Dion3: Full-Stack Orthogonal Updates
The Muon optimizer incurs a significant overhead cost due to its cubic-time Newton-Schulz orthogonalization step. When weights are sharded, communication overhead compounds this computational cost, eroding the benefits of Muon in many settings. We present Dion3, a revision of Muon that targets this overhead at every level of the stack. Our Gram Newton-Schulz algorithm reduces the FLOP cost of orthogonalization, our CuteDSL kernels accelerate it by exploiting symmetry, and our megabatching strategy reduces communication overhead. Moreover, we propose a simple change to the update rule that cuts costs even further: selecting only a fraction of the momentum matrix's rows to orthogonalize at ...
| Authors | Noah Amsel, Jack Zhang, Kwangjun Ahn et al. |
|---|---|
| Primary category | cs.LG |
| Published | 12 August 2026 |
| Last updated at source | 12 August 2026 |
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