Graph Isomorphism Network

Intermediate Google DeepMind, Meta+2

The problem, from first principles

Graph Isomorphism Network (GIN) uses the Weisfeiler-Lehman test to aggregate node information. It has provably high expressive power for distinguishing non-isomorphic graphs.

h_i^{(l+1)} = \text{MLP}^{(l)}\left((1 + \epsilon^{(l)}) h_i^{(l)} + \sum_{j \in \mathcal{N}(i)} h_j^{(l)}\right)

Where epsilon is a learnable parameter (can be fixed).

From theory to code

Implement:

gin_layer(features, adj, weight, epsilon=0.0)

Constraints

features shape: (num_nodes, input_dim).
adj shape: (num_nodes, num_nodes).
weight shape: (input_dim, output_dim).
epsilon: scalar, learnable or fixed.
Return shape: (num_nodes, output_dim).

Keywords

deep-learninggraph-neural-networksgin

Python

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