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.
Abstract (translated)
我们介绍了图Hopfield网络，其能量函数将联想记忆检索与图拉普拉斯平滑相结合用于节点分类。在该联合能量上的梯度下降会产生一个迭代更新过程，该过程交替进行霍普菲尔德检索和拉普拉斯传播。记忆检索提供了依赖于具体场景的好处：对于稀疏的引文网络最多可提高2.0个百分点，在特征掩蔽下的额外鲁棒性最高可达5个百分点；这种迭代能量下降架构本身是一个强大的归纳偏置，所有变体（包括禁用内存的NoMem消融）在亚马逊共购图上均优于标准基线。调整可以无需架构更改即可实现异ophilous基准测试中的图形锐化。
URL
https://arxiv.org/abs/2603.03464
