通过热力学机制平衡图表示学习中的能量,防止特征坍缩。
Energy-Balanced Hyperspherical Graph Representation Learning via Structural Binding and Entropic Dispersion
- 在超球面上优化自由能,结合局部凝聚与全局分散力。
- 在多个数据集上提升分类、聚类和链接预测性能,缓解过平滑问题。
- 适合关注模型稳定性和表征质量的图学习研究者。
图表示学习可被建模为在潜在流形上节点系统寻求能量平衡的物理过程。然而,现有图神经网络在消息传递过程中常出现不可控的能量耗散,因缺乏显式热力学约束,导致系统趋于热寂状态——表现为特征坍缩或过平滑。为此,我们提出 HyperGRL,一种受热力学驱动的框架,通过最小化由两种竞争势能组成的亥姆霍兹自由能目标,将节点嵌入单位超球面。首先,引入结构绑定能(基于邻域均值对齐),作为局部结合力,增强结构相关节点的局部凝聚性,形成紧凑簇;其次,为对抗表示坍缩,设计无采样均匀性带来的平均场排斥势,作为全局熵力,最大化表示分散度。关键在于,我们设计自适应恒温器,以熵引导动态调节训练过程中的系统“温度”,引导表示向兼顾局部凝聚力与全局可区分性的稳健亚稳态演化。大量实验表明,HyperGRL 在节点分类、聚类与链接预测任务中表现优异,在多种基准数据集上均获得更具判别力与鲁棒性的表示,有效缓解过平滑问题。
原文摘要 · Abstract (English)
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 Potential (via Sampling-Free Uniformity), which acts as a global entropic force to maximize representation dispersion without the need for negative sampling. Crucially, to govern the trade-off between local alignment and global uniformity, we devise an Adaptive Thermostat. This entropy-guided strategy dynamically regulates the system's "temperature" during training, guiding the representation towards a robust metastable state that balances local cohesion with global discriminability. Extensive experiments on node classification, node clustering, and link prediction show that HyperGRL consistently achieves strong performance across diverse benchmark datasets, yielding more discriminative and robust representations while alleviating over-smoothing.
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