{"ID":2864665,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.23230","arxiv_id":"2509.23230","title":"A Generative Model for Controllable Feature Heterophily in Graphs","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.","short_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...","url_abs":"https://arxiv.org/abs/2509.23230","url_pdf":"https://arxiv.org/pdf/2509.23230v1","authors":"[\"Haoyu Wang\",\"Renyuan Ma\",\"Gonzalo Mateos\",\"Luana Ruiz\"]","published":"2025-09-27T10:31:19Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"eess.SP\"]","methods":"[]","has_code":false}