Question about local_group_norm function

[kooweat]

Hello,
Thank you for your sharing your wonderful work.

Besides, I have two questions regarding a function,
local_group_norm function defined in ops.py (starting from line 47), which I think
is not explained in your paper.
It's some how different from the usual group norm layer that I know of.

1. To condition the generated output with the artistic style, you applied local group norm.
   In the local_group_norm function, mean of inputs(N,H,W,C//G,G) over each group is estimated
   (i.e., N,H,W,C//G,G -> 1,1,1,G)
   then, you apply separable_conv2d to the estimated means to learn "new mean" value.
   What does it mean? What's your intention doing this?
   and how does it different from the usual group norm?

2. Also, have you tried applying the usual group norm?
   How would the result be different if we apply the usual group norm with the condition of
   offset and scale learned from style?

To be specific, what would it be like to change the local group norm function as follows,

    def local_group_norm(input, style=None, name="local_group_norm", G=32, window_size=32):
        epsilon = 1e-5
        with tf.variable_scope(name):
            N, H, W, C = tf.shape(input)[0], tf.shape(input)[1], tf.shape(input)[2], tf.shape(input)[3]

            depth = input.get_shape()[3]
            if style is None:
                scale = tf.get_variable("scale",
                                        [depth],
                                        initializer=tf.random_normal_initializer(1.0, 0.02, dtype=tf.float32))
                offset = tf.get_variable("offset",
                                         [depth],
                                         initializer=tf.constant_initializer(0.0))
            else:
                scale = \
                    tf.layers.dense(inputs=style,
                                    units=depth,
                                    activation=lrelu,
                                    name='scale_1')
                offset = tf.layers.dense(inputs=style,
                                         units=depth,
                                         activation=lrelu,
                                         name='offset_1')
                scale = tf.expand_dims(scale, axis=1)
                scale = tf.expand_dims(scale, axis=2)
                offset = tf.expand_dims(offset, axis=1)
                offset = tf.expand_dims(offset, axis=2)

            input = tf.reshape(input, [N, H, W, C // G, G])
            mean, var = tf.nn.moments(input, [1, 2, 3], keep_dims=True)
            input = (input - mean) / tf.sqrt(var + epsilon)
            input = tf.reshape(input, [N, H, W, C])
            return tf.multiply(input, scale) + offset

Thanks in advance.