Graph Neural Network

Some data is not a sequence and not a grid — molecules, road networks, citations, social graphs. A graph neural network takes the structure as given rather than making the model discover it, and computes each node's representation from its neighbours. The graph is a hard constraint on what can influence what, which is both the strength and the ceiling.

The design is a relational inductive bias: you hand the model the edges, and in exchange it needs far less data than a model that must infer which pairs relate. That bias is also the failure mode — a graph built from the wrong assumption cannot be unlearned, because it is not a parameter. Permutation equivariance falls out for free, which is why node ordering never appears anywhere in the architecture.

A layer maps node features H super ^(l)  to H super ^(l+1)  using only each node's neighbourhood, so the whole network is equivariant to relabelling: permuting the nodes permutes the output identically. After L layers a node's representation depends on exactly its L-hop neighbourhood and nothing beyond it — a receptive field defined by the graph rather than by a kernel size.