arXiv:2510.01377v2 Announce Type: replace-cross Abstract: In this paper, we propose DeMuon, a method for decentralized matrix optimization over a given communication topology. DeMuon incorporates matrix orthogonalization via Newton-Schulz iterations-a technique inherited from its centralized predecessor, Muon-and employs gradient tracking to mitigate heterogeneity among local functions. Under heavy-tailed noise conditions and additional mild assumptions, we establish the iteration complexity of DeMuon for reaching an approximate stochastic stationary point. This complexity result matches the b
The paper 'DeMuon: A Decentralized Muon for Matrix Optimization over Graphs' (published June 3, 2026) reflects ongoing research in distributed optimization techniques for AI, addressing scalability and robustness in complex computational environments.
This development is crucial for advancing decentralized AI systems, enabling more resilient and scalable machine learning applications across various domains, especially in scenarios with privacy constraints or distributed data sources.
The introduction of DeMuon offers a new method for decentralized matrix optimization, potentially leading to more efficient and robust training of large-scale AI models in distributed settings, even under challenging conditions like heavy-tailed noise.
- · Distributed AI platforms
- · Edge computing providers
- · Researchers in optimization and machine learning
- · Centralized compute architectures that struggle with scalability
- · Systems highly sensitive to data heterogeneity
Improved performance and reliability of decentralized machine learning algorithms.
Accelerated development and deployment of federated learning and multi-agent AI systems in sensitive sectors like finance or healthcare.
Enhanced resilience of critical AI infrastructure against single points of failure or adversarial attacks, fostering a more distributed and robust AI ecosystem.
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