SignMuon: Communication-Efficient Distributed Muon Optimization
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914571072045056 |
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| author | Mishra, Neel Trivedi, Kushagara Kumar, Pawan |
| author_facet | Mishra, Neel Trivedi, Kushagara Kumar, Pawan |
| contents | Distributed training of large neural networks is bottlenecked by full-precision gradient communication and by coordinatewise optimizers that ignore the matrix structure of weight tensors. We propose Sign-Muon, a 1-bit, matrix-aware optimizer that combines majority-vote sign aggregation from signSGD with the polar-step framework of Muon. Each worker forms a Muon-style direction by taking the polar factor of its momentum via a Newton--Schulz iteration, transmits only the entrywise signs, and aggregates by majority vote; an optional local polar step further enforces orthogonality at no extra communication cost.
Under spectral-norm smoothness and bounded-variance stochastic gradients, the spectral-norm normalized sign step yields an $\mathcal{O}(1/\sqrt{T})$ nonconvex rate for an $\ell_1$-based stationarity measure. With unimodal symmetric noise, majority vote across $M$ workers cuts the stochastic term by $1/\sqrt{M}$, matching signSGD. In the $α$-$β$ model, distributed Sign-Muon needs only one integer sum-allreduce per iteration; all orthogonalization is local, giving a $32\times$ bandwidth reduction over float32 ($4\times$ for int8).
Across 330 CIFAR-10/ResNet-50 configurations Sign-Muon attains the best validation accuracy (92.15\%); its 4-GPU majority-vote variant reaches 92.02\% with 37\% less training time at matched effective batch. On nanoGPT, Sign-Muon achieves lower perplexity and better anytime performance than other sign-based baselines, with favorable weak-scaling up to 16 GPUs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16311 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | SignMuon: Communication-Efficient Distributed Muon Optimization Mishra, Neel Trivedi, Kushagara Kumar, Pawan Machine Learning Distributed, Parallel, and Cluster Computing Distributed training of large neural networks is bottlenecked by full-precision gradient communication and by coordinatewise optimizers that ignore the matrix structure of weight tensors. We propose Sign-Muon, a 1-bit, matrix-aware optimizer that combines majority-vote sign aggregation from signSGD with the polar-step framework of Muon. Each worker forms a Muon-style direction by taking the polar factor of its momentum via a Newton--Schulz iteration, transmits only the entrywise signs, and aggregates by majority vote; an optional local polar step further enforces orthogonality at no extra communication cost. Under spectral-norm smoothness and bounded-variance stochastic gradients, the spectral-norm normalized sign step yields an $\mathcal{O}(1/\sqrt{T})$ nonconvex rate for an $\ell_1$-based stationarity measure. With unimodal symmetric noise, majority vote across $M$ workers cuts the stochastic term by $1/\sqrt{M}$, matching signSGD. In the $α$-$β$ model, distributed Sign-Muon needs only one integer sum-allreduce per iteration; all orthogonalization is local, giving a $32\times$ bandwidth reduction over float32 ($4\times$ for int8). Across 330 CIFAR-10/ResNet-50 configurations Sign-Muon attains the best validation accuracy (92.15\%); its 4-GPU majority-vote variant reaches 92.02\% with 37\% less training time at matched effective batch. On nanoGPT, Sign-Muon achieves lower perplexity and better anytime performance than other sign-based baselines, with favorable weak-scaling up to 16 GPUs. |
| title | SignMuon: Communication-Efficient Distributed Muon Optimization |
| topic | Machine Learning Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2605.16311 |