Question about layers of this model about hgp-sl

[cszhangzhen]

Hi, Thanks for your interest in our work!

Here are my answers:

A1, We remove the adding self-loops operation in our new-defined GCN module, since the structure learning module has already taken self-loops into consideration. The original GCNConv is used only in the first layer and we add self-loops manually like GCN paper described.

A2, Yes, you are right. We actually use the symmetric version of (i.e. the I - \tilde{D}^{-1/2}\tilde{A}\tilde{D}^{-1/2}) in NodeInformationScore.

However, your analysis is not correct.

The edge_weight after add_remaining_self_loops will have self-loops, thus the final result of the norm function is I - D^{-1/2}(A+I)D^{-1/2} = - D^{-1/2}AD^{-1/2} instead of the I - D^{-1/2}AD^{-1/2}.

After structure learning module, it has automatically learned the self-loops, i.e., \tilde{A} ≠ A + I and \tilde{D}_{ii} = \sum_{i} \tilde{A}_{ij}, and each node has different self-loop values. Therefore, - D^{-1/2}(A+I)D^{-1/2} ≠ - D^{-1/2}AD^{-1/2}. Also, note that for edge_weight, we use add_remaining_self_loops to fill zeros instead of ones, which make the edge_index be consistent with the learned structure information.

[lygztq]

Thanks! Now I understand how your NodeInformationScore works.