arXiv 2201.131572022-01-31cs.LGcs.DM

Equivariant neural networks for recovery of Hadamard matrices

Inductiva Research Labs（Inductiva Research Labs（Inductiva研究实验室））

Augusto Peres, Eduardo Dias, Luís Sarmento, Hugo Penedones

英文摘要：

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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