LionMuon alternates Lion sign steps and Muon spectral steps with shared dual-EMA momentum to match Lion memory while outperforming both at P=2 on 124M-720M models, backed by heavy-tailed complexity bounds that predict the optimal period.
Muon converges under heavy-tailed noise: Nonconvex h\"{o}lder-smooth empirical risk minimiza- tion.arXiv preprint arXiv:2603.15059,
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LionMuon: Alternating Spectral and Sign Descent for Efficient Training
LionMuon alternates Lion sign steps and Muon spectral steps with shared dual-EMA momentum to match Lion memory while outperforming both at P=2 on 124M-720M models, backed by heavy-tailed complexity bounds that predict the optimal period.