Equivariant neural networks for recovery of Hadamard matrices

• URL: http://arxiv.org/abs/2201.13157v1
• Date: Mon, 31 Jan 2022 12:07:07 GMT
• Title: Equivariant neural networks for recovery of Hadamard matrices
• Authors: Augusto Peres, Eduardo Dias, Lu\'is Sarmento, Hugo Penedones
• Abstract summary: 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.
• Score: 0.7742297876120561
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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.

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