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Decentralized Online Riemannian Optimization for Strongly Geodesically Convex Functions

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We study decentralized online optimization for strongly geodesically convex (strongly g-convex) losses on Riemannian manifolds with bounded sectional curvature, including positively curved manifolds. In centralized Riemannian optimization, strong g-convexity…

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Lipschitzian SLLNs for random functions

We prove strong laws of large numbers for locally Lipschitz functions in the Lipschitz pseudometric. Our results hold under either a topological or a model-theoretic condition, with the latter encompassing functions jointly definable in o-minimal structures…

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Research arXiv

Expanding Flow Maps

Flow-based generative models have enabled remarkable progress in fast and controllable generation across continuous and discrete state spaces, yet existing parameterizations are constrained to fixed dimensions or fixed sequence lengths. Here, we introduce…

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