How Graph Convolutional Neural Networks forward propagate?

Question

In the basic variant of GCN we have the following:

Here we aggregate the information from the adjacent node and pass it to a neural network, then transform our own information and add them all.
But the main question is: how can we ensure that $W_{k}(sum(frac{h_k}{N(V)})$ will be the same size as $B_{k}h_{v}$ and does $B_{k}$ emply another neural network?

razvanc92 · Answer

I think the picture you're presenting is mostly for educational purposes and that's why they are excluding the node itself from it's neighbors and using two distinct networks (most of the papers I've read they are using the same network for the neighbors and for the center node). But you are right the two networks needs to have the same input and output shapes otherwise the point-wise summation between the two terms is not possible.

Answered by razvanc92 on December 13, 2021

How Graph Convolutional Neural Networks forward propagate?

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