Beyond lazy training for over-parameterized tensor decomposition

Journal Article

Over-parametrization is an important technique in training neural networks. In both theory and practice, training a larger network allows the optimization algorithm to avoid bad local optimal solutions. In this paper we study a closely related tensor decomposition problem: given an l-th order tensor in (Rd)?l of rank r (where r « d), can variants of gradient descent find a rank m decomposition where m > r? We show that in a lazy training regime (similar to the NTK regime for neural networks) one needs at least m = ?(dl-1), while a variant of gradient descent can find an approximate tensor when m = O*(r2.5l log d). Our results show that gradient descent on over-parametrized objective could go beyond the lazy training regime and utilize certain low-rank structure in the data.

Duke Authors

Cited Authors

  • Wang, X; Wu, C; Lee, JD; Ma, T; Ge, R

Published Date

  • January 1, 2020

Published In

Volume / Issue

  • 2020-December /

International Standard Serial Number (ISSN)

  • 1049-5258

Citation Source

  • Scopus