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.

翻译：我们提出了图霍普菲尔德网络，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。对该联合能量进行梯度下降，可得到交替进行霍普菲尔德检索与拉普拉斯传播的迭代更新过程。记忆检索在不同场景下均带来显著优势：在稀疏引文网络上性能提升高达2.0个百分点，在特征掩码条件下额外获得5个百分点的鲁棒性提升；该迭代能量下降架构本身即构成强归纳偏置，所有变体（包括禁用记忆的NoMem消融模型）在亚马逊共购图数据集上均超越标准基线方法。通过参数调优，无需改变架构即可实现面向异配性基准的图锐化处理。