Message Passing Framework

Intermediate Google DeepMind, Meta+2

The problem, from first principles

Message Passing is a general framework for GNNs. Each node sends "messages" to neighbors. Neighbors aggregate these messages. Each node updates its representation using the aggregate.

m_i^{(l+1)} = \sum_{j \in \mathcal{N}(i)} f(h_i^{(l)}, h_j^{(l)})

h_i^{(l+1)} = g(h_i^{(l)}, m_i^{(l+1)})

Where f is a message function and g is an update function.

From theory to code

Implement:

message_passing(features, adj, message_fn)

Constraints

features shape: (num_nodes, feature_dim).
adj shape: (num_nodes, num_nodes).
message_fn: callable that takes (sender_features, receiver_features).
Return shape: (num_nodes, feature_dim).

Keywords

deep-learninggraph-neural-networksmessage-passing

Python

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