Graph Hopfield Networks: Energy-Based Node Classification with Associative Memory
This work addresses node classification in graph-structured data, offering a novel energy-based approach that enhances performance and robustness, though it appears incremental as it builds on existing Hopfield and graph smoothing concepts.
The paper tackles node classification by introducing Graph Hopfield Networks, which combine associative memory retrieval with graph Laplacian smoothing in an energy-based framework, achieving up to 2.0 percentage point improvements on sparse citation networks and up to 5 percentage points additional robustness under feature masking.
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.