Equivariant neural networks for recovery of Hadamard matrices
This work addresses a fundamental mathematical problem related to the Hadamard conjecture, potentially offering insights through machine learning techniques, though it appears incremental as it applies known equivariance principles to a specific domain.
The authors tackled the problem of recovering deleted entries in Hadamard matrices using a message passing neural network that is equivariant to row and column permutations, achieving advantages over traditional architectures like MLPs, CNNs, and Transformers on this combinatorial optimization task.
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.