TY - GEN

T1 - Implicit Regularization in Tensor Factorization

AU - Razin, Noam

AU - Maman, Asaf

AU - Cohen, Nadav

N1 - Publisher Copyright:
Copyright © 2021 by the author(s)

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85161355072&partnerID=8YFLogxK

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AN - SCOPUS:85161355072

T3 - Proceedings of Machine Learning Research

SP - 8913

EP - 8924

BT - Proceedings of the 38th International Conference on Machine Learning, ICML 2021

PB - ML Research Press

T2 - 38th International Conference on Machine Learning, ICML 2021

Y2 - 18 July 2021 through 24 July 2021

ER -