Direction-magnitude decomposition yields two new methods for low-rank matrix factorization that converge exponentially faster than standard gradient descent on the Burer-Monteiro formulation.
A dynamics theory of implicit regularization in deep low-rank matrix factorization.arXiv preprint arXiv:2212.14150, 2022
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Direction-Magnitude Decomposition for Low-Rank Matrix Optimization: Faster Convergence and Saddle-to-saddle Dynamics
Direction-magnitude decomposition yields two new methods for low-rank matrix factorization that converge exponentially faster than standard gradient descent on the Burer-Monteiro formulation.