arXiv:2608. 09763v1 Announce Type: new Abstract: Muon's polar update is exact for an unweighted spectral geometry.
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arXiv:2605. 17109v3 Announce Type: replace-cross Abstract: In recent years, Muon has emerged as the dominant method for training large language models, and transformers more broadly.
arXiv:2606. 08388v1 Announce Type: new Abstract: Muon replaces a matrix gradient $G=U\Sigma V^\top$ by its polar factor $UV^\top$.
arXiv:2606. 04662v1 Announce Type: cross Abstract: Muon improves training efficiency over Adam in large language-model training by about two times, but the local geometric source of this advantage remains unclear.
arXiv:2607. 19771v1 Announce Type: cross Abstract: Muon and related matrix-sign optimizers are increasingly used to pre-train large language models, but their effect on the internal geometry of individual weight matrices is not well understood.
arXiv:2512. 04632v2 Announce Type: replace Abstract: Orthogonality-based optimizers, such as Muon, have recently shown strong performance across large-scale training and community-driven efficiency challenges.
arXiv:2602. 05725v3 Announce Type: replace Abstract: Muon updates matrix parameters via the matrix sign of the gradient and has shown strong empirical gains, yet its dynamics and scaling behavior remain unclear in theory.