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.