Question about the propagation in matrix form

[RaptorMai]

Hi,

Thank you so much for the amazing work. I have one question about the implementation.
In the paper, the propagation rule in matrix form is

but in the code, it seems you add leaky_relu to both parts then add them together. I am kind of confused about why does the implementation match the equation?

            side_embeddings = tf.concat(temp_embed, 0)
            # transformed sum messages of neighbors.
            sum_embeddings = tf.nn.leaky_relu(
                tf.matmul(side_embeddings, self.weights['W_gc_%d' % k]) + self.weights['b_gc_%d' % k])

            # bi messages of neighbors.
            bi_embeddings = tf.multiply(ego_embeddings, side_embeddings)
            # transformed bi messages of neighbors.
            bi_embeddings = tf.nn.leaky_relu(
                tf.matmul(bi_embeddings, self.weights['W_bi_%d' % k]) + self.weights['b_bi_%d' % k])

            # non-linear activation.
            ego_embeddings = sum_embeddings + bi_embeddings

            # message dropout.
            ego_embeddings = tf.nn.dropout(ego_embeddings, 1 - self.mess_dropout[k])

            # normalize the distribution of embeddings.
            norm_embeddings = tf.math.l2_normalize(ego_embeddings, axis=1) 

[ustcxiexk]

I have the same question

[b3326023]

Same question here, and I have another questions:

bi_embeddings = tf.multiply(ego_embeddings, side_embeddings)
whats dose bi mean? I didn't see it in the paper.