Physical Muon: Orthogonalization as an Equilibrium Computation
cs.LG, cs.ET, stat.ML
Submitted: 2026-09-29
Updated: 2026-09-29
Terminology
Sources
- Dion: Distributed Orthonormalized Updates
- The Polar Express: Optimal Matrix Sign Methods and Their Application to the Muon Algorithm
- The Spectral Dynamics and Noise Geometry of Muon
- Old Optimizer, New Norm: An Anthology
- Symbolic Discovery of Optimization Algorithms
- CacheMuon: Using Temporal Preconditioning To Approximate Polar Factor
- Understanding and Embracing Imperfection in Physical Learning Networks
- Adam: A Method for Stochastic Optimization
- Cautious Optimizers: Improving Training with One Line of Code
- Muon is Scalable for LLM Training
- Decoupled Weight Decay Regularization
- Move on Muon : A Hamiltonian probability gradient flow perspective of Muon optimizer
- The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale
- Muon Dynamics as a Spectral Wasserstein Flow
- Adafactor: Adaptive Learning Rates with Sublinear Memory Cost
- Generative Models on Analog Hardware with Dynamics
- OLion: Approaching the Hadamard Ideal by Intersecting Spectral and $\ell_{\infty}$ Implicit Biases
- Why Transformers Need Adam: A Hessian Perspective
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