Muon Is Theoretically Wrong For Convolutions, But Empirically Effective
Muon, an optimizer known for its efficiency, has a clear interpretation for matrix-valued updates, but convolutional kernels are stored as four-dimensional tensors. Standard implementations reshape these tensors into matrices, a shortcut which breaks the theoretical understanding behind Muon. To investigate this, we formalize the corresponding optimization objective directly in convolutional operator geometry and introduce Convolutional Newton-Schulz (Conv-NS), which approximates the polar factor in this geometry while preserving kernel support. When applied in fast training experiments, Conv-NS and reshape-based Muon are both computationally efficient and achieve comparable accuracy on C...
| Authors | Thibaut Boissin, Thomas Massena, Mathieu Serrurier et al. |
|---|---|
| Primary category | cs.LG |
| Published | 5 October 2026 |
| Last updated at source | 5 October 2026 |
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