[2512.24062] Energy-Balanced Hyperspherical Graph Representation Learning via Structural Binding and Entropic Dispersion

Computer Science > Machine Learning arXiv:2512.24062 (cs) [Submitted on 30 Dec 2025 (v1), last revised 7 Apr 2026 (this version, v2)] Title:Energy-Balanced Hyperspherical Graph Representation Learning via Structural Binding and Entropic Dispersion Authors:Rui Chen, Junjun Guo, Hongbin Wang, Yan Xiang, Yantuan Xian, Zhengtao Yu View a PDF of the paper titled Energy-Balanced Hyperspherical Graph Representation Learning via Structural Binding and Entropic Dispersion, by Rui Chen and 5 other authors View PDF HTML (experimental) Abstract:Graph Representation Learning (GRL) can be fundamentally modeled as a physical process of seeking an energy equilibrium state for a node system on a latent manifold. However, existing Graph Neural Networks (GNNs) often suffer from uncontrolled energy dissipation during message passing, driving the system towards a state of Thermal Death--manifested as feature collapse or over-smoothing--due to the absence of explicit thermodynamic constraints. To address this, we propose HyperGRL, a thermodynamics-driven framework that embeds nodes on a unit hypersphere by minimizing a Helmholtz free energy objective composed of two competing potentials. First, we introduce Structural Binding Energy (via Neighbor-Mean Alignment), which functions as a local binding force to strengthen structural cohesion, encouraging structurally related nodes to form compact local clusters. Second, to counteract representation collapse, we impose a Mean-Field Repulsive Potentia...