Implicit Regularization in Matrix Factorization

05/25/2017

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by   Suriya Gunasekar, et al.

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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.