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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2603.17970 |
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| _version_ | 1866917351868334080 |
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| author | Southworth, Ben S. Thomas, Stephen |
| author_facet | Southworth, Ben S. Thomas, Stephen |
| contents | Orthogonalized-momentum optimizers such as Muon improve transformer training by approximately whitening/orthogonalizing matrix-valued momentum updates via a short polar-decomposition iteration. However, polar-factor approximations typically require multiple large matrix multiplications, and the resulting overhead can be substantial and hardware-dependent. We introduce MUD (MomentUm Decorrelation), a complementary whitening approach that replaces Muon's polar update with a triangular (Cholesky-like) whitening surrogate inspired by classical Gram--Schmidt and Gauss-Seidel ideas. We show that row-orthonormal matrices are fixed points of the MUD map, relate the inner step to symmetric Gauss-Seidel preconditioning of the Gram matrix, and prove quadratic local convergence near the fixed point. In terms of time-to-perplexity, MUD yields consistent 10-50\% wall-clock improvements over tuned AdamW and Muon in time-to-perplexity, typically converging slightly slower per step than Muon but with substantially lower optimizer overhead -- relative to Muon, MUD improves peak tokens/s by roughly $1.3-2.6\times$ across most settings and up to nearly $3\times$ on GPT-2 large on an A100. We also demonstrate training a ESM-2 150M protein language model, where MUD matches Muon-level validation perplexity in significantly less wall-clock time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17970 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Beyond Muon: MUD (MomentUm Decorrelation) for Faster Transformer Training Southworth, Ben S. Thomas, Stephen Machine Learning Numerical Analysis Optimization and Control Orthogonalized-momentum optimizers such as Muon improve transformer training by approximately whitening/orthogonalizing matrix-valued momentum updates via a short polar-decomposition iteration. However, polar-factor approximations typically require multiple large matrix multiplications, and the resulting overhead can be substantial and hardware-dependent. We introduce MUD (MomentUm Decorrelation), a complementary whitening approach that replaces Muon's polar update with a triangular (Cholesky-like) whitening surrogate inspired by classical Gram--Schmidt and Gauss-Seidel ideas. We show that row-orthonormal matrices are fixed points of the MUD map, relate the inner step to symmetric Gauss-Seidel preconditioning of the Gram matrix, and prove quadratic local convergence near the fixed point. In terms of time-to-perplexity, MUD yields consistent 10-50\% wall-clock improvements over tuned AdamW and Muon in time-to-perplexity, typically converging slightly slower per step than Muon but with substantially lower optimizer overhead -- relative to Muon, MUD improves peak tokens/s by roughly $1.3-2.6\times$ across most settings and up to nearly $3\times$ on GPT-2 large on an A100. We also demonstrate training a ESM-2 150M protein language model, where MUD matches Muon-level validation perplexity in significantly less wall-clock time. |
| title | Beyond Muon: MUD (MomentUm Decorrelation) for Faster Transformer Training |
| topic | Machine Learning Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/2603.17970 |