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.
@article{arxiv.2201.13157,
title = {Equivariant neural networks for recovery of Hadamard matrices},
author = {Augusto Peres and Eduardo Dias and Luís Sarmento and Hugo Penedones},
journal= {arXiv preprint arXiv:2201.13157},
year = {2022}
}