%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 }