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Implicit Regularization in Matrix Factorization
Suriya Gunasekar · Blake Woodworth · Srinadh Bhojanapalli · Behnam Neyshabur · Nati Srebro

Tue Dec 05 11:40 AM -- 11:45 AM (PST) @ Hall C
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.