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Implicit Regularization in Matrix Factorization

Machine Learning 2017-05-26 v1 Machine Learning

Abstract

We study implicit regularization when optimizing an underdetermined quadratic objective over a matrix XX with gradient descent on a factorization of XX. We conjecture and provide empirical and theoretical evidence that with small enough step sizes and initialization close enough to the origin, gradient descent on a full dimensional factorization converges to the minimum nuclear norm solution.

Keywords

Cite

@article{arxiv.1705.09280,
  title  = {Implicit Regularization in Matrix Factorization},
  author = {Suriya Gunasekar and Blake Woodworth and Srinadh Bhojanapalli and Behnam Neyshabur and Nathan Srebro},
  journal= {arXiv preprint arXiv:1705.09280},
  year   = {2017}
}