Physical Muon: Orthogonalization as an Equilibrium Computation
Physical neural networks and analog in-memory computing could reduce the energy cost of neural network training. Realizing this potential, however, requires optimizers that combine effective learning with physical implementability. SGD fits local analog updates but struggles on transformers, while Adam family is unstable against analog bias. Muon offers strong training performance, but its Newton--Schulz orthogonalization relies on dense matrix-matrix products. To address this obstacle, we introduce Physical Muon, which computes the orthogonalization as the equilibrium of a continuous-time flow. Random probes approximate the flow using matrix-vector products, reciprocal reads, and local r...
| Authors | Yuren Hao |
|---|---|
| Primary category | cs.LG |
| Published | 29 September 2026 |
| Last updated at source | 29 September 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 Information may be incomplete or out of date.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.