Tight Complexity of Muon under Heavy-Tailed Noise
A growing lesson from neural network optimization is that optimizer design should respect how the model is parametrized. The layerwise input-output structure of neural networks motivates Muon and Scion, whose updates also support hyperparameter transfer. At the same time, stochastic gradient noise in deep learning is often far from sub-Gaussian and may exhibit heavy tails. These observations have shaped recent algorithmic principles for training neural networks, yet their joint theoretical consequences are underexplored. In particular, it is unclear what dimension dependence is unavoidable for gradient-based methods when the problem class is defined using an input-output norm and the stoc...
| Authors | Jiayu Zhang, Tianyi Lin |
|---|---|
| Primary category | math.OC |
| Published | 18 May 2026 |
| Last updated at source | 11 October 2026 |
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 17 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.