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cs.LG2026
Adam Improves Muon: Adaptive Moment Estimation with Orthogonalized Momentum
Minxin Zhang, Yuxuan Liu, Hayden Schaeffer
Efficient stochastic optimization typically integrates an update direction that performs well in the deterministic regime with a mechanism adapting to stochastic perturbations. Whi…
cs.LG2025
AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates
Minxin Zhang, Yuxuan Liu, Hayden Schaeffer
The recently proposed Muon optimizer updates weight matrices via orthogonalized momentum and has demonstrated strong empirical success in large language model training. However, it…