How Does Muon Work in Private Deep Learning? Scalable Differentially Private Training via Orthogonalization
Training deep neural networks requires optimizers that balance computational efficiency with formal data privacy. While orthogonalized update rules, such as the recently introduced Muon optimizer, have shown strong empirical performance and scalability, their behavior under Differential Privacy (DP) is not yet understood. In this paper, we propose DP-Muon, a differentially private variant of the Muon optimizer. By analyzing Muon's orthogonalized updates through the lens of a Linear Minimization Oracle (LMO), we show that the leading effect of per-example clipping is a positive rescaling of the gradient, to which the LMO is blind, so that only a small directional residual controlled by the...
| Authors | Alexander Gaponov, Grigory Malinovsky, Egor Shulgin et al. |
|---|---|
| Primary category | cs.LG |
| Published | 17 October 2026 |
| Last updated at source | 17 October 2026 |
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