From Graph ML to Deep Relational Learning | Towards Data Science

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Abstraction: GNN principles unified via relational logic and symmetry perspective

Key points:

Modern GNNs follow a generic "aggregate and combine" formula: each node aggregates neighbor representations then combines with its own; GraphSAGE and GCN are specific instances
GNNs are bounded by the Weisfeiler-Lehman (WL) graph isomorphism test — they cannot distinguish graphs WL cannot distinguish
Geometric Deep Learning (Bronstein et al.) frames DL architectures through symmetry priors: CNNs exploit translation invariance, RNNs exploit recursive symmetry, GNNs exploit permutation invariance on graphs
Relational logic (Datalog/Prolog) is a natural formalism for expressing these symmetries; node2(X) <= W node1(Y), edge(X,Y) encodes a full GCN layer in NeuraLogic
"Lifted Relational Neural Networks" (Sourek et al. 2018) extend lifted graphical models into deep learning, generalizing GNNs to arbitrary relational structures
XOR example illustrates that weight tying based on known symmetries greatly improves training, analogous to how convolution exploits spatial symmetry

Connections: Pytorch Geometric · Graph Neural Networks · Relational Learning · Geometric Deep Learning