A new arXiv preprint reports the first empirical evidence that the Muon optimizer exhibits the Flat Minima Hypothesis, a property previously associated with other optimizers. The authors studied Muon through the lens of sharpness, finding that it tends to converge to flat minima, which are often linked to better generalization.
The paper also derives Muon's implicit preconditioner, a mathematical tool that reveals how the optimizer shapes its update steps. Using this derivation, the authors analyze Muon's potential to operate at the edge of stability, a regime where training dynamics hover near the boundary of divergence.
Because the abstract is brief, the full methodology and experimental details are not yet available. The findings are preliminary but suggest that Muon may share desirable properties with other optimizers that favor flat solutions and stable yet aggressive training.