When to use what Schatten-$p$ norm in deep learning?
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Computer Science > Machine Learning
Title:When to use what Schatten-$p$ norm in deep learning?
Abstract:Schatten-$\infty$ based optimizers such as Muon have shown promising empirical performance, but there remains seemingly conflicting observations regarding whether they are beneficial. We resolve this conflict by showing that the conclusion is regime dependent. Even when the objective is smooth in the Schatten-$\infty$ geometry, smaller Schatten-$p$ geometries can be optimal, specifically in the low-dimensional regime, which we show includes Chinchilla scaling. This conclusion follows from a new noise-robust acceleration result for the SODA framework for $p>2$. The same analysis explains why Muon-like methods do not require warmup, why they naturally favor large batches, and yields a batch size scaling rule for arbitrary $p$.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2606.15268 [cs.LG] |
| (or arXiv:2606.15268v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2606.15268
arXiv-issued DOI via DataCite (pending registration)
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