arXiv Machine Learning
When and How Does Muon Precondition? The Role of Structured Gradient Noise
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arXiv Machine Learning
Jun 4
Muon in Associative Memory Learning: Training Dynamics and Scaling Laws
arXiv:2602. 05725v3 Announce Type: replace Abstract: Muon updates matrix parameters via the matrix sign of the gradient and has shown strong empirical gains, yet its dynamics and scaling behavior remain unclear in theory.
arXiv AI
Aug 25
A Physical Response-and-Memory Model for Muon Optimization
The paper introduces a physical response-and-memory model for the Muon optimizer, explaining its semi‑orthogonalized momentum update as the maximally dissipative direction under an output‑side safety budget. It treats the weight matrix as a responsive medium with internal stress, showing that momentum corresponds to accumulated stress whose relaxation occurs over multiple timescales—fast and slow. Based on this, the authors propose the Bi‑Maxwell optimizer, which uses a two‑timescale memory kernel and achieves target loss in fewer steps on a public large‑language‑model benchmark.
arXiv Machine Learning
Jun 30
To Use or not to Use Muon: How Simplicity Bias in Optimizers Matters
arXiv:2603. 00742v2 Announce Type: replace Abstract: While Adam has long been the ubiquitous default optimizer for deep neural networks, Muon has recently seen rapid adoption due to its superior training speed.
arXiv Machine Learning
Jul 15
AMUSE: Anytime Muon with Stable Gradient Evaluation
arXiv:2605. 22432v2 Announce Type: replace Abstract: Modern deep learning commonly relies on AdamW with prescribed learning rate schedules, but recent works challenge both components: Schedule-Free optimization removes explicit schedules via iterate averaging, and Muon improves the update geometry by orthogonalizing momentum for matrix parameters.
arXiv Machine Learning
Sep 11
Musec: MomentUm SpEctral Clipping for Stable Muon-type Training
Musec introduces MomentUm SpEctral Clipping, an optimizer-level, architecture‑agnostic technique that replaces Muon’s spectral flattening with selective spectral clipping to stabilize training. By clipping singular values above a threshold while preserving the momentum’s spectral structure, Musec addresses loss spikes and unbounded weight growth without requiring architecture‑specific changes. Soft Musec, an efficient implementation using smooth spectral saturation via coupled Newton‑Schulz iterations, offers convergence guarantees in nonconvex nonsmooth stochastic optimization and empirically improves stability across diverse learning rates and model sizes.
arXiv Machine Learning
6d ago
Sharpness-aware Orthogonalized Momentum Algorithms
arXiv:2610.32465v1 Announce Type: new Abstract: Adversarial sharpness penalty per iteration of a base optimizer, known as sharpness-aware minimization (SAM), is an accepted technique to improve gener...