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

Alex Wa, Abinav Rao, Rishi Athavale

Keywords: associative memory, modern Hopfield networks, Graph Hopfield Networks, energy-based models, graph neural networks, node classification, Laplacian smoothing, graph sharpening, heterophily

TL;DR: Graph Hopfield Networks minimize a joint energy combining Hopfield memory retrieval with Laplacian propagation, giving a simple iterative update that boosts sparse-graph accuracy, feature-masking robustness, and heterophily via graph sharpening.

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 $\lambda \leq 0$ enables graph sharpening for heterophilous benchmarks without architectural changes.

Submission Number: 43