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Graph Neural Networks (Multi-Layer GNN)

Receptive Field Expansion via Two Message Passing Hops
Task Description: Graph Neural Networks stack multiple message passing layers to expand their receptive field. Click on a node to trace its calculations. Notice how changing the operator changes how features propagate from 1-hop away in Layer 1 ($h^{(1)}$) to 2-hops away in Layer 2 ($h^{(2)}$). For instance, under Sum aggregation, Node D can now detect Node A's original features via the path $A \rightarrow B \rightarrow D$.
$$\mathbf{h}_v^{(l)} = \bigoplus_{u \in \mathcal{N}(v)} W_{v,u} \mathbf{h}_u^{(l-1)}$$
Node $h_v^{(0)}$ Layer 1 $h_v^{(1)}$ Layer 2 $h_v^{(2)}$ $\mathcal{N}(v)$
Operator:
Node A
Node B
Node C
Node D