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.
Description
[1705.09280] Implicit Regularization in Matrix Factorization
%0 Journal Article
%1 gunasekar2017implicit
%A Gunasekar, Suriya
%A Woodworth, Blake
%A Bhojanapalli, Srinadh
%A Neyshabur, Behnam
%A Srebro, Nathan
%D 2017
%K deep-learning foundations machine-learning matrix-factorization readings stable theory
%T Implicit Regularization in Matrix Factorization
%U http://arxiv.org/abs/1705.09280
%X 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.
@article{gunasekar2017implicit,
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.},
added-at = {2019-06-10T11:36:18.000+0200},
author = {Gunasekar, Suriya and Woodworth, Blake and Bhojanapalli, Srinadh and Neyshabur, Behnam and Srebro, Nathan},
biburl = {https://www.bibsonomy.org/bibtex/2c5a74bd703dfa814562e933a40d52cfc/kirk86},
description = {[1705.09280] Implicit Regularization in Matrix Factorization},
interhash = {c98b4313e02b4f5608994b99b017f036},
intrahash = {c5a74bd703dfa814562e933a40d52cfc},
keywords = {deep-learning foundations machine-learning matrix-factorization readings stable theory},
note = {cite arxiv:1705.09280},
timestamp = {2019-11-14T20:39:23.000+0100},
title = {Implicit Regularization in Matrix Factorization},
url = {http://arxiv.org/abs/1705.09280},
year = 2017
}