SignMuon: Communication-Efficient Distributed Muon Optimization
SignMuon is a 1-bit, matrix-aware optimizer that combines majority-vote sign aggregation from signSGD with the polar-step framework of Muon. It achieves non-convex convergence rate of O(1/√T) under spectral-norm smoothness and bounded-variance stochastic gradients. Evaluated on 330 CIFAR-10/ResNet-50 configurations, SignMuon attains the best validation accuracy of 92.15%; its 4-GPU majority-vote variant reduces training time by 37% at matched effective batch. On nanoGPT, SignMuon achieves lower perplexity and better anytime performance, with favorable weak-scaling up to 16 GPUs.
[2605.16311] SignMuon: Communication-Efficient Distributed Muon Optimization
[Submitted on 4 May 2026]
Title:SignMuon: Communication-Efficient Distributed Muon Optimization
View a PDF of the paper titled SignMuon: Communication-Efficient Distributed Muon Optimization, by Neel Mishra and 2 other authors
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Abstract: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 $\alpha$-$\beta$ 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.
Comments: 40 pages, 9 figures
Subjects:
Machine Learning (cs.LG); Distributed, Parallel, and Cluster Computing (cs.DC)
Cite as: arXiv:2605.16311 [cs.LG]
(or arXiv:2605.16311v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2605.16311
arXiv-issued DOI via DataCite
Submission history
From: Pawan Kumar [view email] [v1] Mon, 4 May 2026 13:29:55 UTC (240 KB)
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