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This paper addresses critical bottlenecks in Federated Learning by integrating spectral optimization methods with communication compression and local steps, effectively removing restrictive assumptions on data heterogeneity. The approach demonstrates improved efficiency and robustness across standard benchmarks while maintaining rigorous convergence guarantees for distributed model training.
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Bridging Compressed Communication and Local Steps via Spectral Method in Federated Learning

arXiv2 min read

arXiv:2610.23434v1 Announce Type: new Abstract: Federated Learning (FL) enables collaborative training of complex models across large-scale networks of edge devices while keeping data localized. However, data heterogeneity and high communication overhead remain fundamental bottlenecks. Recently, the spectral optimizer Muon has demonstrated remarkable advantages over Adam-like methods in centralized training. While recent efforts have attempted to transition Muon to FL, naive integrations into traditional architectures fail short. Crucially, existing approaches do not support the the communication compression and local steps --- the two foundational techniques of efficient FL. To address this limitation, we introduce a novel spectral FL method that utilizes both local updates and compression. We establish rigorous convergence guarantees under mild assumptions, notably eliminating the restrictive bounded heterogeneity condition. Empirical evaluation on standard image classification benchmarks validates the efficiency and robustness of our approach.

Abstract:Federated Learning (FL) enables collaborative training of complex models across large-scale networks of edge devices while keeping data localized. However, data heterogeneity and high communication overhead remain fundamental bottlenecks. Recently, the spectral optimizer Muon has demonstrated remarkable advantages over Adam-like methods in centralized training. While recent efforts have attempted to transition Muon to FL, naive integrations into traditional architectures fail short. Crucially, existing approaches do not support the the communication compression and local steps --- the two foundational techniques of efficient FL. To address this limitation, we introduce a novel spectral FL method that utilizes both local updates and compression. We establish rigorous convergence guarantees under mild assumptions, notably eliminating the restrictive bounded heterogeneity condition. Empirical evaluation on standard image classification benchmarks validates the efficiency and robustness of our approach.

Machine Learning (cs.LG)

arXiv:2610.23434 [cs.LG]

(or arXiv:2610.23434v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.23434 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Full text under the publisher's open licence · 224 words

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