Learning Graphs through Continuous Information Entropy Fields
2026-06-22 • Machine Learning
Machine Learning
AI summaryⓘ
The authors propose a new way to understand graphs by imagining them as snapshots of an underlying invisible field that holds information. Their model, called the Field-informed Graph Network (FGN), learns this hidden field from the features of nodes and uses it to guide how information flows between nodes. This method balances keeping the graph's structure intact while making the field smooth and clear. Through experiments, the authors show that their approach improves prediction tasks on graphs and creates meaningful internal representations that handle changes well.
graph theorygraph learninginformation entropyscalar fieldmessage passingnode classificationgraph classificationinformation diffusiongraph neural networksstructural fidelity
Authors
Hui Cong, Bo Sun, Ziheng Jiao, Yisheng An
Abstract
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.