A primary application of transposed convolutional layers is to perfectly reverse the spatial dimensionality transformations introduced by standard convolutional layers. If an input tensor $\mathsf{X}$ is passed through a convolutional layer $f$ to produce an output $\mathsf{Y} = f(\mathsf{X})$, a transposed convolutional layer $g$ can be constructed to invert this shape change. By configuring $g$ with the exact same spatial hyperparameters (kernel size, padding, and stride) as $f$, and setting its output channel count to match the channels of $\mathsf{X}$, the resulting tensor $g(\mathsf{Y})$ will possess the identical shape as the original input $\mathsf{X}$. This property can be verified programmatically in frameworks like PyTorch and MXNet by ensuring tconv(conv(X)).shape == X.shape when both layers share identical parameters.

# PyTorch
X = torch.rand(size=(1, 10, 16, 16))
conv = nn.Conv2d(10, 20, kernel_size=5, padding=2, stride=3)
tconv = nn.ConvTranspose2d(20, 10, kernel_size=5, padding=2, stride=3)
tconv(conv(X)).shape == X.shape

# MXNet
X = np.random.uniform(size=(1, 10, 16, 16))
conv = nn.Conv2D(20, kernel_size=5, padding=2, strides=3)
tconv = nn.Conv2DTranspose(10, kernel_size=5, padding=2, strides=3)
conv.initialize()
tconv.initialize()
tconv(conv(X)).shape == X.shape