message passing neural networks

Message Passing Neural Networks (MPNNs) are a general framework unifying most graph neural network architectures — where node representations are updated by aggregating "messages" received from their neighbors.

What Is Message Passing?

- Phases:
1. Message: $m_{ij} = \phi(h_i, h_j, e_{ij})$ (Compute message from neighbor $j$ to node $i$).
2. Aggregate: $m_i = \sum m_{ij}$ (Sum/Max/Mean all incoming messages).
3. Update: $h_i' = \psi(h_i, m_i)$ (Update node state).
- Analogy: Processing a molecule. Atom A asks Atom B "what are you?" and updates its own state based on the answer.

Why It Matters

• Chemistry: Predicting molecular properties (is this toxic?) by passing messages freely between atoms.
• Social Networks: Classifying users based on their friends.
• Universality: GCN, GAT, and GraphSAGE are all specific instances of the MPNN framework.

Message Passing Neural Networks are information diffusion algorithms — allowing local information to propagate globally across a graph structure.