arXiv Machine Learning
Jun 16

When to use what Schatten-$p$ norm in deep learning?

arXiv:2606. 15268v1 Announce Type: new Abstract: Schatten-$\infty$ based optimizers such as Muon have shown promising empirical performance, but there remains seemingly conflicting observations regarding whether they are beneficial.

By Thomas Pethick
arXiv Machine Learning
Aug 20

LionMuon: Alternating Spectral and Sign Descent for Efficient Training

LionMuon is a new optimizer that alternates between Lion’s sign-based updates and Muon’s spectral matrix-sign updates on a fixed period P, sharing a single dual-EMA momentum buffer. This design keeps the memory footprint the same as Lion and half that of AdamW while reducing the average iteration cost compared to Muon. Experiments on 124M, 355M, and 720M models show LionMuon Pareto-dominates Muon, Lion, Signum, and AdamW across datasets and architectures, achieving lower validation loss with less compute.

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