AF-Muon: An AdamW-Free Muon Optimizer for Tied-Embedding Models
Muon improves large-scale training by applying a spectral-norm steepest-descent update to matrix parameters, but practical models also contain parameter blocks that do not fit dense-matrix geometry. One important case is the tied vocabulary table, which appears in language models and other token generators and can receive multiple structurally different gradient sources, from sparse input lookups to dense output-classifier updates. In the reference recipe these blocks are handed to an auxiliary AdamW optimizer, which restores second-moment state and updates the aliased table as a generic tensor. We propose AF-Muon, an AdamW-free extension of Muon that keeps the Muon matrix update for hidd...
| Authors | Arash Lagzian, Paniz Halvachi, Junming Zhang et al. |
|---|---|
| Primary category | cs.LG |
| Published | 1 October 2026 |
| Last updated at source | 1 October 2026 |
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