arXiv:2509.07779v2 Announce Type: replace-cross Abstract: We study decentralized online Riemannian optimization over manifolds with possibly positive curvature, going beyond the Hadamard manifold setting. Decentralized optimization techniques rely on a consensus step that is well understood in Euclidean spaces because of their linearity. However, in positively curved Riemannian spaces, a main technical challenge is that geodesic distances may not induce a globally convex structure. In this work, we first analyze a curvature-aware Riemannian consensus step that enables a linear convergence beyo
This publication from arXiv continues to advance research in decentralized optimization, a foundational aspect of distributed AI systems, reflecting ongoing efforts to improve their mathematical underpinnings.
Improved decentralized optimization techniques, especially in non-Euclidean spaces, are critical for scalable and robust AI, particularly for multi-agent systems and federated learning applications.
The ability to perform decentralized online Riemannian optimization beyond Hadamard manifolds means that more complex, non-linear data structures and algorithmic designs can be efficiently supported in distributed AI.
- · AI researchers
- · Distributed AI developers
- · Companies implementing federated learning
- · Autonomous systems developers
- · Centralized compute architectures (relative to decentralized)
More sophisticated and efficient decentralized AI algorithms can be developed and deployed.
This could accelerate the development of complex multi-agent systems and decentralized decision-making in various applications.
These advancements might contribute to new architectures for general artificial intelligence, enabling more robust and adaptable systems.
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Read at arXiv cs.LG