# Equivariant neural networks for recovery of Hadamard matrices

arXiv: https://arxiv.org/abs/2201.13157 · HTML: https://mlsanity.com/paper/2201.13157/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 27 references that are in the map.
- First posted on arXiv 31 Jan 2022.

## Builds on (most cited first, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups](https://mlsanity.com/paper/1802.03690/) (2018)
- [Equivariance Through Parameter-Sharing](https://mlsanity.com/paper/1702.08389/) (2017)
- [Exploratory Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1909.04063/) (2019)
- [The general theory of permutation equivarant neural networks and higher order graph variational encoders](https://mlsanity.com/paper/2004.03990/) (2020)

## Built on by (most cited first, 1 of 1)

- [Generating Hadamard matrices with transformers](https://mlsanity.com/paper/2604.11101/) (2026)

## Abstract (arXiv)

We propose a message passing neural network architecture designed to be equivariant to column and row permutations of a matrix. We illustrate its advantages over traditional architectures like multi-layer perceptrons (MLPs), convolutional neural networks (CNNs) and even Transformers, on the combinatorial optimization task of recovering a set of deleted entries of a Hadamard matrix. We argue that this is a powerful application of the principles of Geometric Deep Learning to fundamental mathematics, and a potential stepping stone toward more insights on the Hadamard conjecture using Machine Learning techniques.