LionMuon: Alternating Spectral and Sign Descent for Efficient Training
In large-scale optimization, the cheapness and effectiveness of update steps are the most crucial factors for a successful optimizer. Sign-based optimizers like Lion or Signum produce cheap per-step updates, whereas Muon's spectral matrix-sign update gives a much stronger direction at a substantially higher per-step cost. In this work, we propose LionMuon, which retains the effectiveness of Muon steps while considerably cutting the averaged iteration cost, similar to sign-based methods. It alternates between Lion's and Muon's updates on a fixed period P, sharing a single dual-EMA momentum buffer between them. The optimizer state memory therefore matches Lion and is exactly half of AdamW's...
| Authors | Arman Bolatov, Artem Riabinin, Nikita Kornilov et al. |
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| Primary category | cs.LG |
| Published | 19 May 2026 |
| Last updated at source | 19 August 2026 |
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