Getting the output shape of deconvolution layer using tf.nn.conv2d_transpose in tensorflow

Question

According to this paper, the output shape is N + H - 1, N is input height or width, H is kernel height or width. This is obvious inverse process of convolution. This tutorial gives a formula to calculate the output shape of convolution which is (W−F+2P)/S+1, W - input size, F - filter size, P - padding size, S - stride. But in Tensorflow, there are test cases like:

  strides = [1, 2, 2, 1]

  # Input, output: [batch, height, width, depth]
  x_shape = [2, 6, 4, 3]
  y_shape = [2, 12, 8, 2]

  # Filter: [kernel_height, kernel_width, output_depth, input_depth]
  f_shape = [3, 3, 2, 3]

So we use y_shape, f_shape and x_shape, according to formula (W−F+2P)/S+1 to calculate padding size P. From (12 - 3 + 2P) / 2 + 1 = 6, we get P = 0.5, which is not an integer. How does deconvolution works in Tensorflow?

Answer 1

for deconvolution,

output_size = strides * (input_size-1) + kernel_size - 2*padding

strides, input_size, kernel_size, padding are integer padding is zero for 'valid'