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math.OC2026
Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case
Xun Qian, Peter Richtárik
Muon-type methods have demonstrated potentially superior performance over Adam and its variants, and have shown hyperparameter transferability across model sizes when specific norm…
math.OC2026
Broximal Alignment for Global Non-Convex Optimization
Kaja Gruntkowska, Hanmin Li, Xun Qian +1
Most non-convex optimization theory is built around gradient dynamics, leaving global convergence largely unexplored. The dominant paradigm focuses on stationarity, certifying only…
cs.LG2026
Communication-Efficient Gluon in Federated Learning
Xun Qian, Alexander Gaponov, Grigory Malinovsky +1
Recent developments have shown that Muon-type optimizers based on linear minimization oracles (LMOs) over non-Euclidean norm balls have the potential to get superior practical perf…