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arXiv · 2212.02105

Matrix factorization with neural networks

Francesco Camilli·Marc Mézard
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Abstract

Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning. We introduce a new `decimation' scheme that maps it to neural network models of associative memory and provide a detailed theoretical analysis of its performance, showing that decimation is able to factorize extensive-rank matrices and to denoise them efficiently. We introduce a decimation algorithm based on ground-state search of the neural network, which shows performances that match the theoretical prediction.

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BibTeXRIS

Francesco Camilli, Marc Mézard. 2022-12-05. Matrix factorization with neural networks. https://doi.org/10.1103/physreve.107.064308

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