How does tf.keras.layers.Conv2D with padding='same' and strides > 1 behave?

Question

I read What is the difference between 'SAME' and 'VALID' padding in tf.nn.max_pool of tensorflow? but this is not true to my experiment.

import tensorflow as tf

inputs = tf.random_normal([1, 64, 64, 3])
print(inputs.shape)
conv = tf.keras.layers.Conv2D(6, 4, strides=2, padding='same')
outputs = conv(inputs)
print(outputs.shape)

produces

(1, 64, 64, 3)
(1, 32, 32, 6)

. However following the above link produces (1, 31, 31, 6) because there is no extra values outside filter ranges without any padding.

How does tf.keras.layers.Conv2D with padding='same' and strides > 1 behave?
I want to know the exact answer and its evidence.

Answer 1

Keras uses TensorFlow implementation of padding. All the details are available in the documentation here

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]))

The total padding applied along the height and width is computed as:

if (in_height % strides[1] == 0):
  pad_along_height = max(filter_height - strides[1], 0)
else:
  pad_along_height = max(filter_height - (in_height % strides[1]), 0)
if (in_width % strides[2] == 0):
  pad_along_width = max(filter_width - strides[2], 0)
else:
  pad_along_width = max(filter_width - (in_width % strides[2]), 0)

Finally, the padding on the top, bottom, left and right are:

pad_top = pad_along_height // 2
pad_bottom = pad_along_height - pad_top
pad_left = pad_along_width // 2
pad_right = pad_along_width - pad_left

Note that the division by 2 means that there might be cases when the padding on both sides (top vs bottom, right vs left) are off by one. In this case, the bottom and right sides always get the one additional padded pixel. For example, when pad_along_height is 5, we pad 2 pixels at the top and 3 pixels at the bottom. Note that this is different from existing libraries such as cuDNN and Caffe, which explicitly specify the number of padded pixels and always pad the same number of pixels on both sides.

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]))

and no padding is used.

Answer 2

In tensorflow, for stride s and input size n, padding with same gives:

⌈n/s⌉

or the ceiling of input size divided by stride.