# Analysis of Semi-Supervised Learning on Hypergraphs

arXiv: https://arxiv.org/abs/2510.25354 · HTML: https://mlsanity.com/paper/2510.25354/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2025.

## Built on by (most cited first, 1 of 1)

- [Higher-Order Regularization Learning on Hypergraphs](https://mlsanity.com/paper/2510.26533/) (2025)

## Abstract (arXiv)

Hypergraphs provide a natural framework for modeling multiway interactions. We analyze a class of variational semi-supervised learning problems posed on random geometric hypergraphs and establish asymptotic consistency in the large-data limit. In particular, we identify scaling regimes that ensure well-posedness--yielding nontrivial label propagation rather than collapse to a constant labeling--and show that discrete minimizers converge, in the continuum, to solutions of a density-weighted p-Laplacian equation. We also propose Higher-Order Hypergraph Learning (HOHL), a multiscale regularization scheme based on powers of Laplacians associated with hypergraph-induced subgraphs. For geometric point clouds, we analyze an efficient multiscale Laplacian surrogate for HOHL and prove convergence to a higher-order Sobolev-type seminorm. Numerical experiments on standard benchmarks support the practical utility of the resulting higher-order regularization.