# The physics of higher-order interactions in complex systems

arXiv: https://arxiv.org/abs/2110.06023 · HTML: https://mlsanity.com/paper/2110.06023/

## Key facts

- Cited by 63 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Oct 2021.

## Built on by (most cited first, 30 of 63)

- [Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networks](https://mlsanity.com/paper/2304.10031/) (2023)
- [Predicting the Future of AI with AI: High-quality link prediction in an exponentially growing knowledge network](https://mlsanity.com/paper/2210.00881/) (2022)
- [TopoBench: A Framework for Benchmarking Topological Deep Learning](https://mlsanity.com/paper/2406.06642/) (2024)
- [A Survey on Hypergraph Neural Networks: An In-Depth and Step-By-Step Guide](https://mlsanity.com/paper/2404.01039/) (2024)
- [Forecasting high-impact research topics via machine learning on evolving knowledge graphs](https://mlsanity.com/paper/2402.08640/) (2024)
- [Higher-order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexes](https://mlsanity.com/paper/2309.12971/) (2023)
- [A Survey on Large-Population Systems and Scalable Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2209.03859/) (2022)
- [Inference of hyperedges and overlapping communities in hypergraphs](https://mlsanity.com/paper/2204.05646/) (2022)
- [Attending to Topological Spaces: The Cellular Transformer](https://mlsanity.com/paper/2405.14094/) (2024)
- [Learning High-Order Relationships of Brain Regions](https://mlsanity.com/paper/2312.02203/) (2023)
- [Dirac signal processing of higher-order topological signals](https://mlsanity.com/paper/2301.10137/) (2023)
- [Unifying Pairwise Interactions in Complex Dynamics](https://mlsanity.com/paper/2201.11941/) (2022)
- [Structure and inference in hypergraphs with node attributes](https://mlsanity.com/paper/2311.03857/) (2023)
- [Topo-MLP : A Simplicial Network Without Message Passing](https://mlsanity.com/paper/2312.11862/) (2023)
- [Inferring Higher-Order Couplings with Neural Networks](https://mlsanity.com/paper/2501.06108/) (2025)
- [CAT-Walk: Inductive Hypergraph Learning via Set Walks](https://mlsanity.com/paper/2306.11147/) (2023)
- [Multi-Scale Simulation of Complex Systems: A Perspective of Integrating Knowledge and Data](https://mlsanity.com/paper/2306.10275/) (2023)
- [Integrating Physics and Topology in Neural Networks for Learning Rigid Body Dynamics](https://mlsanity.com/paper/2411.11467/) (2024)
- [HOPSE: Scalable Higher-Order Positional and Structural Encoder for Combinatorial Representations](https://mlsanity.com/paper/2505.15405/) (2025)
- [Nonbacktracking spectral clustering of nonuniform hypergraphs](https://mlsanity.com/paper/2204.13586/) (2022)
- [Demystifying Higher-Order Graph Neural Networks](https://mlsanity.com/paper/2406.12841/) (2024)
- [Learning Interpretable Network Dynamics via Universal Neural Symbolic Regression](https://mlsanity.com/paper/2411.06833/) (2024)
- [Hypergraph Attacks via Injecting Homogeneous Nodes into Elite Hyperedges](https://mlsanity.com/paper/2412.18365/) (2024)
- [Deep Ensembles for Graphs with Higher-order Dependencies](https://mlsanity.com/paper/2205.13988/) (2022)
- [Kernel-based Joint Independence Tests for Multivariate Stationary and Non-stationary Time Series](https://mlsanity.com/paper/2305.08529/) (2023)
- [Interaction Measures, Partition Lattices and Kernel Tests for High-Order Interactions](https://mlsanity.com/paper/2306.00904/) (2023)
- [Explosive neural networks via higher-order interactions in curved statistical manifolds](https://mlsanity.com/paper/2408.02326/) (2024)
- [ICML Topological Deep Learning Challenge 2024: Beyond the Graph Domain](https://mlsanity.com/paper/2409.05211/) (2024)
- [All the World's a (Hyper)Graph: A Data Drama](https://mlsanity.com/paper/2206.08225/) (2022)
- [Zoo Guide to Network Embedding](https://mlsanity.com/paper/2305.03474/) (2023)

## Abstract (arXiv)

Complex networks have become the main paradigm for modelling the dynamics of interacting systems. However, networks are intrinsically limited to describing pairwise interactions, whereas real-world systems are often characterized by higher-order interactions involving groups of three or more units. Higher-order structures, such as hypergraphs and simplicial complexes, are therefore a better tool to map the real organization of many social, biological and man-made systems. Here, we highlight recent evidence of collective behaviours induced by higher-order interactions, and we outline three key challenges for the physics of higher-order systems.