Implicit Regularization in Tensor Factorization

Noam Razin, Asaf Maman, Nadav Cohen

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Recent efforts to unravel the mystery of implicit regularization in deep learning have led to a theoretical focus on matrix factorization - matrix completion via linear neural network. As a step further towards practical deep learning, we provide the first theoretical analysis of implicit regularization in tensor factorization - tensor completion via certain type of non-linear neural network. We circumvent the notorious difficulty of tensor problems by adopting a dynamical systems perspective, and characterizing the evolution induced by gradient descent. The characterization suggests a form of greedy low tensor rank search, which we rigorously prove under certain conditions, and empirically demonstrate under others. Motivated by tensor rank capturing the implicit regularization of a non-linear neural network, we empirically explore it as a measure of complexity, and find that it captures the essence of datasets on which neural networks generalize. This leads us to believe that tensor rank may pave way to explaining both implicit regularization in deep learning, and the properties of real-world data translating this implicit regularization to generalization.

Original languageEnglish
Title of host publicationProceedings of the 38th International Conference on Machine Learning, ICML 2021
PublisherML Research Press
Number of pages12
ISBN (Electronic)9781713845065
StatePublished - 2021
Event38th International Conference on Machine Learning, ICML 2021 - Virtual, Online
Duration: 18 Jul 202124 Jul 2021

Publication series

NameProceedings of Machine Learning Research


Conference38th International Conference on Machine Learning, ICML 2021
CityVirtual, Online

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


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