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Implicit Regularization in Matrix Factorization

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arxiv 1705.09280 v1 pith:DN3H53WL submitted 2017-05-25 stat.ML cs.LG

Suriya Gunasekar , Blake Woodworth , Srinadh Bhojanapalli , Behnam Neyshabur , Nathan Srebro This is my paper · ORCID
classification stat.MLcs.LG
keywords factorizationdescentenoughgradientimplicitmatrixregularizationclose
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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.

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