PyTorch ConvTranspose2d 的定义与计算过程

1. CONVTRANSPOSE2D (ConvTranspose2d)

https://pytorch.org/docs/stable/generated/torch.nn.ConvTranspose2d.html

torch.nn.ConvTranspose2d(in_channels, out_channels, kernel_size, stride=1, padding=0, output_padding=0, groups=1, bias=True, dilation=1, padding_mode='zeros', device=None, dtype=None)

Applies a 2D transposed convolution operator over an input image composed of several input planes.
二维转置卷积运算符。

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 as it does not compute a true inverse of convolution).
该模块可以看作是 Conv2d 相对于其输入的梯度。它也被称为分数步长卷积或反卷积/逆卷积 (尽管它不是实际的反卷积/逆卷积操作，因为它不是卷积的逆向计算)。

gradient ['ɡreɪdiənt]：n. 倾斜度，梯度变化曲线 adj. 倾斜的，步行的
fractionally [ˈfrækʃənəli]：adv. 很小，很少
cross-correlation：互相关

the visualizations: https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md
the paper: https://www.matthewzeiler.com/mattzeiler/deconvolutionalnetworks.pdf

This module supports TensorFloat32.

On certain ROCm devices, when using float16 inputs this module will use different precision for backward.

• stride controls the stride for the cross-correlation.
  步长。

• padding controls the amount of implicit zero padding on both sides for dilation * (kernel_size - 1) - padding number of points. See note below for details.

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

• dilation controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but the link here has a nice visualization of what dilation does.

  {groups_note}

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:
  The :attr:padding argument effectively adds dilation * (kernel_size - 1) - padding
  amount of zero padding to both sizes of the input. This is set so that
  when a :class:~torch.nn.Conv2d and a :class:~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 > 1,
  :class:~torch.nn.Conv2d maps multiple input shapes to the same output
  shape. :attr:output_padding is provided to resolve this ambiguity by
  effectively increasing the calculated output shape on one side. Note
  that :attr:output_padding is only used to find output shape, but does
  not actually add zero-padding to output.

  Note:
  {cudnn_reproducibility_note}

Parameters

• in_channels (int): Number of channels in the input image
  输入的通道数。

• out_channels (int): Number of channels produced by the convolution
  输出的通道数。

• kernel_size (int or tuple): Size of the convolving kernel
  卷积核的大小。

• stride (int or tuple, optional): Stride of the convolution. Default: 1
  卷积的步长。

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

• output_padding (int or tuple, optional): Additional size added to one side of each dimension in the output shape. Default: 0

• groups (int, optional): Number of blocked connections from input channels to output channels. Default: 1

• bias (bool, optional): If True, adds a learnable bias to the output. Default: True
  偏置。

• dilation (int or tuple, optional): Spacing between kernel elements. Default: 1

Shape

• Input: (N,Cin,Hin,Win)(N, C_{in}, H_{in}, W_{in})(N,Cin​,Hin​,Win​) or (Cin,Hin,Win)(C_{in}, H_{in}, W_{in})(Cin​,Hin​,Win​)
• Output: (N,Cout,Hout,Wout)(N, C_{out}, H_{out}, W_{out})(N,Cout​,Hout​,Wout​) or (Cout,Hout,Wout)(C_{out}, H_{out}, W_{out})(Cout​,Hout​,Wout​), where

Hout=(Hin−1)×stride[0]−2×padding[0]+dilation[0]×(kernel_size[0]−1)+output_padding[0]+1H_{out} = (H_{in} - 1) \times \text{stride}[0] - 2 \times \text{padding}[0] + \text{dilation}[0] \times (\text{kernel\_size}[0] - 1) + \text{output\_padding}[0] + 1Hout​=(Hin​−1)×stride[0]−2×padding[0]+dilation[0]×(kernel_size[0]−1)+output_padding[0]+1

Wout=(Win−1)×stride[1]−2×padding[1]+dilation[1]×(kernel_size[1]−1)+output_padding[1]+1W_{out} = (W_{in} - 1) \times \text{stride}[1] - 2 \times \text{padding}[1] + \text{dilation}[1] \times (\text{kernel\_size}[1] - 1) + \text{output\_padding}[1] + 1Wout​=(Win​−1)×stride[1]−2×padding[1]+dilation[1]×(kernel_size[1]−1)+output_padding[1]+1

Variables

• weight (Tensor): the learnable weights of the module of shape
  (in_channels,out_channelsgroups,kernel_size[0],kernel_size[1])(\text{in\_channels}, \frac{\text{out\_channels}}{\text{groups}}, \text{kernel\_size[0]}, \text{kernel\_size[1]})(in_channels,groupsout_channels​,kernel_size[0],kernel_size[1]). The values of these weights are sampled from U(−k,k)\mathcal{U}(-\sqrt{k}, \sqrt{k})U(−k​,k​) where k=groupsCout∗∏i=01kernel_size[i]k = \frac{groups}{C_\text{out} * \prod_{i=0}^{1}\text{kernel\_size}[i]}k=Cout​∗∏i=01​kernel_size[i]groups​
• bias (Tensor): the learnable bias of the module of shape (out_channels)(\text{out\_channels})(out_channels). If bias is True, then the values of these weights are sampled from U(−k,k)\mathcal{U}(-\sqrt{k}, \sqrt{k})U(−k​,k​) where k=groupsCout∗∏i=01kernel_size[i]k = \frac{groups}{C_\text{out} * \prod_{i=0}^{1}\text{kernel\_size}[i]}k=Cout​∗∏i=01​kernel_size[i]groups​

Examples::

    >>> # With square kernels and equal stride>>> m = nn.ConvTranspose2d(16, 33, 3, stride=2)>>> # non-square kernels and unequal stride and with padding>>> m = nn.ConvTranspose2d(16, 33, (3, 5), stride=(2, 1), padding=(4, 2))>>> input = torch.randn(20, 16, 50, 100)>>> output = m(input)>>> # exact output size can be also specified as an argument>>> input = torch.randn(1, 16, 12, 12)>>> downsample = nn.Conv2d(16, 16, 3, stride=2, padding=1)>>> upsample = nn.ConvTranspose2d(16, 16, 3, stride=2, padding=1)>>> h = downsample(input)>>> h.size()torch.Size([1, 16, 6, 6])>>> output = upsample(h, output_size=input.size())>>> output.size()torch.Size([1, 16, 12, 12])

References

https://yongqiang.blog.csdn.net/