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arXiv Machine Learning By Ping Li, Vincent Y. F. Tan

Last-Iterate Stationarity of Muon with Finitely Many Newton-Schulz Iterations

Read the original on arXiv Machine Learning →

The paper investigates the last-iterate convergence properties of the Muon optimization algorithm, which employs a fixed number of Newton–Schulz iterations for large-scale language‑model training. It shows that without input stabilization Muon can cycle even on smooth convex quadratics, while with positive stabilization and a momentum coefficient below one, last‑iterate gradient convergence is achieved under a small constant learning rate. For stochastic gradients, the authors demonstrate that fixed learning rates can fail, but decreasing learning rates combined with increasing momentum yield almost‑sure and mean‑square convergence, and they provide counterexamples and density‑one convergence rates.

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