Data geometry makes time identifiable from noisy interpolants at rate O(1/sqrt(d-k)), rendering the time-blindness gap asymptotically negligible relative to coupling variance.
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UNVERDICTED 7representative citing papers
Gaussian particles in a linearized Bures-Wasserstein space perform consensus optimization for variational inference and outperform deterministic gradient methods on low-dimensional non-log-concave targets.
Provides asymptotic distributions for entropic OT plans and potentials under vanishing regularization and links self-transport barycentric projections to score functions.
Establishes Kantorovich duality for linearized non-quadratic quantum optimal transport realized by channels, determines optimal primal-dual solutions for qubits under state restrictions, and proves the triangle inequality for the square of the induced quantum Wasserstein divergences.
Short histories of observations can recover the underlying manifold for transporting discontinuous densities when direct source-target pairs are insufficient due to folds or marginalization.
Proves Monge well-posedness and OT-map regularity for linear-quadratic costs (extending Hindawi-Pomet-Rifford 2011 to non-negative costs) and obtains general entropy interpolation inequalities.
A mirror descent algorithm computes exact Wasserstein barycenters for mixed discrete and continuous input measures with convergence guarantees.
citing papers explorer
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What Time Is It? How Data Geometry Makes Time Conditioning Optional for Flow Matching
Data geometry makes time identifiable from noisy interpolants at rate O(1/sqrt(d-k)), rendering the time-blindness gap asymptotically negligible relative to coupling variance.
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Variational inference via Gaussian interacting particles in the Bures-Wasserstein geometry
Gaussian particles in a linearized Bures-Wasserstein space perform consensus optimization for variational inference and outperform deterministic gradient methods on low-dimensional non-log-concave targets.
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The entropic optimal (self-)transport problem: Limit distributions for decreasing regularization with application to score function estimation
Provides asymptotic distributions for entropic OT plans and potentials under vanishing regularization and links self-transport barycentric projections to score functions.
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Strong Kantorovich duality for quantum optimal transport with generic cost and optimal couplings on quantum bits
Establishes Kantorovich duality for linearized non-quadratic quantum optimal transport realized by channels, determines optimal primal-dual solutions for qubits under state restrictions, and proves the triangle inequality for the square of the induced quantum Wasserstein divergences.
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A geometric approach to the transport of discontinuous densities
Short histories of observations can recover the underlying manifold for transporting discontinuous densities when direct source-target pairs are insufficient due to folds or marginalization.
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Linear quadratic optimal transport and interpolation inequalities
Proves Monge well-posedness and OT-map regularity for linear-quadratic costs (extending Hindawi-Pomet-Rifford 2011 to non-negative costs) and obtains general entropy interpolation inequalities.
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A Unified Approach for Computing Wasserstein Barycenters of Discrete and Continuous Measures
A mirror descent algorithm computes exact Wasserstein barycenters for mixed discrete and continuous input measures with convergence guarantees.