# Broad Spectrum Structure Discovery in Large-Scale Higher-Order Networks

arXiv: https://arxiv.org/abs/2505.21748 · HTML: https://mlsanity.com/paper/2505.21748/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 73 references that are in the map.
- First posted on arXiv 27 May 2025.

## Builds on (most cited first, 30 of 32)

- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Networks beyond pairwise interactions: structure and dynamics](https://mlsanity.com/paper/2006.01764/) (2020)
- [Simplicial Closure and higher-order link prediction](https://mlsanity.com/paper/1802.06916/) (2018)
- [Contact patterns in a high school: a comparison between data collected using wearable sensors, contact diaries and friendship surveys](https://mlsanity.com/paper/1506.03645/) (2015)
- [Generative hypergraph clustering: from blockmodels to modularity](https://mlsanity.com/paper/2101.09611/) (2021)
- [How Much and When Do We Need Higher-order Information in Hypergraphs? A Case Study on Hyperedge Prediction](https://mlsanity.com/paper/2001.11181/) (2020)
- [Bayesian Poisson Tucker Decomposition for Learning the Structure of International Relations](https://mlsanity.com/paper/1606.01855/) (2016)
- [Gamma Belief Networks](https://mlsanity.com/paper/1512.03081/) (2015)
- [Data on face-to-face contacts in an office building suggests a low-cost vaccination strategy based on community linkers](https://mlsanity.com/paper/1409.7017/) (2014)
- [Community detection, link prediction, and layer interdependence in multilayer networks](https://mlsanity.com/paper/1701.01369/) (2017)
- [Hypergraph Cuts with General Splitting Functions](https://mlsanity.com/paper/2001.02817/) (2020)
- [Community detection with node attributes in multilayer networks](https://mlsanity.com/paper/2004.09160/) (2020)
- [Inference of hyperedges and overlapping communities in hypergraphs](https://mlsanity.com/paper/2204.05646/) (2022)
- [Hypergraph Artificial Benchmark for Community Detection (h-ABCD)](https://mlsanity.com/paper/2210.15009/) (2022)
- [Structure and inference in hypergraphs with node attributes](https://mlsanity.com/paper/2311.03857/) (2023)
- [Higher-order motif analysis in hypergraphs](https://mlsanity.com/paper/2108.03192/) (2021)
- [Core-periphery detection in hypergraphs](https://mlsanity.com/paper/2202.12769/) (2022)
- [A tensor factorization model of multilayer network interdependence](https://mlsanity.com/paper/2206.01804/) (2022)
- [A framework to generate hypergraphs with community structure](https://mlsanity.com/paper/2212.08593/) (2022)
- [Community Detection in Large Hypergraphs](https://mlsanity.com/paper/2301.11226/) (2023)
- [Combinatorial Characterizations and Impossibilities for Higher-order Homophily](https://mlsanity.com/paper/2103.11818/) (2021)
- [Model-based clustering in simple hypergraphs through a stochastic blockmodel](https://mlsanity.com/paper/2210.05983/) (2022)
- [Encapsulation Structure and Dynamics in Hypergraphs](https://mlsanity.com/paper/2307.04613/) (2023)
- [Higher-order correlations reveal complex memory in temporal hypergraphs](https://mlsanity.com/paper/2303.09316/) (2023)
- [Core-periphery Models for Hypergraphs](https://mlsanity.com/paper/2206.00783/) (2022)
- [The temporal dynamics of group interactions in higher-order social networks](https://mlsanity.com/paper/2306.09967/) (2023)
- [Hierarchical Compound Poisson Factorization](https://mlsanity.com/paper/1604.03853/) (2016)
- [Simplicial contagion in temporal higher-order networks](https://mlsanity.com/paper/2105.04455/) (2021)
- [Message-Passing on Hypergraphs: Detectability, Phase Transitions and Higher-Order Information](https://mlsanity.com/paper/2312.00708/) (2023)
- [A Stochastic Block Hypergraph model](https://mlsanity.com/paper/2312.12536/) (2023)

## Built on by (most cited first, 3 of 3)

- [Near-Universal Multiplicative Updates for Nonnegative Einsum Factorization](https://mlsanity.com/paper/2602.02759/) (2026)
- [How do Probabilistic Graphical Models and Graph Neural Networks Look at Network Data?](https://mlsanity.com/paper/2506.11869/) (2025)
- [Learning Multi-Order Block Structure in Higher-Order Networks](https://mlsanity.com/paper/2511.21350/) (2025)

## Abstract (arXiv)

Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior of complex systems but is made challenging by their combinatorial complexity and computational demands. In this paper, we introduce a class of probabilistic models that efficiently represents and discovers a broad spectrum of mesoscale structure in large-scale hypergraphs. The key insight enabling this approach is to treat classes of similar units as themselves nodes in a latent hypergraph. By modeling observed node interactions through latent interactions among classes using low-rank representations, our approach tractably captures rich structural patterns while ensuring model identifiability. This allows for direct interpretation of distinct node- and class-level structures. Empirically, our model improves link prediction over state-of-the-art methods and discovers interpretable structures in diverse real-world systems, including pharmacological and social networks, advancing the ability to incorporate large-scale higher-order data into the scientific process.