Paper ID: 2201.13157

Equivariant neural networks for recovery of Hadamard matrices

Augusto Peres, Eduardo Dias, Luís Sarmento, Hugo Penedones

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.

Submitted: Jan 31, 2022