Graph Representation Learning by William L. Hamilton

Author:William L. Hamilton [Hamilton, William L.]
Language: eng
Format: epub, pdf
Publisher: Morgan & Claypool Publishers
Published: 2021-02-15T00:00:00+00:00

(5.46)

(5.47)

(5.48)

(5.49)

The important innovation in this generalized message passing framework is that, during message passing, we generate hidden embeddings for each edge in the graph, as well as an embedding corresponding to the entire graph. This allows the message passing model to easily integrate edge and graph-level features, and recent work has also shown this generalized message passing approach to have benefits compared to a standard GNN in terms of logical expressiveness [Barceló et al., 2020]. Generating embeddings for edges and the entire graph during message passing also makes it trivial to define loss functions based on graph or edge-level classification tasks.

In terms of the message-passing operations in this generalized message-passing framework, we first update the edge embeddings based on the embeddings of their incident nodes (Equation (5.46)). Next, we update the node embeddings by aggregating the edge embeddings for all their incident edges (Equations (5.47) and (5.48)). The graph embedding is used in the update equation for both node and edge representations, and the graph-level embedding itself is updated by aggregating over all the node and edge embeddings at the end of each iteration (Equation (5.49)). All of the individual update and aggregation operations in such a generalized message-passing framework can be implemented using the techniques discussed in this chapter (e.g., using a pooling method to compute the graph-level update).

1the different iterations of message passing are also sometimes known as the different “layers” of the GNN.

2In general, the parameters Wself, Wneigh, and b can be shared across the GNN message passing iterations or trained separately for each layer.

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