arXiv Machine Learning
The Row Normalization Puzzle in Muon
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
Related stories
arXiv AI
Jun 9
Muon$^2$: Boosting Muon via Adaptive Second-Moment Preconditioning
arXiv:2604. 09967v2 Announce Type: replace-cross Abstract: Muon has emerged as a promising optimizer for large-scale foundation model pre-training by exploiting the matrix structure of neural network updates through iterative orthogonalization.
arXiv Machine Learning
Jun 29
Aurora: A Leverage-Aware Spectral Optimizer
arXiv:2606. 27715v1 Announce Type: new Abstract: We show that for tall matrix parameters, like projection matrices in the MLP layers, the Muon update can have row norms that are arbitrarily non-uniform.
arXiv Machine Learning
Jun 16
CacheMuon: Using Temporal Preconditioning To Approximate Polar Factor
arXiv:2606. 16371v1 Announce Type: new Abstract: Muon is an optimizer that computes updates using the polar factor of the momentum matrix and has shown strong empirical performance across a range of training settings.
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 AI
4d ago
Normalize-Then-Precondition: A Hierarchical Approach to Marginal Scale and Interaction Geometry for LLM Training
arXiv:2609.36692v1 Announce Type: cross Abstract: Matrix optimizers have emerged as a promising direction, with Muon standing out as a prominent design. Revisiting Muon through its full-Gram represen...
arXiv Machine Learning
Jun 2
How Much Orthogonalization Does Muon Need?
arXiv:2606. 00371v1 Announce Type: new Abstract: Muon optimizers improve neural-network training by replacing ill-conditioned momentum updates with approximately semi-orthogonal updates.