of the module of shape `(num_embeddings x embedding_dim)` initialized from ![](img/dd84ddbf2f8040d87fb315eeeba51f6d.jpg). |
| --- | --- |

Inputs: `input` (LongTensor) and `offsets` (LongTensor, optional)

> *   If `input` is 2D of shape `B x N`,
>     
>     
>     
>     it will be treated as `B` bags (sequences) each of fixed length `N`, and this will return `B` values aggregated in a way depending on the `mode`. `offsets` is ignored and required to be `None` in this case.
>     
>     
> *   If `input` is 1D of shape `N`,
>     
>     
>     
>     it will be treated as a concatenation of multiple bags (sequences). `offsets` is required to be a 1D tensor containing the starting index positions of each bag in `input`. Therefore, for `offsets` of shape `B`, `input` will be viewed as having `B` bags. Empty bags (i.e., having 0-length) will have returned vectors filled by zeros.

Output shape: `B x embedding_dim`

Examples:

```py
>>> # 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

```py
class torch.nn.CosineSimilarity(dim=1, eps=1e-08)
```

Returns cosine similarity between ![](img/abdadb44ea35aecb39004dd7f55d9543.jpg) and ![](img/88fdc6eeb68ef4aacf7cd6bd43fa176e.jpg), computed along dim.

![](img/93f92bee7ec6c9e48618f7c929ab51e3.jpg)

Parameters: 

*   **dim** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ _optional_) – Dimension where cosine similarity is computed. Default: 1
*   **eps** ([_float_](https://docs.python.org/3/library/functions.html#float "(in Python v3.7)")_,_ _optional_) – Small value to avoid division by zero. Default: 1e-8



```py
Shape:
```

*   Input1: ![](img/c2101d997ef86641ad9f92513b080e8a.jpg) where D is at position `dim`
*   Input2: ![](img/c2101d997ef86641ad9f92513b080e8a.jpg), same shape as the Input1
*   Output: ![](img/999c5fb65c1a9ba017a0d60c030400c5.jpg)

Examples:

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

```

### PairwiseDistance

```py
class torch.nn.PairwiseDistance(p=2.0, eps=1e-06, keepdim=False)
```

Computes the batchwise pairwise distance between vectors ![](img/2f0f406e2d42300da1a9891d89381576.jpg), ![](img/60787776d6fd54b3adfd3762b910bd3f.jpg) using the p-norm:

![](img/4206b08d53423c6d6f77c51751d33cae.jpg)

Parameters: 

*   **p** (_real_) – the norm degree. Default: 2
*   **eps** ([_float_](https://docs.python.org/3/library/functions.html#float "(in Python v3.7)")_,_ _optional_) – Small value to avoid division by zero. Default: 1e-6
*   **keepdim** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Determines whether or not to keep the batch dimension. Default: False



```py
Shape:
```

*   Input1: ![](img/3dc464d2e10c731f17264e33e497c1a8.jpg) where `D = vector dimension`
*   Input2: ![](img/3dc464d2e10c731f17264e33e497c1a8.jpg), same shape as the Input1
*   Output: ![](img/2a3e2b832e04fe8d66596083b23da518.jpg). If `keepdim` is `False`, then ![](img/f1b7cdb5b976f1adde1e8b2850a1c127.jpg).

Examples:

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

```

## Loss functions

### L1Loss

```py
class torch.nn.L1Loss(size_average=None, reduce=None, reduction='mean')
```

Creates a criterion that measures the mean absolute error (MAE) between each element in the input `x` and target `y`.

The loss can be described as:

![](img/415564bfa6c89ba182a02fe2a3d0ca49.jpg)

where ![](img/9341d9048ac485106d2b2ee8de14876f.jpg) is the batch size. If reduce is `True`, then:

![](img/dd1952e377a9b618cc6538b18165a417.jpg)

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

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

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

Parameters: 

*   **size_average** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field `size_average` is set to `False`, the losses are instead summed for each minibatch. Ignored when reduce is `False`. Default: `True`
*   **reduce** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). 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`
*   **reduction** (_string__,_ _optional_) – Specifies the reduction to apply to the output: ‘none’ &#124; ‘mean’ &#124; ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: `size_average` and `reduce` are in the process of being deprecated, and in the meantime, specifying either of those two args will override `reduction`. Default: ‘mean’



```py
Shape:
```

*   Input: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg) where `*` means, any number of additional dimensions
*   Target: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg), same shape as the input
*   Output: scalar. If reduce is `False`, then ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg), same shape as the input

Examples:

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

```

### MSELoss

```py
class torch.nn.MSELoss(size_average=None, reduce=None, reduction='mean')
```

Creates a criterion that measures the mean squared error (squared L2 norm) between each element in the input `x` and target `y`.

The loss can be described as:

![](img/e67b64ef5017709a433d1214a681717e.jpg)

where ![](img/9341d9048ac485106d2b2ee8de14876f.jpg) is the batch size. If reduce is `True`, then:

![](img/f3a00c026a75843dd3a04c64f9cecb47.jpg)

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_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field `size_average` is set to `False`, the losses are instead summed for each minibatch. Ignored when reduce is `False`. Default: `True`
*   **reduce** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). 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`
*   **reduction** (_string__,_ _optional_) – Specifies the reduction to apply to the output: ‘none’ &#124; ‘mean’ &#124; ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: `size_average` and `reduce` are in the process of being deprecated, and in the meantime, specifying either of those two args will override `reduction`. Default: ‘mean’



```py
Shape:
```

*   Input: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg) where `*` means, any number of additional dimensions
*   Target: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg), same shape as the input

Examples:

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

```

### CrossEntropyLoss

```py
class torch.nn.CrossEntropyLoss(weight=None, size_average=None, ignore_index=-100, reduce=None, reduction='mean')
```

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 ![](img/cca0c8da541b81bec031e4e52161d2c7.jpg) or ![](img/f30f7531b252dc52c6bb945ebb508cc4.jpg) with ![](img/6573879e7d2cf58e8dfdbf8baa9f7a1a.jpg) 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:

![](img/29028e6a28821a298d2a456d6bb175f9.jpg)

or in the case of the `weight` argument being specified:

![](img/bc344720164c2bc94ebd3f405b898216.jpg)

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 ![](img/f30f7531b252dc52c6bb945ebb508cc4.jpg) with ![](img/6573879e7d2cf58e8dfdbf8baa9f7a1a.jpg), where ![](img/a5db490cd70a38a0bb9f3de58c51589f.jpg) is the number of dimensions, and a target of appropriate shape (see below).

Parameters: 

*   **weight** ([_Tensor_](tensors.html#torch.Tensor "torch.Tensor")_,_ _optional_) – a manual rescaling weight given to each class. If given, has to be a Tensor of size `C`
*   **size_average** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the 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_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ _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_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). 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`
*   **reduction** (_string__,_ _optional_) – Specifies the reduction to apply to the output: ‘none’ &#124; ‘mean’ &#124; ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: `size_average` and `reduce` are in the process of being deprecated, and in the meantime, specifying either of those two args will override `reduction`. Default: ‘mean’



```py
Shape:
```

*   ```py
    Input: \((N, C)\) where C = number of classes, or
    ```

    ![](img/ddeb501040934760370435d1c223e6b6.jpg) with ![](img/6573879e7d2cf58e8dfdbf8baa9f7a1a.jpg) in the case of `K`-dimensional loss.
*   ```py
    Target: \((N)\) where each value is \(0 \leq \text{targets}[i] \leq C-1\), or
    ```

    ![](img/5981db74a9cd434c7580e6ba530e21b6.jpg) with ![](img/6573879e7d2cf58e8dfdbf8baa9f7a1a.jpg) in the case of K-dimensional loss.
*   ```py
    Output: scalar. If reduce is False, then the same size
    ```

    as the target: ![](img/2a3e2b832e04fe8d66596083b23da518.jpg), or ![](img/5981db74a9cd434c7580e6ba530e21b6.jpg) with ![](img/6573879e7d2cf58e8dfdbf8baa9f7a1a.jpg) in the case of K-dimensional loss.

Examples:

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

```

### CTCLoss

```py
class torch.nn.CTCLoss(blank=0, reduction='mean')
```

The Connectionist Temporal Classification loss.

Parameters: 

*   **blank** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ _optional_) – blank label. Default ![](img/28256dd5af833c877d63bfabfaa7b301.jpg).
*   **reduction** (_string__,_ _optional_) – Specifies the reduction to apply to the output: ‘none’ &#124; ‘mean’ &#124; ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the output losses will be divided by the target lengths and then the mean over the batch is taken. Default: ‘mean’



```py
Inputs:
```

```py
log_probs: Tensor of size \((T, N, C)\) where C = number of characters in alphabet including blank,
```

<cite>T = input length</cite>, and <cite>N = batch size</cite>. The logarithmized probabilities of the outputs (e.g. obtained with [`torch.nn.functional.log_softmax()`](#torch.nn.functional.log_softmax "torch.nn.functional.log_softmax")).

```py
targets: Tensor of size \((N, S)\) or (sum(target_lengths)).
```

Targets (cannot be blank). In the second form, the targets are assumed to be concatenated.

```py
input_lengths: Tuple or tensor of size \((N)\).
```

Lengths of the inputs (must each be ![](img/0063f9a7d145aadc1082a0c4c8712a62.jpg))

```py
target_lengths: Tuple or tensor of size  \((N)\).
```

Lengths of the targets

Example:

```py
>>> ctc_loss = nn.CTCLoss()
>>> log_probs = torch.randn(50, 16, 20).log_softmax(2).detach().requires_grad_()
>>> targets = torch.randint(1, 20, (16, 30), dtype=torch.long)
>>> input_lengths = torch.full((16,), 50, dtype=torch.long)
>>> target_lengths = torch.randint(10,30,(16,), dtype=torch.long)
>>> loss = ctc_loss(log_probs, targets, input_lengths, target_lengths)
>>> loss.backward()

```

```py
Reference:
```

A. Graves et al.: Connectionist Temporal Classification: Labelling Unsegmented Sequence Data with Recurrent Neural Networks: [https://www.cs.toronto.edu/~graves/icml_2006.pdf](https://www.cs.toronto.edu/~graves/icml_2006.pdf)

Note

In order to use CuDNN, the following must be satisfied: `targets` must be in concatenated format, all `input_lengths` must be `T`. ![](img/e465f6009cd227a31d00f005c2cb1c5b.jpg), `target_lengths` ![](img/3a2535723ad2261fbfc71d099a993883.jpg), the integer arguments must be of dtype `torch.int32`.

The regular implementation uses the (more common in PyTorch) `torch.long` dtype.

Note

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting `torch.backends.cudnn.deterministic = True`. Please see the notes on [Reproducibility](notes/randomness.html) for background.

### NLLLoss

```py
class torch.nn.NLLLoss(weight=None, size_average=None, ignore_index=-100, reduce=None, reduction='mean')
```

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 ![](img/cca0c8da541b81bec031e4e52161d2c7.jpg) or ![](img/f30f7531b252dc52c6bb945ebb508cc4.jpg) with ![](img/6573879e7d2cf58e8dfdbf8baa9f7a1a.jpg) 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:

![](img/edf1079de0e5df9633d0de83b68250f2.jpg)

where ![](img/9341d9048ac485106d2b2ee8de14876f.jpg) is the batch size. If `reduce` is `True` (default), then

![](img/6eeb4eee2867f6565cb78f3d2e8503f2.jpg)

Can also be used for higher dimension inputs, such as 2D images, by providing an input of size ![](img/f30f7531b252dc52c6bb945ebb508cc4.jpg) with ![](img/6573879e7d2cf58e8dfdbf8baa9f7a1a.jpg), where ![](img/a5db490cd70a38a0bb9f3de58c51589f.jpg) 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_](tensors.html#torch.Tensor "torch.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_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the 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_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ _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_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). 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`
*   **reduction** (_string__,_ _optional_) – Specifies the reduction to apply to the output: ‘none’ &#124; ‘mean’ &#124; ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: `size_average` and `reduce` are in the process of being deprecated, and in the meantime, specifying either of those two args will override `reduction`. Default: ‘mean’



```py
Shape:
```

*   ```py
    Input: \((N, C)\) where C = number of classes, or
    ```

    ![](img/ddeb501040934760370435d1c223e6b6.jpg) with ![](img/6573879e7d2cf58e8dfdbf8baa9f7a1a.jpg) in the case of `K`-dimensional loss.
*   ```py
    Target: \((N)\) where each value is \(0 \leq \text{targets}[i] \leq C-1\), or
    ```

    ![](img/5981db74a9cd434c7580e6ba530e21b6.jpg) with ![](img/6573879e7d2cf58e8dfdbf8baa9f7a1a.jpg) in the case of K-dimensional loss.
*   ```py
    Output: scalar. If reduce is False, then the same size
    ```

    as the target: ![](img/2a3e2b832e04fe8d66596083b23da518.jpg), or ![](img/5981db74a9cd434c7580e6ba530e21b6.jpg) with ![](img/6573879e7d2cf58e8dfdbf8baa9f7a1a.jpg) in the case of K-dimensional loss.

Examples:

```py
>>> 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)
>>> conv = nn.Conv2d(16, C, (3, 3))
>>> m = nn.LogSoftmax()
>>> # each element in target has to have 0 <= value < C
>>> target = torch.empty(N, 8, 8, dtype=torch.long).random_(0, C)
>>> output = loss(m(conv(data)), target)
>>> output.backward()

```

### PoissonNLLLoss

```py
class torch.nn.PoissonNLLLoss(log_input=True, full=False, size_average=None, eps=1e-08, reduce=None, reduction='mean')
```

Negative log likelihood loss with Poisson distribution of target.

The loss can be described as:

![](img/f50aaec015c8f6f2ef26d16a60023ea1.jpg)

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_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – if `True` the loss is computed as ![](img/18729f59c6d4705e1945b3d7b3e09e32.jpg), if `False` the loss is ![](img/036591dc90f1dafaa138920518e2b05b.jpg).
*   **full** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) –

    whether to compute full loss, i. e. to add the Stirling approximation term

    ![](img/b063f11c809ea98839d91fc34d0b4bf0.jpg)

*   **size_average** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field `size_average` is set to `False`, the losses are instead summed for each minibatch. Ignored when reduce is `False`. Default: `True`
*   **eps** ([_float_](https://docs.python.org/3/library/functions.html#float "(in Python v3.7)")_,_ _optional_) – Small value to avoid evaluation of ![](img/f6dcd4f69520c309a6d71002bd330cb8.jpg) when `log_input == False`. Default: 1e-8
*   **reduce** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). 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`
*   **reduction** (_string__,_ _optional_) – Specifies the reduction to apply to the output: ‘none’ &#124; ‘mean’ &#124; ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: `size_average` and `reduce` are in the process of being deprecated, and in the meantime, specifying either of those two args will override `reduction`. Default: ‘mean’



Examples:

```py
>>> 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

```py
class torch.nn.KLDivLoss(size_average=None, reduce=None, reduction='mean')
```

The [Kullback-Leibler divergence](https://en.wikipedia.org/wiki/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`](#torch.nn.NLLLoss "torch.nn.NLLLoss"), the `input` given is expected to contain _log-probabilities_. However, unlike [`NLLLoss`](#torch.nn.NLLLoss "torch.nn.NLLLoss"), `input` is not restricted to a 2D Tensor. The targets are given as _probabilities_ (i.e. without taking the logarithm).

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

The unreduced (i.e. with `reduce` set to `False`) loss can be described as:

![](img/eba993f61a08816ebd5f577851d521f2.jpg)

where the index ![](img/9341d9048ac485106d2b2ee8de14876f.jpg) spans all dimensions of `input` and ![](img/db4a9fef02111450bf98261889de550c.jpg) has the same shape as `input`. If `reduce` is `True` (the default), then:

![](img/d88944e162eff94bddc1b9a94bcaa3a6.jpg)

In default reduction mode ‘mean’, the losses are averaged for each minibatch over observations **as well as** over dimensions. ‘batchmean’ mode gives the correct KL divergence where losses are averaged over batch dimension only. ‘mean’ mode’s behavior will be changed to the same as ‘batchmean’ in the next major release.

Parameters: 

*   **size_average** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field `size_average` is set to `False`, the losses are instead summed for each minibatch. Ignored when reduce is `False`. Default: `True`
*   **reduce** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). 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`
*   **reduction** (_string__,_ _optional_) – Specifies the reduction to apply to the output: ‘none’ &#124; ‘batchmean’ &#124; ‘sum’ &#124; ‘mean’. ‘none’: no reduction will be applied. ‘batchmean’: the sum of the output will be divided by batchsize. ‘sum’: the output will be summed. ‘mean’: the output will be divided by the number of elements in the output. Default: ‘mean’



:param .. note:: `size_average` and `reduce` are in the process of being deprecated,: and in the meantime, specifying either of those two args will override `reduction`. :param .. note:: `reduction=’mean’` doesn’t return the true kl divergence value, please use: `reduction=’batchmean’` which aligns with KL math definition.

> In the next major release, ‘mean’ will be changed to be the same as ‘batchmean’.

```py
Shape:
```

*   input: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg) where `*` means, any number of additional dimensions
*   target: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg), same shape as the input
*   ```py
    output: scalar by default. If reduce is False, then \((N, *)\),
    ```

    the same shape as the input

### BCELoss

```py
class torch.nn.BCELoss(weight=None, size_average=None, reduce=None, reduction='mean')
```

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

The loss can be described as:

![](img/f233882012c0c24fcad1869a163b5b7c.jpg)

where ![](img/9341d9048ac485106d2b2ee8de14876f.jpg) is the batch size. If reduce is `True`, then

![](img/d88944e162eff94bddc1b9a94bcaa3a6.jpg)

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_](tensors.html#torch.Tensor "torch.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_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field `size_average` is set to `False`, the losses are instead summed for each minibatch. Ignored when reduce is `False`. Default: `True`
*   **reduce** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). 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`
*   **reduction** (_string__,_ _optional_) – Specifies the reduction to apply to the output: ‘none’ &#124; ‘mean’ &#124; ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: `size_average` and `reduce` are in the process of being deprecated, and in the meantime, specifying either of those two args will override `reduction`. Default: ‘mean’



```py
Shape:
```

*   Input: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg) where `*` means, any number of additional dimensions
*   Target: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg), same shape as the input
*   Output: scalar. If `reduce` is False, then `(N, *)`, same shape as input.

Examples:

```py
>>> 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

```py
class torch.nn.BCEWithLogitsLoss(weight=None, size_average=None, reduce=None, reduction='mean', pos_weight=None)
```

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:

![](img/0c49aad6f81ec7936e313096f7a53f97.jpg)

where ![](img/9341d9048ac485106d2b2ee8de14876f.jpg) is the batch size. If reduce is `True`, then

![](img/0a16102d9320f70f18d7c8b152000489.jpg)

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.

It’s possible to trade off recall and precision by adding weights to positive examples. In this case the loss can be described as:

![](img/d5ca42e0ee1490d1dea4d5f38cc120d7.jpg)

where ![](img/76dc369e067e5fa42a4b32b6afd5e570.jpg) is the positive weight of class ![](img/493731e423d5db62086d0b8705dda0c8.jpg). ![](img/65abc7465f8ac5056f8562962f0ae02e.jpg) increases the recall, ![](img/989afd86a6407cf24295ae8d52ff0080.jpg) increases the precision.

For example, if a dataset contains 100 positive and 300 negative examples of a single class, then `pos_weight` for the class should be equal to ![](img/6a003751ded2d5e5198d93ee7db1ba5d.jpg). The loss would act as if the dataset contains ![](img/fb2ad75ea1ac3ba3ae507a3c8a34db12.jpg) positive examples.

Parameters: 

*   **weight** ([_Tensor_](tensors.html#torch.Tensor "torch.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_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field `size_average` is set to `False`, the losses are instead summed for each minibatch. Ignored when reduce is `False`. Default: `True`
*   **reduce** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). 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`
*   **reduction** (_string__,_ _optional_) – Specifies the reduction to apply to the output: ‘none’ &#124; ‘mean’ &#124; ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: `size_average` and `reduce` are in the process of being deprecated, and in the meantime, specifying either of those two args will override `reduction`. Default: ‘mean’
*   **pos_weight** – a weight of positive examples. Must be a vector with length equal to the number of classes.



### MarginRankingLoss

```py
class torch.nn.MarginRankingLoss(margin=0.0, size_average=None, reduce=None, reduction='mean')
```

Creates a criterion that measures the loss given inputs `x1`, `x2`, two 1D mini-batch `Tensor`s, 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:

![](img/1664f71bed4b6591f02c8bbb10f2d389.jpg)

Parameters: 

*   **margin** ([_float_](https://docs.python.org/3/library/functions.html#float "(in Python v3.7)")_,_ _optional_) – Has a default value of `0`.
*   **size_average** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field `size_average` is set to `False`, the losses are instead summed for each minibatch. Ignored when reduce is `False`. Default: `True`
*   **reduce** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). 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`
*   **reduction** (_string__,_ _optional_) – Specifies the reduction to apply to the output: ‘none’ &#124; ‘mean’ &#124; ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: `size_average` and `reduce` are in the process of being deprecated, and in the meantime, specifying either of those two args will override `reduction`. Default: ‘mean’



```py
Shape:
```

*   Input: ![](img/3dc464d2e10c731f17264e33e497c1a8.jpg) where `N` is the batch size and `D` is the size of a sample.
*   Target: ![](img/2a3e2b832e04fe8d66596083b23da518.jpg)
*   Output: scalar. If `reduce` is False, then `(N)`.

### HingeEmbeddingLoss

```py
class torch.nn.HingeEmbeddingLoss(margin=1.0, size_average=None, reduce=None, reduction='mean')
```

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 ![](img/493731e423d5db62086d0b8705dda0c8.jpg)-th sample in the mini-batch is

![](img/1e176ed632f1cbc86eb8db4bf6034f24.jpg)

and the total loss functions is

![](img/0a16102d9320f70f18d7c8b152000489.jpg)

where ![](img/97b4908568a8d2f8549d90e683a8efa2.jpg).

Parameters: 

*   **margin** ([_float_](https://docs.python.org/3/library/functions.html#float "(in Python v3.7)")_,_ _optional_) – Has a default value of `1`.
*   **size_average** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field `size_average` is set to `False`, the losses are instead summed for each minibatch. Ignored when reduce is `False`. Default: `True`
*   **reduce** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). 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`
*   **reduction** (_string__,_ _optional_) – Specifies the reduction to apply to the output: ‘none’ &#124; ‘mean’ &#124; ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: `size_average` and `reduce` are in the process of being deprecated, and in the meantime, specifying either of those two args will override `reduction`. Default: ‘mean’



```py
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

```py
class torch.nn.MultiLabelMarginLoss(size_average=None, reduce=None, reduction='mean')
```

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:

![](img/f4d7e37a53b15d27b3a25c9dc586cd00.jpg)

where ![](img/b75aa938b45ed55c0aa471218a7224ce.jpg) to ![](img/c915dd214c2340e40ac8e79013465783.jpg), ![](img/4da95e4f78bfe10987f5549ced63a7e6.jpg) to ![](img/ec0f8a278c4b73ccb95d3a4c1d129697.jpg), ![](img/8058aac8e03495c71f75b04169d5baca.jpg), and ![](img/27b5f368a27d1e15b3656796a28a4411.jpg) for all ![](img/31df9c730e19ca29b59dce64b99d98c1.jpg) and ![](img/d8fdd0e28cfb03738fc5227885ee035a.jpg).

`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_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field `size_average` is set to `False`, the losses are instead summed for each minibatch. Ignored when reduce is `False`. Default: `True`
*   **reduce** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). 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`
*   **reduction** (_string__,_ _optional_) – Specifies the reduction to apply to the output: ‘none’ &#124; ‘mean’ &#124; ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: `size_average` and `reduce` are in the process of being deprecated, and in the meantime, specifying either of those two args will override `reduction`. Default: ‘mean’



```py
Shape:
```

*   Input: ![](img/861a7d7a604a97f5620afad259a4c26d.jpg) or ![](img/9b9aebaa467ad07dca05b5086bd21ca2.jpg) where `N` is the batch size and `C` is the number of classes.
*   Target: ![](img/861a7d7a604a97f5620afad259a4c26d.jpg) or ![](img/9b9aebaa467ad07dca05b5086bd21ca2.jpg), same shape as the input.
*   Output: scalar. If `reduce` is False, then `(N)`.

### SmoothL1Loss

```py
class torch.nn.SmoothL1Loss(size_average=None, reduce=None, reduction='mean')
```

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:

![](img/cd503c18d22f0e18a5109f3f13d028b2.jpg)

where ![](img/bbfcb7c1428a33547e15f8853dbe6e4f.jpg) is given by:

![](img/621fa336f1f8b6169430fa6b42a00b6d.jpg)

`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_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field `size_average` is set to `False`, the losses are instead summed for each minibatch. Ignored when reduce is `False`. Default: `True`
*   **reduce** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). 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`
*   **reduction** (_string__,_ _optional_) – Specifies the reduction to apply to the output: ‘none’ &#124; ‘mean’ &#124; ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: `size_average` and `reduce` are in the process of being deprecated, and in the meantime, specifying either of those two args will override `reduction`. Default: ‘mean’



```py
Shape:
```

*   Input: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg) where `*` means, any number of additional dimensions
*   Target: ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg), same shape as the input
*   Output: scalar. If reduce is `False`, then ![](img/eb7a3f5bc15cc379e78f768e821eb094.jpg), same shape as the input

### SoftMarginLoss

```py
class torch.nn.SoftMarginLoss(size_average=None, reduce=None, reduction='mean')
```

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

![](img/811f3185227a964c048126484987ef1c.jpg)

Parameters: 

*   **size_average** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field `size_average` is set to `False`, the losses are instead summed for each minibatch. Ignored when reduce is `False`. Default: `True`
*   **reduce** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). 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`
*   **reduction** (_string__,_ _optional_) – Specifies the reduction to apply to the output: ‘none’ &#124; ‘mean’ &#124; ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: `size_average` and `reduce` are in the process of being deprecated, and in the meantime, specifying either of those two args will override `reduction`. Default: ‘mean’



```py
Shape:
```

*   Input: Tensor of arbitrary shape.
*   Target: Same shape as input.
*   Output: scalar. If reduce is `False`, then same shape as the input

### MultiLabelSoftMarginLoss

```py
class torch.nn.MultiLabelSoftMarginLoss(weight=None, size_average=None, reduce=None, reduction='mean')
```

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:

![](img/342414ff43adf5d0fa0b62fcde9538a2.jpg)

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

Parameters: 

*   **weight** ([_Tensor_](tensors.html#torch.Tensor "torch.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_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field `size_average` is set to `False`, the losses are instead summed for each minibatch. Ignored when reduce is `False`. Default: `True`
*   **reduce** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). 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`
*   **reduction** (_string__,_ _optional_) – Specifies the reduction to apply to the output: ‘none’ &#124; ‘mean’ &#124; ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: `size_average` and `reduce` are in the process of being deprecated, and in the meantime, specifying either of those two args will override `reduction`. Default: ‘mean’



```py
Shape:
```

*   Input: ![](img/9b9aebaa467ad07dca05b5086bd21ca2.jpg) where `N` is the batch size and `C` is the number of classes.
*   Target: ![](img/9b9aebaa467ad07dca05b5086bd21ca2.jpg), same shape as the input.
*   Output: scalar. If `reduce` is False, then `(N)`.

### CosineEmbeddingLoss

```py
class torch.nn.CosineEmbeddingLoss(margin=0.0, size_average=None, reduce=None, reduction='mean')
```

Creates a criterion that measures the loss given input tensors ![](img/abdadb44ea35aecb39004dd7f55d9543.jpg), ![](img/88fdc6eeb68ef4aacf7cd6bd43fa176e.jpg) 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:

![](img/f894a052d4408e0269216f8b803d074a.jpg)

Parameters: 

*   **margin** ([_float_](https://docs.python.org/3/library/functions.html#float "(in Python v3.7)")_,_ _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_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field `size_average` is set to `False`, the losses are instead summed for each minibatch. Ignored when reduce is `False`. Default: `True`
*   **reduce** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). 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`
*   **reduction** (_string__,_ _optional_) – Specifies the reduction to apply to the output: ‘none’ &#124; ‘mean’ &#124; ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: `size_average` and `reduce` are in the process of being deprecated, and in the meantime, specifying either of those two args will override `reduction`. Default: ‘mean’



### MultiMarginLoss

```py
class torch.nn.MultiMarginLoss(p=1, margin=1.0, weight=None, size_average=None, reduce=None, reduction='mean')
```

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, ![](img/fffe5e09046ebb236f89daa5091946f6.jpg)):

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

![](img/0f825c52299de2e574d5903469e1af9c.jpg)

where `i == 0` to `x.size(0)` and ![](img/99e4beebf24a180393aa15ec3740cf3a.jpg).

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

The loss function then becomes:

![](img/03b7ccf64bc071a7c2abbeab89f12d08.jpg)

Parameters: 

*   **p** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ _optional_) – Has a default value of `1`. `1` and `2` are the only supported values
*   **margin** ([_float_](https://docs.python.org/3/library/functions.html#float "(in Python v3.7)")_,_ _optional_) – Has a default value of `1`.
*   **weight** ([_Tensor_](tensors.html#torch.Tensor "torch.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_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field `size_average` is set to `False`, the losses are instead summed for each minibatch. Ignored when reduce is `False`. Default: `True`
*   **reduce** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). 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`
*   **reduction** (_string__,_ _optional_) – Specifies the reduction to apply to the output: ‘none’ &#124; ‘mean’ &#124; ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: `size_average` and `reduce` are in the process of being deprecated, and in the meantime, specifying either of those two args will override `reduction`. Default: ‘mean’



### TripletMarginLoss

```py
class torch.nn.TripletMarginLoss(margin=1.0, p=2.0, eps=1e-06, swap=False, size_average=None, reduce=None, reduction='mean')
```

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 ![](img/3dc464d2e10c731f17264e33e497c1a8.jpg).

The distance swap is described in detail in the paper [Learning shallow convolutional feature descriptors with triplet losses](http://www.iis.ee.ic.ac.uk/%7Evbalnt/shallow_descr/TFeat_paper.pdf) by V. Balntas, E. Riba et al.

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

![](img/a2c4faa5dd95a547388c1b7f69bbc4db.jpg)

where

![](img/bac339e9cf6ad679fa9ce3ce33c431ab.jpg)

Parameters: 

*   **margin** ([_float_](https://docs.python.org/3/library/functions.html#float "(in Python v3.7)")_,_ _optional_) – Default: `1`.
*   **p** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ _optional_) – The norm degree for pairwise distance. Default: `2`.
*   **swap** ([_float_](https://docs.python.org/3/library/functions.html#float "(in Python v3.7)")_,_ _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_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there multiple elements per sample. If the field `size_average` is set to `False`, the losses are instead summed for each minibatch. Ignored when reduce is `False`. Default: `True`
*   **reduce** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – Deprecated (see `reduction`). 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`
*   **reduction** (_string__,_ _optional_) – Specifies the reduction to apply to the output: ‘none’ &#124; ‘mean’ &#124; ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the sum of the output will be divided by the number of elements in the output, ‘sum’: the output will be summed. Note: `size_average` and `reduce` are in the process of being deprecated, and in the meantime, specifying either of those two args will override `reduction`. Default: ‘mean’



```py
Shape:
```

*   Input: ![](img/3dc464d2e10c731f17264e33e497c1a8.jpg) where `D` is the vector dimension.
*   Output: scalar. If `reduce` is False, then `(N)`.

```py
>>> 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

```py
class torch.nn.PixelShuffle(upscale_factor)
```

Rearranges elements in a tensor of shape ![](img/1bc8a113de558f2e7d966e72ae39cb95.jpg) to a tensor of shape ![](img/d4e6de257f72abc5a96af64211b7f909.jpg).

This is useful for implementing efficient sub-pixel convolution with a stride of ![](img/71c5422a7f21b7096aa6d904d5a4f78d.jpg).

Look at the paper: [Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network](https://arxiv.org/abs/1609.05158) by Shi et. al (2016) for more details.

| Parameters: | **upscale_factor** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – factor to increase spatial resolution by |
| --- | --- |

```py
Shape:
```

*   Input: ![](img/d6770cccc0ae9886c3b91d55efa20b28.jpg)
*   Output: ![](img/a162cf8e9185f67b3f5b084d1031dc7e.jpg)

Examples:

```py
>>> pixel_shuffle = nn.PixelShuffle(3)
>>> input = torch.randn(1, 9, 4, 4)
>>> output = pixel_shuffle(input)
>>> print(output.size())
torch.Size([1, 1, 12, 12])

```

### Upsample

```py
class torch.nn.Upsample(size=None, scale_factor=None, mode='nearest', align_corners=None)
```

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_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _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_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _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



```py
Shape:
```

*   Input: ![](img/964aa6df63e83f4468aa090441f01972.jpg), ![](img/ff71b16eb10237262566c6907acaaf1f.jpg) or ![](img/c187d190013d0785320e3412fe8cd669.jpg)
*   Output: ![](img/ac2661719f40fc422e2b1590a1e7b4a4.jpg), ![](img/a0ef05f779873fc4dcbf020b1ea14754.jpg) or ![](img/41ca4c8d4c65c979d2d643c6f62ea280.jpg), where

![](img/da11a1265058248a851d6d0331110214.jpg)

![](img/828543b18440713aad6ad023732327ec.jpg)

![](img/5a7c5c22409d4ab3c83641508bf72cb6.jpg)

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.

Note

If you want downsampling/general resizing, you should use `interpolate()`.

Examples:

```py
>>> input = torch.arange(1, 5).view(1, 1, 2, 2).float()
>>> 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

```py
class torch.nn.UpsamplingNearest2d(size=None, scale_factor=None)
```

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_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – a tuple of ints `(H_out, W_out)` output sizes
*   **scale_factor** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ _optional_) – the multiplier for the image height or width



Warning

This class is deprecated in favor of `interpolate()`.

```py
Shape:
```

*   Input: ![](img/ff71b16eb10237262566c6907acaaf1f.jpg)
*   Output: ![](img/a0ef05f779873fc4dcbf020b1ea14754.jpg) where

![](img/682de298a3561bebd964280ba0d59633.jpg)

![](img/2a53007c25abe7f8f65f1a2e958fa146.jpg)

Examples:

```py
>>> 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

```py
class torch.nn.UpsamplingBilinear2d(size=None, scale_factor=None)
```

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_](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.7)")_,_ _optional_) – a tuple of ints `(H_out, W_out)` output sizes
*   **scale_factor** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ _optional_) – the multiplier for the image height or width



Warning

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

```py
Shape:
```

*   Input: ![](img/ff71b16eb10237262566c6907acaaf1f.jpg)
*   Output: ![](img/a0ef05f779873fc4dcbf020b1ea14754.jpg) where

![](img/682de298a3561bebd964280ba0d59633.jpg)

![](img/2a53007c25abe7f8f65f1a2e958fa146.jpg)

Examples:

```py
>>> 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

```py
class torch.nn.DataParallel(module, device_ids=None, output_device=None, dim=0)
```

Implements data parallelism at the module level.

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

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

See also: [Use nn.DataParallel instead of multiprocessing](notes/cuda.html#cuda-nn-dataparallel-instead)

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.

The parallelized `module` must have its parameters and buffers on `device_ids[0]` before running this [`DataParallel`](#torch.nn.DataParallel "torch.nn.DataParallel") module.

Warning

In each forward, `module` is **replicated** on each device, so any updates to the runing module in `forward` will be lost. For example, if `module` has a counter attribute that is incremented in each `forward`, it will always stay at the initial value becasue the update is done on the replicas which are destroyed after `forward`. However, [`DataParallel`](#torch.nn.DataParallel "torch.nn.DataParallel") guarantees that the replica on `device[0]` will have its parameters and buffers sharing storage with the base parallelized `module`. So **in-place** updates to the parameters or buffers on `device[0]` will be recorded. E.g., [`BatchNorm2d`](#torch.nn.BatchNorm2d "torch.nn.BatchNorm2d") and [`spectral_norm()`](#torch.nn.utils.spectral_norm "torch.nn.utils.spectral_norm") rely on this behavior to update the buffers.

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()`](#torch.nn.Module.register_forward_pre_hook "torch.nn.Module.register_forward_pre_hook") be executed before `all` `len(device_ids)` [`forward()`](#torch.nn.Module.forward "torch.nn.Module.forward") calls, but that each such hook be executed before the corresponding [`forward()`](#torch.nn.Module.forward "torch.nn.Module.forward") call of that device.

Warning

When `module` returns a scalar (i.e., 0-dimensional tensor) in `forward()`, this wrapper will return a vector of length equal to number of devices used in data parallelism, containing the result from each device.

Note

There is a subtlety in using the `pack sequence -&gt; recurrent network -&gt; unpack sequence` pattern in a [`Module`](#torch.nn.Module "torch.nn.Module") wrapped in [`DataParallel`](#torch.nn.DataParallel "torch.nn.DataParallel"). See [My recurrent network doesn’t work with data parallelism](notes/faq.html#pack-rnn-unpack-with-data-parallelism) section in FAQ for details.

Parameters: 

*   **module** ([_Module_](#torch.nn.Module "torch.nn.Module")) – module to be parallelized
*   **device_ids** (_list of python:int_ _or_ [_torch.device_](tensor_attributes.html#torch.torch.device "torch.torch.device")) – CUDA devices (default: all devices)
*   **output_device** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_torch.device_](tensor_attributes.html#torch.torch.device "torch.torch.device")) – device location of output (default: device_ids[0])


| Variables: | **module** ([_Module_](#torch.nn.Module "torch.nn.Module")) – the module to be parallelized |
| --- | --- |

Example:

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

```

### DistributedDataParallel

```py
class torch.nn.parallel.DistributedDataParallel(module, device_ids=None, output_device=None, dim=0, broadcast_buffers=True, process_group=None, bucket_cap_mb=25, check_reduction=False)
```

Implements distributed data parallelism that is based on torch.distributed package at the module level.

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

The batch size should be larger than the number of GPUs used locally. 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](distributed.html#distributed-basics) and [Use nn.DataParallel instead of multiprocessing](notes/cuda.html#cuda-nn-dataparallel-instead). The same constraints on input as in [`torch.nn.DataParallel`](#torch.nn.DataParallel "torch.nn.DataParallel") apply.

Creation of this class requires that `torch.distributed` to be already initialized, by calling [`torch.distributed.init_process_group()`](distributed.html#torch.distributed.init_process_group "torch.distributed.init_process_group")

`DistributedDataParallel` can be used in the following two ways:

1.  Single-Process Multi-GPU

In this case, a single process will be spawned on each host/node and each process will operate on all the GPUs of the node where it’s running. To use `DistributedDataParallel` in this way, you can simply construct the model as the following:

```py
>>> torch.distributed.init_process_group(backend="nccl")
>>> model = DistributedDataParallel(model) # device_ids will include all GPU devices be default

```

1.  Multi-Process Single-GPU

This is the highly recommended way to use `DistributedDataParallel`, with multiple processes, each of which operates on a single GPU. This is currently the fastest approach to do data parallel training using PyTorch and applies to both single-node(multi-GPU) and multi-node data parallel training. It is proven to be significantly faster than [`torch.nn.DataParallel`](#torch.nn.DataParallel "torch.nn.DataParallel") for single-node multi-GPU data parallel training.

Here is how to use it: on each host with N GPUs, you should spawn up N processes, while ensuring that each process invidually works on a single GPU from 0 to N-1\. Therefore, it is your job to ensure that your training script operates on a single given GPU by calling:

```py
>>> torch.cuda.set_device(i)

```

where i is from 0 to N-1\. In each process, you should refer the following to construct this module:

```py
>>> torch.distributed.init_process_group(backend='nccl', world_size=4, init_method='...')
>>> model = DistributedDataParallel(model, device_ids=[i], output_device=i)

```

In order to spawn up multiple processes per node, you can use either `torch.distributed.launch` or `torch.multiprocessing.spawn`

Note

`nccl` backend is currently the fastest and highly recommended backend to be used with Multi-Process Single-GPU distributed training and this applies to both single-node and multi-node distributed training

Warning

This module works only with the `gloo` and `nccl` backends.

Warning

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

Warning

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

Warning

This module assumes all parameters are registered in the model of each distributed processes are in the same order. The module itself will conduct gradient all-reduction following the reverse order of the registered parameters of the model. In other wise, it is users’ responsibility to ensure that each distributed process has the exact same model and thus the exact parameter registeration order.

Warning

This module assumes all buffers and gradients are dense.

Warning

This module doesn’t work with [`torch.autograd.grad()`](autograd.html#torch.autograd.grad "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.

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.

Warning

You should never try to change your model’s parameters after wrapping up your model with DistributedDataParallel. In other words, when wrapping up your model with DistributedDataParallel, the constructor of DistributedDataParallel will register the additional gradient reduction functions on all the parameters of the model itself at the time of construction. If you change the model’s parameters after the DistributedDataParallel construction, this is not supported and unexpected behaviors can happen, since some parameters’ gradient reduction functions might not get called.

Note

Parameters are never broadcast between processes. The module performs an 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.

Parameters: 

*   **module** ([_Module_](#torch.nn.Module "torch.nn.Module")) – module to be parallelized
*   **device_ids** (_list of python:int_ _or_ [_torch.device_](tensor_attributes.html#torch.torch.device "torch.torch.device")) – CUDA devices (default: all devices)
*   **output_device** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)") _or_ [_torch.device_](tensor_attributes.html#torch.torch.device "torch.torch.device")) – device location of output (default: device_ids[0])
*   **broadcast_buffers** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")) – flag that enables syncing (broadcasting) buffers of the module at beginning of the forward function. (default: True)
*   **process_group** – the process group to be used for distributed data all-reduction. If None, the default process group, which is created by ``torch.distributed.init_process_group``, will be used. (default: None)
*   **bucket_cap_mb** – DistributedDataParallel will bucket parameters into multiple buckets so that gradient reduction of each bucket can potentially overlap with backward computation. bucket_cap_mb controls the bucket size in MegaBytes (MB) (default: 25)
*   **check_reduction** – when setting to True, it enables DistributedDataParallel to automatically check if the previous iteration’s backward reductions were successfully issued at the beginning of every iteration’s forward function. You normally don’t need this option enabled unless you are observing weird behaviors such as different ranks are getting different gradients, which should not happen if DistributedDataParallel is corrected used. (default: False)


| Variables: | **module** ([_Module_](#torch.nn.Module "torch.nn.Module")) – the module to be parallelized |
| --- | --- |

```py
Example::
```

```py
>>> torch.distributed.init_process_group(backend='nccl', world_size=4, init_method='...')
>>> net = torch.nn.DistributedDataParallel(model, pg)

```

### DistributedDataParallelCPU

```py
class torch.nn.parallel.DistributedDataParallelCPU(module)
```

Implements distributed data parallelism for CPU at the module level.

This module supports the `mpi` and `gloo` backends.

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

This module could be used in conjunction with the DistributedSampler, (see :class `torch.utils.data.distributed.DistributedSampler`) which will load a subset of the original datset for each node with the same batch size. So strong scaling should be configured like this:

n = 1, batch size = 12

n = 2, batch size = 64

n = 4, batch size = 32

n = 8, batch size = 16

Creation of this class requires the distributed package to be already initialized in the process group mode (see [`torch.distributed.init_process_group()`](distributed.html#torch.distributed.init_process_group "torch.distributed.init_process_group")).

Warning

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

Warning

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

Warning

This module assumes all gradients are dense.

Warning

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

Warning

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

Note

Parameters are broadcast between nodes in the __init__() function. The module performs an all-reduce step on gradients and assumes that they will be modified by the optimizer in all nodes in the same way.

| Parameters: | **module** – module to be parallelized |
| --- | --- |

Example:

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

```

## Utilities

### clip_grad_norm_

```py
torch.nn.utils.clip_grad_norm_(parameters, max_norm, norm_type=2)
```

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_](tensors.html#torch.Tensor "torch.Tensor")_] or_ [_Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – an iterable of Tensors or a single Tensor that will have gradients normalized
*   **max_norm** ([_float_](https://docs.python.org/3/library/functions.html#float "(in Python v3.7)") _or_ [_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – max norm of the gradients
*   **norm_type** ([_float_](https://docs.python.org/3/library/functions.html#float "(in Python v3.7)") _or_ [_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – type of the used p-norm. Can be `'inf'` for infinity norm.


| Returns: | Total norm of the parameters (viewed as a single vector). |
| --- | --- |

### clip_grad_value_

```py
torch.nn.utils.clip_grad_value_(parameters, clip_value)
```

Clips gradient of an iterable of parameters at specified value.

Gradients are modified in-place.

Parameters: 

*   **parameters** (_Iterable__[_[_Tensor_](tensors.html#torch.Tensor "torch.Tensor")_] or_ [_Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – an iterable of Tensors or a single Tensor that will have gradients normalized
*   **clip_value** ([_float_](https://docs.python.org/3/library/functions.html#float "(in Python v3.7)") _or_ [_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")) – maximum allowed value of the gradients The gradients are clipped in the range [-clip_value, clip_value]



### parameters_to_vector

```py
torch.nn.utils.parameters_to_vector(parameters)
```

Convert parameters to one vector

| Parameters: | **parameters** (_Iterable__[_[_Tensor_](tensors.html#torch.Tensor "torch.Tensor")_]_) – an iterator of Tensors that are the parameters of a model. |
| --- | --- |
| Returns: | The parameters represented by a single vector |
| --- | --- |

### vector_to_parameters

```py
torch.nn.utils.vector_to_parameters(vec, parameters)
```

Convert one vector to the parameters

Parameters: 

*   **vec** ([_Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – a single vector represents the parameters of a model.
*   **parameters** (_Iterable__[_[_Tensor_](tensors.html#torch.Tensor "torch.Tensor")_]_) – an iterator of Tensors that are the parameters of a model.



### weight_norm

```py
torch.nn.utils.weight_norm(module, name='weight', dim=0)
```

Applies weight normalization to a parameter in the given module.

![](img/06160be4a838f9d6d20cabc64f32670e.jpg)

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`.

See [https://arxiv.org/abs/1602.07868](https://arxiv.org/abs/1602.07868)

Parameters: 

*   **module** ([_nn.Module_](#torch.nn.Module "torch.nn.Module")) – containing module
*   **name** ([_str_](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.7)")_,_ _optional_) – name of weight parameter
*   **dim** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ _optional_) – dimension over which to compute the norm


| Returns: | The original module with the weight norm hook |
| --- | --- |

Example:

```py
>>> 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

```py
torch.nn.utils.remove_weight_norm(module, name='weight')
```

Removes the weight normalization reparameterization from a module.

Parameters: 

*   **module** ([_nn.Module_](#torch.nn.Module "torch.nn.Module")) – containing module
*   **name** ([_str_](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.7)")_,_ _optional_) – name of weight parameter



Example

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

```

### spectral_norm

```py
torch.nn.utils.spectral_norm(module, name='weight', n_power_iterations=1, eps=1e-12, dim=None)
```

Applies spectral normalization to a parameter in the given module.

![](img/1ca46cc2506aac38bf00645f64b1a3e3.jpg)

Spectral normalization stabilizes the training of discriminators (critics) in Generaive Adversarial Networks (GANs) by rescaling the weight tensor with spectral norm ![](img/2469b2bd2a1ab19ebfcee223dcb52bb1.jpg) of the weight matrix calculated using power iteration method. If the dimension of the weight tensor is greater than 2, it is reshaped to 2D in power iteration method to get spectral norm. This is implemented via a hook that calculates spectral norm and rescales weight before every `forward()` call.

See [Spectral Normalization for Generative Adversarial Networks](https://arxiv.org/abs/1802.05957) .

Parameters: 

*   **module** ([_nn.Module_](#torch.nn.Module "torch.nn.Module")) – containing module
*   **name** ([_str_](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.7)")_,_ _optional_) – name of weight parameter
*   **n_power_iterations** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ _optional_) – number of power iterations to calculate spectal norm
*   **eps** ([_float_](https://docs.python.org/3/library/functions.html#float "(in Python v3.7)")_,_ _optional_) – epsilon for numerical stability in calculating norms
*   **dim** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ _optional_) – dimension corresponding to number of outputs, the default is 0, except for modules that are instances of ConvTranspose1/2/3d, when it is 1


| Returns: | The original module with the spectal norm hook |
| --- | --- |

Example:

```py
>>> m = spectral_norm(nn.Linear(20, 40))
Linear (20 -> 40)
>>> m.weight_u.size()
torch.Size([20])

```

### remove_spectral_norm

```py
torch.nn.utils.remove_spectral_norm(module, name='weight')
```

Removes the spectral normalization reparameterization from a module.

Parameters: 

*   **module** ([_nn.Module_](#torch.nn.Module "torch.nn.Module")) – containing module
*   **name** ([_str_](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.7)")_,_ _optional_) – name of weight parameter



Example

```py
>>> m = spectral_norm(nn.Linear(40, 10))
>>> remove_spectral_norm(m)

```

### PackedSequence

```py
torch.nn.utils.rnn.PackedSequence(data, batch_sizes=None)
```

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()`](#torch.nn.utils.rnn.pack_padded_sequence "torch.nn.utils.rnn.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()`](#torch.nn.utils.rnn.pack_padded_sequence "torch.nn.utils.rnn.pack_padded_sequence"). For instance, given data `abc` and `x` the [`PackedSequence`](#torch.nn.utils.rnn.PackedSequence "torch.nn.utils.rnn.PackedSequence") would contain data `axbc` with `batch_sizes=[2,1,1]`.

| Variables: | 

*   **data** ([_Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – Tensor containing packed sequence
*   **batch_sizes** ([_Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – Tensor of integers holding information about the batch size at each sequence step



### pack_padded_sequence

```py
torch.nn.utils.rnn.pack_padded_sequence(input, lengths, batch_first=False)
```

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`](#torch.nn.utils.rnn.PackedSequence "torch.nn.utils.rnn.PackedSequence") object by accessing its `.data` attribute.

Parameters: 

*   **input** ([_Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – padded batch of variable length sequences.
*   **lengths** ([_Tensor_](tensors.html#torch.Tensor "torch.Tensor")) – list of sequences lengths of each batch element.
*   **batch_first** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – if `True`, the input is expected in `B x T x *` format.


| Returns: | a [`PackedSequence`](#torch.nn.utils.rnn.PackedSequence "torch.nn.utils.rnn.PackedSequence") object |
| --- | --- |

### pad_packed_sequence

```py
torch.nn.utils.rnn.pad_packed_sequence(sequence, batch_first=False, padding_value=0.0, total_length=None)
```

Pads a packed batch of variable length sequences.

It is an inverse operation to [`pack_padded_sequence()`](#torch.nn.utils.rnn.pack_padded_sequence "torch.nn.utils.rnn.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 -&gt; recurrent network -&gt; unpack sequence` pattern in a [`Module`](#torch.nn.Module "torch.nn.Module") wrapped in [`DataParallel`](#torch.nn.DataParallel "torch.nn.DataParallel"). See [this FAQ section](notes/faq.html#pack-rnn-unpack-with-data-parallelism) for details.

Parameters: 

*   **sequence** (_PackedSequence_) – batch to pad
*   **batch_first** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – if `True`, the output will be in `B x T x *` format.
*   **padding_value** ([_float_](https://docs.python.org/3/library/functions.html#float "(in Python v3.7)")_,_ _optional_) – values for padded elements.
*   **total_length** ([_int_](https://docs.python.org/3/library/functions.html#int "(in Python v3.7)")_,_ _optional_) – if not `None`, the output will be padded to have length `total_length`. This method will throw [`ValueError`](https://docs.python.org/3/library/exceptions.html#ValueError "(in Python v3.7)") if `total_length` is less than the max sequence length in `sequence`.


| Returns: | Tuple of Tensor containing the padded sequence, and a Tensor containing the list of lengths of each sequence in the batch. |
| --- | --- |

### pad_sequence

```py
torch.nn.utils.rnn.pad_sequence(sequences, batch_first=False, padding_value=0)
```

Pad a list of variable length Tensors with zero

`pad_sequence` stacks a list of Tensors along a new dimension, and pads them to equal length. For example, if the input is list of sequences with size `L x *` and if batch_first is False, and `T x B x *` otherwise.

`B` is batch size. It is equal to the number of elements in `sequences`. `T` is length of the longest sequence. `L` is length of the sequence. `*` is any number of trailing dimensions, including none.

Example

```py
>>> 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 the longest sequence. This function assumes trailing dimensions and type of all the Tensors in sequences are same.

Parameters: 

*   **sequences** ([_list_](https://docs.python.org/3/library/stdtypes.html#list "(in Python v3.7)")_[_[_Tensor_](tensors.html#torch.Tensor "torch.Tensor")_]_) – list of variable length sequences.
*   **batch_first** ([_bool_](https://docs.python.org/3/library/functions.html#bool "(in Python v3.7)")_,_ _optional_) – output will be in `B x T x *` if True, or in `T x B x *` otherwise
*   **padding_value** ([_float_](https://docs.python.org/3/library/functions.html#float "(in Python v3.7)")_,_ _optional_) – value for padded elements. Default: 0.


| Returns: | Tensor of size `T x B x *` if `batch_first` is `False`. Tensor of size `B x T x *` otherwise |
| --- | --- |

### pack_sequence

```py
torch.nn.utils.rnn.pack_sequence(sequences)
```

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

```py
>>> 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_](https://docs.python.org/3/library/stdtypes.html#list "(in Python v3.7)")_[_[_Tensor_](tensors.html#torch.Tensor "torch.Tensor")_]_) – A list of sequences of decreasing length. |
| --- | --- |
| Returns: | a [`PackedSequence`](#torch.nn.utils.rnn.PackedSequence "torch.nn.utils.rnn.PackedSequence") object |
| --- | --- |