Implicit Regularization in Matrix Factorization

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.

Authors

• Suriya Gunasekar
• Blake Woodworth
• Srinadh Bhojanapalli
• Behnam Neyshabur
• Nati Srebro

Keywords

No keywords are indexed for this paper.