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Latent-Hysteresis Graph ODEs: Modeling Coupled Topology-Feature Evolution via Continuous Phase Transitions

arXiv 2604.24293 ↗First posted 27 Apr 2026cs.LG cs.AIcited by 0

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Abstract (arXiv)

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 monostability trap: in the long-time regime, information leakage is unavoidable and the dynamics converge to a single global consensus attractor. We propose the 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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 34 of its 43 references that are in the map. First posted on arXiv 27 Apr 2026.

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References · 34

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22 more
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  22. 2024Rethinking Structure Learning For Graph Neural Networkscited by 2

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