The GNN message passing approach can also be generalized to leverage edge and graph-level information at each stage of message passing. One of the most important in the generalized message passing framework is that we generate hidden embeddings for each edge in the graph, as well as an embedding corresponding to the entire graph during message passing.

University of Michigan - Ann Arbor

Google

One of the defining features of a GNN is that it uses a form of *neural message passing* in which vector messages are exchanged between nodes and updated using neural networks

Neural Message Passing

Neural Message Passing can be broken down into three steps

Steps of Neural Message Passing

There are several ways of generalizing or improving the “AGGREGATE” operator:

1)	Neighborhood Normalization

2)	Set Aggregators

3)	Neighborhood Attention


Generalized Neighborhood Aggregation

To use mini-batch training, one can work with a subset of nodes during message passing.

Subsampling of Graph-level Message Passing

Generalized Message Passing

During each message-passing iteration in a Graph Neural Network (GNN), a hidden embedding $$h^{(k)}_u$$ corresponding to each node $$u \in V$$ is updated according to information aggregated from $$u$$’s graph neighborhood $$N(u)$$. The message-passing update can be expressed by: $$h^{(k+1)}_u = UPDATE^{(k)}(h^{(k)}_u, AGGREGATE^{(k)}(\{h^{(k)}_v, \forall v \in N(u)\}))$$ or alternatively as: $$h^{(k+1)}_u = UPDATE^{(k)}(h^{(k)}_u, m^{(k)}_{N(u)})$$ where $$UPDATE$$ and $$AGGREGATE$$ are arbitrary differentiable functions (neural networks) and $$m_{N(u)}$$ is the "message" that is aggregated from $$u$$'s graph neighborhood $$N(u)$$.

Learn Before

Related