Suriya Gunasekar, Blake Woodworth, Srinadh Bhojanapalli, Behnam Neyshabur, Nathan Srebro
Published 2017-05-25Version 1
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.
Causal Inference with Noisy and Missing Covariates via Matrix Factorization
Learning with Gradient Descent and Weakly Convex Losses
The Implicit Bias of Gradient Descent on Separable Data
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