Implicit Regularization in Hierarchical Tensor Factorization and Deep Convolutional Neural Networks

Noam Razin, Asaf Maman, Nadav Cohen

Research output: Contribution to journalConference articlepeer-review


In the pursuit of explaining implicit regularization in deep learning, prominent focus was given to matrix and tensor factorizations, which correspond to simplified neural networks. It was shown that these models exhibit an implicit tendency towards low matrix and tensor ranks, respectively. Drawing closer to practical deep learning, the current paper theoretically analyzes the implicit regularization in hierarchical tensor factorization, a model equivalent to certain deep convolutional neural networks. Through a dynamical systems lens, we overcome challenges associated with hierarchy, and establish implicit regularization towards low hierarchical tensor rank. This translates to an implicit regularization towards locality for the associated convolutional networks. Inspired by our theory, we design explicit regularization discouraging locality, and demonstrate its ability to improve the performance of modern convolutional networks on non-local tasks, in defiance of conventional wisdom by which architectural changes are needed. Our work highlights the potential of enhancing neural networks via theoretical analysis of their implicit regularization.

Original languageEnglish
Pages (from-to)18422-18462
Number of pages41
JournalProceedings of Machine Learning Research
StatePublished - 2022
Event39th International Conference on Machine Learning, ICML 2022 - Baltimore, United States
Duration: 17 Jul 202223 Jul 2022

All Science Journal Classification (ASJC) codes

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


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