[2603.03464] Graph Hopfield Networks: Energy-Based Node Classification with Associative Memory

Computer Science > Machine Learning arXiv:2603.03464 (cs) [Submitted on 3 Mar 2026] Title:Graph Hopfield Networks: Energy-Based Node Classification with Associative Memory Authors:Abinav Rao, Alex Wa, Rishi Athavale View a PDF of the paper titled Graph Hopfield Networks: Energy-Based Node Classification with Associative Memory, by Abinav Rao and 2 other authors View PDF HTML (experimental) 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. Comments: Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Information Retrieval (cs.IR) Cite as: arXiv:2603.03464 [cs.LG]   (or arXiv:2603.03464v1 [cs.LG] for this version)   https://doi.org/10.48550/arXiv.2603.03464 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Abinav Rao [view email] [v1] T...