A Generative Model for Controllable Feature Heterophily in Graphs

2025-09-27

AI Summary

This work addresses the challenge of controllably generating feature heterophily in graph learning—a longstanding difficulty in synthetic graph data generation. We propose the first generative model enabling precise, continuous control over the degree of graph signal heterophily. Methodologically, our approach integrates Lipschitz-constrained graph submodeling with Gaussian spectral filtering based on a rescaled Laplacian operator, ensuring stable and differentiable modulation of homophily/heterophily strength. Theoretically, we establish the first unified framework characterizing the synergistic interplay between graph substructure and spectral filtering in heterophily control; we prove concentration and almost-sure convergence of the empirical heterophily score, revealing the intrinsic coupling between graph topology and feature generation. Empirically, the model achieves accurate and robust heterophily control across diverse graph families—including Erdős–Rényi, stochastic block models, and real-world graphs—as well as under various spectral filters, thereby introducing a new paradigm for heterophily-aware learning and synthetic graph data generation.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Natural Language Processing: Generation

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems

Abstract

We introduce a principled generative framework for graph signals that enables explicit control of feature heterophily, a key property underlying the effectiveness of graph learning methods. Our model combines a Lipschitz graphon-based random graph generator with Gaussian node features filtered through a smooth spectral function of the rescaled Laplacian. We establish new theoretical guarantees: (i) a concentration result for the empirical heterophily score; and (ii) almost-sure convergence of the feature heterophily measure to a deterministic functional of the graphon degree profile, based on a graphon-limit law for polynomial averages of Laplacian eigenvalues. These results elucidate how the interplay between the graphon and the filter governs the limiting level of feature heterophily, providing a tunable mechanism for data modeling and generation. We validate the theory through experiments demonstrating precise control of homophily across graph families and spectral filters.

Problem

• Modeling graph signals with controllable feature heterophily levels
• Establishing theoretical guarantees for heterophily concentration and convergence
• Providing tunable mechanisms for graph data modeling and generation

Innovation

• Generative model controls graph feature heterophily
• Combines Lipschitz graphon generator with Gaussian features
• Uses spectral function of Laplacian for tunable mechanism