✍Tips and Tricks in Python

How to calculate the output size when using Conv2DTranspose layer

Warning: There is no magical formula or Holy Grail here, though a new world might open the door for you.

TL;NR: If not sure, man, keep reading!

conv2D

same: input_size/stride

Deconv2D

same: input_size*stride

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For conv2D

For the 'VALID' scheme, the output height and width are computed as:

out_height = ceil(float(in_height - filter_height + 1) / float(strides[1]))
out_width = ceil(float(in_width - filter_width + 1) / float(strides[2]))

First, consider the 'SAME' padding scheme. A detailed explanation of the reasoning behind it is given in these notes. Here, we summarize the mechanics of this padding scheme. When using 'SAME', the output height and width are computed as:

out_height = ceil(float(in_height) / float(strides[1]))
out_width = ceil(float(in_width) / float(strides[2]))

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’

for ‘same’ padding, looks like padding is 1.

Regarding 'SAME' padding, the Convolution documentation offers some detailed explanations (further details in those notes). Especially, when using 'SAME' padding, the output shape is defined so:

# for `tf.layers.conv2d` with `SAME` padding: out_height = ceil(float(in_height) / float(strides[1])) out_width = ceil(float(in_width) / float(strides[2]))

In this case, the output shape depends only on the input shape and stride. The padding size is computed from there to fill this shape requirement (while, with 'VALID' padding, it's the output shape which depends on the padding size)

Now for transposed convolutions… As this operation is the backward counterpart of a normal convolution (its gradient), it means that the output shape of a normal convolution corresponds to the input shape to its counterpart transposed operation. In other words, while the output shape of tf.layers.conv2d() is divided by the stride, the output shape of tf.layers.conv2d_transpose() is multiplied by it:

# for `tf.layers.conv2d_transpose()` with `SAME` padding:
out_height = in_height * strides[1]
out_width = in_width * strides[2]

But once again, the padding size is calculated to obtain this output shape, not the other way around (for SAME padding). Since the normal relation between those values (i.e. the relation you found) is:

# for `tf.layers.conv2d_transpose()` with given padding:
out_height = strides[1] * (in_height - 1) + kernel_size[0] - 2 * padding_height
out_width = strides[2] * (in_width - 1) + kernel_size[1] - 2 * padding_width

Rearranging the equations we get

padding_height = [strides[1] * (in_height - 1) + kernel_size[0] - out_height] / 2
padding_width = [[strides[2] * (in_width - 1) + kernel_size[1] - out_width] / 2

note: if e.g. 2 * padding_height is an odd number, then padding_height_top = floor(padding_height); and padding_height_bottom = ceil(padding_height) (same for resp. padding_width, padding_width_left and padding_width_right)

Replacing out_height and out_width with their expressions, and using your values (for the 1st transposed convolution):

padding = [2 * (128 - 1) + 4 - (128 * 2)] / 2 = 1

You thus have a padding of 1 added on every side of your data, in order to obtain the output dim out_dim = in_dim * stride = strides * (in_dim - 1) + kernel_size - 2 * padding = 256

Here is a video on this topic:

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