# Set2Graph: Learning Graphs From Sets

arXiv: https://arxiv.org/abs/2002.08772 · HTML: https://mlsanity.com/paper/2002.08772/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2020.

## Built on by (most cited first, 16 of 16)

- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Pure Transformers are Powerful Graph Learners](https://mlsanity.com/paper/2207.02505/) (2022)
- [A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups](https://mlsanity.com/paper/2104.09459/) (2021)
- [SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators](https://mlsanity.com/paper/2204.01613/) (2022)
- [Universal Approximation of Functions on Sets](https://mlsanity.com/paper/2107.01959/) (2021)
- [Machine Learning in the Search for New Fundamental Physics](https://mlsanity.com/paper/2112.03769/) (2021)
- [Top-N: Equivariant set and graph generation without exchangeability](https://mlsanity.com/paper/2110.02096/) (2021)
- [Transformers Generalize DeepSets and Can be Extended to Graphs and Hypergraphs](https://mlsanity.com/paper/2110.14416/) (2021)
- [Multiresolution Equivariant Graph Variational Autoencoder](https://mlsanity.com/paper/2106.00967/) (2021)
- [Equivariant Hypergraph Neural Networks](https://mlsanity.com/paper/2208.10428/) (2022)
- [Learning Hypergraphs From Signals With Dual Smoothness Prior](https://mlsanity.com/paper/2211.01717/) (2022)
- [GradMetaNet: An Equivariant Architecture for Learning on Gradients](https://mlsanity.com/paper/2507.01649/) (2025)
- [Set-to-Sequence Methods in Machine Learning: a Review](https://mlsanity.com/paper/2103.09656/) (2021)
- [A Markov Random Field model for Hypergraph-based Machine Learning](https://mlsanity.com/paper/2308.14172/) (2023)
- [Pruning Edges and Gradients to Learn Hypergraphs from Larger Sets](https://mlsanity.com/paper/2106.13919/) (2021)
- [SetPINNs: Set-based Physics-informed Neural Networks](https://mlsanity.com/paper/2409.20206/) (2024)

## Abstract (arXiv)

Many problems in machine learning can be cast as learning functions from sets to graphs, or more generally to hypergraphs; in short, Set2Graph functions. Examples include clustering, learning vertex and edge features on graphs, and learning features on triplets in a collection. A natural approach for building Set2Graph models is to characterize all linear equivariant set-to-hypergraph layers and stack them with non-linear activations. This poses two challenges: (i) the expressive power of these networks is not well understood; and (ii) these models would suffer from high, often intractable computational and memory complexity, as their dimension grows exponentially. This paper advocates a family of neural network models for learning Set2Graph functions that is both practical and of maximal expressive power (universal), that is, can approximate arbitrary continuous Set2Graph functions over compact sets. Testing these models on different machine learning tasks, mainly an application to particle physics, we find them favorable to existing baselines.