# Higher-Order Regularization Learning on Hypergraphs

arXiv: https://arxiv.org/abs/2510.26533 · HTML: https://mlsanity.com/paper/2510.26533/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 102 references that are in the map.
- First posted on arXiv 30 Oct 2025.

## Builds on (most cited first, 30 of 43)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Graph Learning: A Survey](https://mlsanity.com/paper/2105.00696/) (2021)
- [FoSR: First-order spectral rewiring for addressing oversquashing in GNNs](https://mlsanity.com/paper/2210.11790/) (2022)
- [Revisiting Over-smoothing and Over-squashing Using Ollivier-Ricci Curvature](https://mlsanity.com/paper/2211.15779/) (2022)
- [Error estimates for spectral convergence of the graph Laplacian on random geometric graphs towards the Laplace--Beltrami operator](https://mlsanity.com/paper/1801.10108/) (2018)
- [On the Trade-off between Over-smoothing and Over-squashing in Deep Graph Neural Networks](https://mlsanity.com/paper/2212.02374/) (2022)
- [Poisson Learning: Graph Based Semi-Supervised Learning At Very Low Label Rates](https://mlsanity.com/paper/2006.11184/) (2020)
- [Random Walks on Hypergraphs with Edge-Dependent Vertex Weights](https://mlsanity.com/paper/1905.08287/) (2019)
- [Mitigating Over-Smoothing and Over-Squashing using Augmentations of Forman-Ricci Curvature](https://mlsanity.com/paper/2309.09384/) (2023)
- [Analysis of p-Laplacian Regularization in Semi-Supervised Learning](https://mlsanity.com/paper/1707.06213/) (2017)
- [The Total Variation on Hypergraphs - Learning on Hypergraphs Revisited](https://mlsanity.com/paper/1312.5179/) (2013)
- [A variational approach to the consistency of spectral clustering](https://mlsanity.com/paper/1508.01928/) (2015)
- [A Survey of Signed Network Mining in Social Media](https://mlsanity.com/paper/1511.07569/) (2015)
- [Submodular Hypergraphs: p-Laplacians, Cheeger Inequalities and Spectral Clustering](https://mlsanity.com/paper/1803.03833/) (2018)
- [Continuum limit of total variation on point clouds](https://mlsanity.com/paper/1403.6355/) (2014)
- [The game theoretic p-Laplacian and semi-supervised learning with few labels](https://mlsanity.com/paper/1711.10144/) (2017)
- [Large Data and Zero Noise Limits of Graph-Based Semi-Supervised Learning Algorithms](https://mlsanity.com/paper/1805.09450/) (2018)
- [Semi-supervised Hypergraph Node Classification on Hypergraph Line Expansion](https://mlsanity.com/paper/2005.04843/) (2020)
- [Spectral Convergence of the connection Laplacian from random samples](https://mlsanity.com/paper/1306.1587/) (2013)
- [Properly-weighted graph Laplacian for semi-supervised learning](https://mlsanity.com/paper/1810.04351/) (2018)
- [Rates of Convergence for Laplacian Semi-Supervised Learning with Low Labeling Rates](https://mlsanity.com/paper/2006.02765/) (2020)
- [A Survey of Data-Efficient Graph Learning](https://mlsanity.com/paper/2402.00447/) (2024)
- [Algorithms for Lipschitz Learning on Graphs](https://mlsanity.com/paper/1505.00290/) (2015)
- [Consistency of Lipschitz learning with infinite unlabeled data and finite labeled data](https://mlsanity.com/paper/1710.10364/) (2017)
- [Hypergraph p-Laplacian: A Differential Geometry View](https://mlsanity.com/paper/1711.08171/) (2017)
- [A random matrix analysis and improvement of semi-supervised learning for large dimensional data](https://mlsanity.com/paper/1711.03404/) (2017)
- [Uniform Convergence Rates for Lipschitz Learning on Graphs](https://mlsanity.com/paper/2111.12370/) (2021)
- [Model-Change Active Learning in Graph-Based Semi-Supervised Learning](https://mlsanity.com/paper/2110.07739/) (2021)
- [Consistency of Cheeger and Ratio Graph Cuts](https://mlsanity.com/paper/1411.6590/) (2014)

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

- [A Categorical Analysis of Large Language Models and Why LLMs Circumvent the Symbol Grounding Problem](https://mlsanity.com/paper/2512.09117/) (2025)

## Abstract (arXiv)

Higher-Order Hypergraph Learning (HOHL) was recently introduced as a principled alternative to classical hypergraph regularization, enforcing higher-order smoothness via powers of multiscale Laplacians induced by the hypergraph structure. Prior work established the well- and ill-posedness of HOHL through an asymptotic consistency analysis in geometric settings. We extend this theoretical foundation by proving the consistency of a truncated version of HOHL and deriving explicit convergence rates when HOHL is used as a regularizer in fully supervised learning. We further demonstrate its strong empirical performance in active learning and in datasets lacking an underlying geometric structure, highlighting HOHL's versatility and robustness across diverse learning settings.