Forge Capsule

Graph Neural Networks: Message Passing and Aggregation

GNN computation: message passing on graph G=(V,E). Node update: h_v^(k)=UPDATE(h_v^(k-1), AGGREGATE({h_u^(k-1): u∈N(v)})). GCN (Kipf 2017): A_hat H W, normalized adjacency. GraphSAGE: sample+aggregate, inductive. GAT: attention over neighbors, multi-head. GIN: WL-test powerful, sum aggregation. MPNN: message passing neural network framework unifies all. Heterogeneous GNN: handle multi-type nodes/edges. GraphRAG: GNN over knowledge graph for retrieval-augmented generation. Forge: knowledge graph edges (SUPPORTS/CONTRADICTS/ELABORATES/ENABLES/EXTENDS) enable GNN training over capsule relationship types.