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.
Saddle-to-saddle dynamics explains a simplicity bias across neural network architectures.arXiv preprint arXiv:2512.20607, 2025
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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.