# Nonlinear Higher-Order Label Spreading

arXiv: https://arxiv.org/abs/2006.04762 · HTML: https://mlsanity.com/paper/2006.04762/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2020.

## Built on by (most cited first, 20 of 20)

- [You are AllSet: A Multiset Function Framework for Hypergraph Neural Networks](https://mlsanity.com/paper/2106.13264/) (2021)
- [Equivariant Hypergraph Diffusion Neural Operators](https://mlsanity.com/paper/2207.06680/) (2022)
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- [Topological Relational Learning on Graphs](https://mlsanity.com/paper/2110.15529/) (2021)
- [A Unifying Generative Model for Graph Learning Algorithms: Label Propagation, Graph Convolutions, and Combinations](https://mlsanity.com/paper/2101.07730/) (2021)
- [A nonlinear diffusion method for semi-supervised learning on hypergraphs](https://mlsanity.com/paper/2103.14867/) (2021)
- [Directional Sheaf Hypergraph Networks: Unifying Learning on Directed and Undirected Hypergraphs](https://mlsanity.com/paper/2510.04727/) (2025)
- [Hypergraph Neural Diffusion: A PDE-Inspired Framework for Hypergraph Message Passing](https://mlsanity.com/paper/2604.10955/) (2026)
- [Modeling Edge-Specific Node Features through Co-Representation Neural Hypergraph Diffusion](https://mlsanity.com/paper/2405.14286/) (2024)
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- [A Unified View on Neural Message Passing with Opinion Dynamics for Social Networks](https://mlsanity.com/paper/2310.01272/) (2023)
- [DLGNet: Hyperedge Classification through Directed Line Graphs for Chemical Reactions](https://mlsanity.com/paper/2410.06969/) (2024)
- [Parameter-Free Hypergraph Neural Network for Few-Shot Node Classification](https://mlsanity.com/paper/2510.21462/) (2025)
- [Probabilistic Label Spreading: Efficient and Consistent Estimation of Soft Labels with Epistemic Uncertainty on Graphs](https://mlsanity.com/paper/2602.04574/) (2026)
- [A flexible PageRank-based graph embedding framework closely related to spectral eigenvector embeddings](https://mlsanity.com/paper/2207.11321/) (2022)
- [Laplacian-based Semi-Supervised Learning in Multilayer Hypergraphs by Coordinate Descent](https://mlsanity.com/paper/2301.12184/) (2023)
- [On the convergence of nonlinear averaging dynamics with three-body interactions on hypergraphs](https://mlsanity.com/paper/2304.07203/) (2023)
- [Learning the Right Layers: a Data-Driven Layer-Aggregation Strategy for Semi-Supervised Learning on Multilayer Graphs](https://mlsanity.com/paper/2306.00152/) (2023)
- [Nonlinear Correct and Smooth for Semi-Supervised Learning](https://mlsanity.com/paper/2310.05757/) (2023)
- [PANDA: Prior-guided Attentional Dual-path Architecture](https://mlsanity.com/paper/2610.13635/) (2026)

## Abstract (arXiv)

Label spreading is a general technique for semi-supervised learning with point cloud or network data, which can be interpreted as a diffusion of labels on a graph. While there are many variants of label spreading, nearly all of them are linear models, where the incoming information to a node is a weighted sum of information from neighboring nodes. Here, we add nonlinearity to label spreading through nonlinear functions of higher-order structure in the graph, namely triangles in the graph. For a broad class of nonlinear functions, we prove convergence of our nonlinear higher-order label spreading algorithm to the global solution of a constrained semi-supervised loss function. We demonstrate the efficiency and efficacy of our approach on a variety of point cloud and network datasets, where the nonlinear higher-order model compares favorably to classical label spreading, as well as hypergraph models and graph neural networks.