提出可实现拓扑与特征协同演化的连续图神经网络，突破传统模型长期依赖的共识陷阱。
Latent-Hysteresis Graph ODEs: Modeling Coupled Topology-Feature Evolution via Continuous Phase Transitions
- 设计具有双阱边势能和双极门控的滞回机制，让边状态在连通与隔离间切换
- 理论证明原模型会因信息泄漏导致全局共识，而新模型可避免这种坍缩
- 适用于需要动态结构演化的真实图数据，如社交网络、分子结构建模
图神经微分方程（Graph ODEs）将图学习从离散的消息传递层扩展到连续时间表示流。尽管支持自适应长程传播，我们发现使用严格正且不可约混合算子的 Graph ODEs 存在固有的「单稳态陷阱」：在长时间状态下，信息泄漏不可避免，系统动态趋于单一全局共识吸引子。为此，我们提出**滞回图微分方程（HGODE）**，将特征演化与由学习到的成对力驱动的潜在拓扑势耦合。通过双阱边势能与双极化门控，使边状态能够极化为连接或绝缘相，同时保持可微性。我们提供了对坍缩机制及所提滞回拓扑动力学的渐近分析，并在理论驱动的合成诊断与真实世界图基准上验证了 HGODE 的有效性。
原文摘要 · Abstract (English)
Graph neural ordinary differential equations (Graph ODEs) extend graph learning from discrete message-passing layers to continuous-time representation flows. While it supports adaptive long-range propagation, we show that Graph ODEs with strictly positive irreducible mixing operators face an inherent \emph{monostability trap}: in the long-time regime, information leakage is unavoidable and the dynamics converge to a single global consensus attractor. We propose the \textbf{Hysteresis Graph ODE (HGODE)}, which couples feature evolution with a latent topological potential driven by a learned pairwise force. A double-well edge potential and bipolarized gate allow edge states to polarize into connected or insulated phases while preserving differentiability. We provide asymptotic analysis of the collapse mechanism and the proposed hysteretic topology dynamics, and validate HGODE on theory-driven synthetic diagnostics and real-world graph benchmarks.
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