Basic Understanding of GAT

References:

1. https://arxiv.org/abs/1710.10903
2. https://petar-v.com/GAT/

Motivation for graph convolutions

Enumerating the desirable traits of image convolutions, we arrive at the following properties we would ideally like our graph convolutional layer to have:

• Computational and storage efficiency (requiring no more than $O(V+E)$ time and memory);
• Fixed number of parameters (independent of input graph size);
• Localization (acting on a local neighborhood of a node);
• Ability to specify arbitrary importances to different neighbors;
• Applicability to inductive problems (arbitrary, unseen graph structures).

Towards a viable graph convolution

A graph of $n$ nodes:

• a set of node features: $({\vec{h}}_1,{\vec{h}}_2,...,{\vec{h}}_n)$
• an adjacency matrix $A$: $A_{ij}=1$ if $i$ and $j$ are connected, and 0 otherwise
• A graph convolutional layer then computes a set of new node features $(h$