%0 Journal Article %1 belabbas2020implicit %A Belabbas, Mohamed Ali %D 2020 %K matrix-factorization optimization readings regularisation %T On implicit regularization: Morse functions and applications to matrix factorization %U http://arxiv.org/abs/2001.04264 %X In this paper, we revisit implicit regularization from the ground up using notions from dynamical systems and invariant subspaces of Morse functions. The key contributions are a new criterion for implicit regularization---a leading contender to explain the generalization power of deep models such as neural networks---and a general blueprint to study it. We apply these techniques to settle a conjecture on implicit regularization in matrix factorization.

@article{belabbas2020implicit, abstract = {In this paper, we revisit implicit regularization from the ground up using notions from dynamical systems and invariant subspaces of Morse functions. The key contributions are a new criterion for implicit regularization---a leading contender to explain the generalization power of deep models such as neural networks---and a general blueprint to study it. We apply these techniques to settle a conjecture on implicit regularization in matrix factorization.}, added-at = {2020-01-14T12:21:12.000+0100}, author = {Belabbas, Mohamed Ali}, biburl = {https://www.bibsonomy.org/bibtex/242b04bcf4393c38ca55626089da7e0a9/kirk86}, description = {[2001.04264] On implicit regularization: Morse functions and applications to matrix factorization}, interhash = {e8b68bbb6d6409631f6e89a287a281d9}, intrahash = {42b04bcf4393c38ca55626089da7e0a9}, keywords = {matrix-factorization optimization readings regularisation}, note = {cite arxiv:2001.04264}, timestamp = {2020-01-14T12:21:12.000+0100}, title = {On implicit regularization: Morse functions and applications to matrix factorization}, url = {http://arxiv.org/abs/2001.04264}, year = 2020 }