用连续熵场解释图结构形成机制，实现自洽演化学习
Learning Graphs through Continuous Information Entropy Fields
- 将边关系建模为隐含熵场的离散体现，通过场调制信息传播
- 在多个基准上超越现有方法，对扰动更鲁棒且场表示结构清晰
- 适合研究图生成机制与可解释性学习的研究者
图论本质上是描述性的，仅记录存在哪些关系，却无法解释其成因，因为它将边视为基本单元。本文提出一种新的图学习解释框架：关系源于潜在的连续信息熵场，图则是该场的离散实例。为此引入场感知图网络（FGN），从节点特征学习标量场，并利用其调制消息传递过程。基于信息论的目标函数在结构保真度与场平滑性间取得平衡，形成自增强循环：场通过场调制加权影响信息扩散，而更新后的节点表征又迭代优化场。结果，FGN通过模拟自身协同演化进行学习。在节点分类与图分类基准上的大量实验表明，其性能更优，对扰动更鲁棒，且场表示具有结构性一致性。
原文摘要 · Abstract (English)
Graph theory is inherently descriptive, capturing what relationships exist but not why they arise, because it treats edges as primitive constructs. This paper proposes a new explanatory framework for graph learning, where relationships emerge from latent continuous information entropy fields, and a graph becomes a discrete instantiation of an underlying field. To formalize this field, we introduce the Field-informed Graph Network (FGN). It learns a scalar field from node features and leverages it to modulate message passing. The information-theoretic objective balances structural fidelity with field smoothness, forming a self-reinforcing loop. In this loop, the field modulates information diffusion through field-modulated weighting, and the updated node representations iteratively refine the field. As a result, FGN learns by simulating its own co-evolution. Extensive experiments on node classification and graph classification benchmarks demonstrate superior performance, robustness to perturbations, and structurally coherent field representations.
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