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Implicit Regularization with Polynomial Growth in Deep Tensor Factorization

2022-07-18 21:04:37
Kais Hariz, Hachem Kadri, Stéphane Ayache, Mahzer Moakher, Thierry Artières
arXiv_AI
     
Abstract

We study the implicit regularization effects of deep learning in tensor factorization. While implicit regularization in deep matrix and 'shallow' tensor factorization via linear and certain type of non-linear neural networks promotes low-rank solutions with at most quadratic growth, we show that its effect in deep tensor factorization grows polynomially with the depth of the network. This provides a remarkably faithful description of the observed experimental behaviour. Using numerical experiments, we demonstrate the benefits of this implicit regularization in yielding a more accurate estimation and better convergence properties.

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URL

https://arxiv.org/abs/2207.08942

PDF

https://arxiv.org/pdf/2207.08942.pdf

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