A 2D transposed convolution expands an image or feature map by applying a learned filter as it places input values into a larger output. Standard convolution is used here to extract features and can reduce spatial size; transposed convolution instead builds higher-resolution feature maps. It is also called deconvolution or an upsampling layer. section 4.3 section 4.2
Upsample a 2×2 image
Start with [[1, 0], [2, 3]] and a 2×2 filter [[2, 3], [4, 5]]. In PyTorch, use nn.ConvTranspose2d(1, 1, kernel_size=2, stride=2) and set its weights to that filter with a zero bias. Each input value multiplies the whole filter and contributes a block to the output: the top-left 1 contributes [[2, 3], [4, 5]], while the top-right 0 contributes zeros. The result has shape (1, 1, 4, 4). A larger stride produces more upsampling. section 4.3.1 section 4.3
tensor([[[[ 2., 3., 0., 0.],
[ 4., 5., 0., 0.],
[ 4., 6., 6., 9.],
[ 8., 10., 12., 15.]]]], grad_fn=<ConvolutionBackward0>)
Inspect the complete 4×4 output to see where each input value contributes its filter-sized block. section 4.3.1
For a DCGAN image generator, stack five ConvTranspose2d layers to mirror the discriminator’s convolutional layers. A 100-value noise vector enters the generator; its final transposed convolution outputs three channels for an RGB image. Batch normalization and ReLU follow intermediate layers, and Tanh brings the final values into the training images’ [−1, 1] range. section 4.5.1
Listing 4.5 Designing a generator in DCGAN
G=nn.Sequential(
nn.ConvTranspose2d(100, 512, 4, 1, 0, bias=False), #1
nn.BatchNorm2d(512),
nn.ReLU(inplace=True),
nn.ConvTranspose2d(512, 256, 4, 2, 1, bias=False), #2
nn.BatchNorm2d(256),
nn.ReLU(inplace=True),
nn.ConvTranspose2d(256, 128, 4, 2, 1, bias=False),
nn.BatchNorm2d(128),
nn.ReLU(inplace=True),
nn.ConvTranspose2d(128, 64, 4, 2, 1, bias=False),
nn.BatchNorm2d(64),
nn.ReLU(inplace=True),
nn.ConvTranspose2d(64, 3, 4, 2, 1, bias=False), #3
nn.Tanh()).to(device) #4
Follow the generator listing from its 100 input channels through successive transposed convolutions to three output channels. section 4.5.1
The same operation can reconstruct images or expand other structured outputs. A VAE decoder uses three transposed convolutions to turn an encoding back into a 256×256 color image; a music generator uses them to extend noise vectors across bars. The practical choice is to check each layer’s channels and output shape against the result the generator needs. section 7.4.1 section 13.4.2
