arXiv:2607.15773cs.LG2026-07

提出反应-扩散框架,解决超图神经网络深度传播中的过度平滑问题。

From Diffusion to Reaction-Diffusion: A Dynamical-Systems View of Oversmoothing in Hypergraph Neural Networks

论文配图:From Diffusion to Reaction-Diffusion: A Dynamical-Systems View of Oversmoothing in Hypergraph Neural Networks
图 1 · 摘自论文原文
  • 从动力系统视角建模消息传递为关联层级扩散过程。
  • 理论证明新模型能保持非零狄利克雷能量,避免表征坍缩。
  • 适合研究深层超图神经网络或对抗过平滑的场景。

高阶耦合虽增强超图神经网络表达力,但加剧深度传播中的表示坍缩,源于强多向特征混合。本文从动力系统角度分析超图过平滑现象,提出反应-扩散框架以实现深度鲁棒学习。通过定义超图梯度与散度算子,将消息传递视为关联层级扩散过程。纯扩散分析显示,其连续半流会指数收缩节点表示中无零模成分,并使狄利克雷能量趋近零,揭示过平滑本质为横向能量耗散。受此启发,提出超图神经反应-扩散(HNRD)模型,在横向分量引入反应机制补偿扩散耗散,稳定判别性差异。建立全局适定性并证明无零模狄利克雷能量有下界。前向欧拉离散化提供可实践的HNRD层,具备深度传播稳定性条件。在基准和合成异质超图上实验表明,HNRD持续优于代表性基线。深度、鲁棒性与效率分析进一步显示,HNRD在深层传播与扰动下仍保持稳定性能与非零狄利克雷能量。该成果为设计兼具高阶表达力与抗坍缩能力的深层超图架构提供理论依据。

原文摘要 · Abstract (English)

Higher-order couplings enhance the expressive power of hypergraph neural networks (HGNNs), but they also intensify representation collapse in deep propagation due to strong multi-way feature mixing. This work investigates hypergraph oversmoothing from a dynamical-systems perspective and develops a reaction--diffusion framework for depth-resistant hypergraph learning. By defining hypergraph gradient and divergence operators, we interpret message passing as an incidence-level diffusion process. The analysis of pure diffusion shows that its continuous semiflow exponentially contracts the null-mode-free component of node representations and drives the Dirichlet energy to zero, revealing hypergraph oversmoothing as an intrinsic transverse-energy dissipation phenomenon. Motivated by this analysis, we propose Hypergraph Neural Reaction--Diffusion (HNRD), which introduces a reaction mechanism acting on the transverse component to compensate diffusion-induced dissipation and stabilize discriminative variations. We establish global well-posedness of the proposed dynamics and prove that the null-mode-free Dirichlet energy remains bounded away from zero. A forward-Euler discretization provides a practical HNRD layer with a stability condition for deep propagation. Experiments on benchmark and synthetic heterophilic hypergraphs demonstrate that HNRD consistently improves over representative hypergraph baselines. Depth, robustness, and efficiency analyses further show that HNRD preserves stable performance and nonzero Dirichlet energy under deep propagation and perturbations. These results provide a principled dynamical framework for designing deep hypergraph architectures that maintain higher-order expressiveness without representation collapse.

超图神经网络过平滑反应-扩散动力系统

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