Graph Hopfield Networks: Energy-Based Node Classification with Associative Memory

TL;DR

Graph Hopfield Networks combine associative memory with graph Laplacian smoothing for improved node classification, demonstrating enhanced accuracy and robustness across various graph datasets through an energy-based iterative approach.

Contribution

This paper introduces Graph Hopfield Networks, integrating associative memory retrieval with graph smoothing, a novel approach that outperforms standard methods on multiple graph classification benchmarks.

Findings

Memory retrieval improves accuracy and robustness.

Iterative energy descent acts as a strong inductive bias.

Outperforms standard baselines on Amazon co-purchase graphs.

Abstract

We introduce Graph Hopfield Networks, whose energy function couples associative memory retrieval with graph Laplacian smoothing for node classification. Gradient descent on this joint energy yields an iterative update interleaving Hopfield retrieval with Laplacian propagation. Memory retrieval provides regime-dependent benefits: up to 2.0~pp on sparse citation networks and up to 5 pp additional robustness under feature masking; the iterative energy-descent architecture itself is a strong inductive bias, with all variants (including the memory-disabled NoMem ablation) outperforming standard baselines on Amazon co-purchase graphs. Tuning enables graph sharpening for heterophilous benchmarks without architectural changes.