# Learning over Families of Sets -- Hypergraph Representation Learning for Higher Order Tasks

arXiv: https://arxiv.org/abs/2101.07773 · HTML: https://mlsanity.com/paper/2101.07773/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 30 references that are in the map.
- First posted on arXiv 19 Jan 2021.

## Builds on (most cited first, 13 of 13)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Hypergraph Convolution and Hypergraph Attention](https://mlsanity.com/paper/1901.08150/) (2019)
- [Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputs](https://mlsanity.com/paper/1811.01900/) (2018)
- [Simplicial Closure and higher-order link prediction](https://mlsanity.com/paper/1802.06916/) (2018)
- [Hyper-SAGNN: a self-attention based graph neural network for hypergraphs](https://mlsanity.com/paper/1911.02613/) (2019)
- [Random Walks on Hypergraphs with Edge-Dependent Vertex Weights](https://mlsanity.com/paper/1905.08287/) (2019)

## Built on by (most cited first, 13 of 13)

- [Multimodal learning with graphs](https://mlsanity.com/paper/2209.03299/) (2022)
- [HYTREL: Hypergraph-enhanced Tabular Data Representation Learning](https://mlsanity.com/paper/2307.08623/) (2023)
- [From Hypergraph Energy Functions to Hypergraph Neural Networks](https://mlsanity.com/paper/2306.09623/) (2023)
- [A nonlinear diffusion method for semi-supervised learning on hypergraphs](https://mlsanity.com/paper/2103.14867/) (2021)
- [A Survey on Hyperlink Prediction](https://mlsanity.com/paper/2207.02911/) (2022)
- [SUREL+: Moving from Walks to Sets for Scalable Subgraph-based Graph Representation Learning](https://mlsanity.com/paper/2303.03379/) (2023)
- [Principled Hyperedge Prediction with Structural Spectral Features and Neural Networks](https://mlsanity.com/paper/2106.04292/) (2021)
- [Optimal and Robust Category-level Perception: Object Pose and Shape Estimation from 2D and 3D Semantic Keypoints](https://mlsanity.com/paper/2206.12498/) (2022)
- [Learning Enhanced Representations for Tabular Data via Neighborhood Propagation](https://mlsanity.com/paper/2206.06587/) (2022)
- [Improving Graph Neural Networks on Multi-node Tasks with the Labeling Trick](https://mlsanity.com/paper/2304.10074/) (2023)
- [All the World's a (Hyper)Graph: A Data Drama](https://mlsanity.com/paper/2206.08225/) (2022)
- [Expressive Higher-Order Link Prediction through Hypergraph Symmetry Breaking](https://mlsanity.com/paper/2402.11339/) (2024)
- [Two-dimensional Taxonomy for N-ary Knowledge Representation Learning Methods](https://mlsanity.com/paper/2506.05626/) (2025)

## Abstract (arXiv)

Graph representation learning has made major strides over the past decade. However, in many relational domains, the input data are not suited for simple graph representations as the relationships between entities go beyond pairwise interactions. In such cases, the relationships in the data are better represented as hyperedges (set of entities) of a non-uniform hypergraph. While there have been works on principled methods for learning representations of nodes of a hypergraph, these approaches are limited in their applicability to tasks on non-uniform hypergraphs (hyperedges with different cardinalities). In this work, we exploit the incidence structure to develop a hypergraph neural network to learn provably expressive representations of variable sized hyperedges which preserve local-isomorphism in the line graph of the hypergraph, while also being invariant to permutations of its constituent vertices. Specifically, for a given vertex set, we propose frameworks for (1) hyperedge classification and (2) variable sized expansion of partially observed hyperedges which captures the higher order interactions among vertices and hyperedges. We evaluate performance on multiple real-world hypergraph datasets and demonstrate consistent, significant improvement in accuracy, over state-of-the-art models.