Learning Graphs through Continuous Information Entropy Fields

Traditional Graph Neural Networks (GNNs) are largely descriptive, focusing on the structure of existing connections rather than the underlying generative mechanisms that cause them to form. This paper addresses this explanatory gap by proposing a framework where graph edges are viewed as discrete samples of a latent, continuous information entropy field. The authors seek to model the co-evolution of this field and the graph structure to improve both representation learning and structural understanding.

The authors introduce the Field-informed Graph Network (FGN), which treats the latent field as an explanatory substrate. The model operates through a self-reinforcing loop:

1. Field-Modulated Message Passing: Node representations are updated using weights derived from the coherence of the latent field, where information flows more freely between nodes with similar field values.
2. Adaptive Field Evolution: The field is iteratively refined based on the updated node representations to better align with the observed graph topology.

This process is formalized via an information-theoretic objective that balances structural fidelity with field smoothness, effectively treating the graph as a dynamic system rather than a static input.

Experiments on node and graph classification benchmarks demonstrate that FGN achieves superior predictive performance compared to standard GNN architectures. The model exhibits increased robustness to structural perturbations, as the learned field acts as a regularizer that filters out noise. Furthermore, the learned fields provide structurally coherent representations, visually capturing community boundaries and relational potentials that are not explicitly provided in the input data.

By shifting the perspective from static edge-based processing to continuous field-based dynamics, this work provides a more physically intuitive way to interpret graph structure. It allows researchers to move beyond simply predicting labels to understanding the underlying potential that drives relational formation, offering a more robust and interpretable foundation for graph representation learning.