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
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Rescaled mirror flows converge to a limit whose primal variable incrementally minimizes quadratic loss over a subdifferential-defined time-dependent hypothesis set.
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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.
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Incremental Learning in Mirror Flows
Rescaled mirror flows converge to a limit whose primal variable incrementally minimizes quadratic loss over a subdifferential-defined time-dependent hypothesis set.