{"ID":2848508,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.25354","arxiv_id":"2510.25354","title":"Analysis of Semi-Supervised Learning on Hypergraphs","abstract":"Hypergraphs provide a natural framework for modeling higher-order interactions, yet their theoretical underpinnings in semi-supervised learning remain limited. We provide an asymptotic consistency analysis of variational learning on random geometric hypergraphs, precisely characterizing the conditions ensuring the well-posedness of hypergraph learning as well as showing convergence to a weighted $p$-Laplacian equation. Motivated by this, we propose Higher-Order Hypergraph Learning (HOHL), which regularizes via powers of Laplacians from skeleton graphs for multiscale smoothness. HOHL converges to a higher-order Sobolev seminorm. Empirically, it performs strongly on standard baselines.","short_abstract":"Hypergraphs provide a natural framework for modeling higher-order interactions, yet their theoretical underpinnings in semi-supervised learning remain limited. We provide an asymptotic consistency analysis of variational learning on random geometric hypergraphs, precisely characterizing the conditions ensuring the well...","url_abs":"https://arxiv.org/abs/2510.25354","url_pdf":"https://arxiv.org/pdf/2510.25354v2","authors":"[\"Adrien Weihs\",\"Andrea L. Bertozzi\",\"Matthew Thorpe\"]","published":"2025-10-29T10:19:32Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math.ST\"]","methods":"[]","has_code":false}