From the Pytorch docs on Conv2Transpose2d, the formula to compute the output of the upsampled convolution (assuming square input and no kernel dilation) is:
$$H_{out} = (H_{in} - 1) \times S - 2P_{in}+P_{out}+1.$$
Here, $H_{out}$ and $H_{in}$ are the heights of the input and output images, $S$ is stride, and $P_{in}$ and $P_{out}$ are input and output padding.
I want to 2x upsample a 256x256 image to 512x512, using a 3x3 convolution, to simulate a convolution with fractional stride of $1/2$.
Given a stride of 2, I worked out that we must have $2 p_{in} - p_{out} = 1$, so $(p_{in}, p_{out}) = (1,1)$ is a solution.
My question is: why is $p_{out}$ necessary to achieve 2x sampling here? From this PyTorch forum post, I learned that $p_{out}$ is asymmetric padding for the right and bottom sides.
However, everywhere I look online (such as slide 54 from Stanford's CS231n 2016 lecture), it says stride 2 and pad 1 produces 2x upsampling, using 3x3 convolution, with no distinction between input/output padding.
Consider the following PyTorch code:
nn.ConvTranspose2d(in_channels, out_channels, stride=2, kernel_size=3, padding=1)
Applying that function to a 256x256 image, the dimensions of the output are 513x513. It is only until I add the parameter output_padding=1 that the dimensions are properly upsampled 2x, as confirmed by the earlier equation.
I'm hoping someone can help clarify the upsampling process in better detail, because I don't understand why "stride 2, pad 1" doesn't work unless the output is padded as well.
Thanks
