Padding in ConvTranspose

[GoktugGuvercin]

While building a model with FLAX, I noticed a small detail about padding option: Setting the parameter padding to a numerical value such as $1$ and a string value like "SAME" are not same, they seem like they use different formula for the calculation of output shape.

input = jax.numpy.ones((4, 8, 8, 64))
layer = nn.ConvTranspose(32, kernel_size=(3,3), strides=(2,2), padding=1)
variables = layer.init(jax.random.PRNGKey(0), input)

y = layer.apply(variables, input)
print(y.shape)

When I execute the code script above, output shape will be (4, 15, 15, 32). In this case, the following formula is used, so the shape of height and width is equal to 15: $H_{new} = s \cdot (H - 1) - 2p + d \cdot (f - 1) + 1$

However, if we replace the value 1 in padding argument of transpose convolution by "SAME" and reexecute the code again, the shape of the output will be (4, 16, 16, 32).

What is the reason lying behind it ?
Is additionally output padding added to have same shape ?

[cgarciae]

Hey @GoktugGuvercin, not entirely sure exactly how SAME is implemented, my guess its that it internally results in something like setting padding=((1, 2), (1, 2)):

layer = nn.ConvTranspose(32, kernel_size=(3,3), strides=(2, 2), padding=((1, 2), (1, 2)))
variables = layer.init(jax.random.PRNGKey(0), input)

y = layer.apply(variables, input)
print(y.shape) # (4, 16, 16, 32)

The intuition I have is that SAME follows this formula: $H_{new} = s \cdot H$