Implicit Regularization in Matrix Factorization

Abstract

We study implicit regularization when optimizing an underdetermined quadratic objective over a matrix $X$ with gradient descent on a factorization of X. 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.

Cite

Text

Gunasekar et al. "Implicit Regularization in Matrix Factorization." Neural Information Processing Systems, 2017.

Markdown

[Gunasekar et al. "Implicit Regularization in Matrix Factorization." Neural Information Processing Systems, 2017.](https://mlanthology.org/neurips/2017/gunasekar2017neurips-implicit/)

BibTeX

@inproceedings{gunasekar2017neurips-implicit,
  title     = {{Implicit Regularization in Matrix Factorization}},
  author    = {Gunasekar, Suriya and Woodworth, Blake E and Bhojanapalli, Srinadh and Neyshabur, Behnam and Srebro, Nati},
  booktitle = {Neural Information Processing Systems},
  year      = {2017},
  pages     = {6151-6159},
  url       = {https://mlanthology.org/neurips/2017/gunasekar2017neurips-implicit/}
}