Schattor: Schatten-family methods for deep learning optimization
Modern deep learning optimization features heterogeneous parameter structures, noisy gradients, and highly nonconvex landscapes, posing significant challenges for both algorithm design and theoretical analysis. Motivated by the limitations of SGD and the success of adaptive optimizers, we propose {\it Schattor}, a family of adaptive first-order methods based on Schatten norms. Schattor unifies SGD and the recently proposed matrix-variate adaptive optimizer Muon within a single Schatten-norm-based framework. We establish dimension-free stationarity guarantees for methods in the Schattor family for stochastic matrix optimization problems via a novel matrix martingale moment bound. We also d...
| Authors | Bohao Ma, Junyu Zhang, Chuan He |
|---|---|
| Primary category | math.OC |
| Published | 14 June 2026 |
| Last updated at source | 14 June 2026 |
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