# LionMuon: Alternating Spectral and Sign Descent for Efficient Training

Source: [LionMuon: Alternating Spectral and Sign Descent for Efficient Training](<https://www.sota2.com/research/paper/6a0d4028f984739ed67378dc>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-06-24T05:00:22.884Z

Authors: Arman Bolatov, Artem Riabinin, Nikita Kornilov, Andrey Veprikov, Samuel Horv\\'ath, Martin Tak\\'a\\v{c}, Aleksandr Beznosikov

Published: 2026-05-19T13:07:59.000Z

## Abstract

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. A simpler single-EMA variant, SignMuon, by itself already outperforms pure Muon. At P = 2, LionMuon Pareto-dominates Muon, Lion, Signum, and AdamW on every dataset and architecture we tested at 124M model size, reaching lower validation loss at lower compute, and the same advantage persists at 355M and 720M scale. On the theory side, we prove sharp complexity bounds under heavy-tailed noise which are governed by period-averaged smoothness and noise that interpolate between Muon's and Lion's constants. These bounds predict the compute-optimal period and the conditions under which LionMuon outruns Muon and Lion. Code: https://github.com/brain-lab-research/lion-muon

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Language Modeling on SlimPajama latest (val)](<https://www.sota2.com/research/sota/language-modeling-on-slimpajama-latest-val.md>): Language Modeling; SlimPajama latest (val); Validation Loss: 3.078.

- [Language Modeling on FineWeb (val)](<https://www.sota2.com/research/sota/language-modeling-on-fineweb-val.md>): Language Modeling; FineWeb (val); Validation Loss: 3.045.

- [Language Modeling on WikiText-103 (val)](<https://www.sota2.com/research/sota/language-modeling-on-wikitext-103-val.md>): Language Modeling; WikiText-103 (val); PPL: not recorded.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2605.19811>)

[PDF](<https://arxiv.org/pdf/2605.19811.pdf>)