New Riemannian geometry for Sinkhorn divergence established

Researchers have developed a new framework for understanding the geometry of Sinkhorn divergence, a widely used measure in optimal transport. This work establishes a formal Riemannian structure and derives key geometric operations like geodesic and parallel transport equations. The findings also demonstrate that these operations lead to $\sqrt{n}$-limiting Gaussian processes for estimators, with consistent nonparametric bootstrap results. AI

IMPACT Establishes new theoretical foundations for geometric operations in optimal transport, potentially impacting future AI model development and analysis.

RANK_REASON The item is an academic paper detailing new theoretical contributions to the geometry of optimal transport methods. [lever_c_demoted from research: ic=1 ai=1.0]

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• Banach space ODE theory
• Gaussian Processes
• Hadamard differentiability
• Levi-Civita covariant derivative
• metric tensor
• optimal transport
• Reproducing kernel Hilbert space (RKHS)
• Sinkhorn divergence
• Wasserstein distance

• paper
• other

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