Proves near-Lipschitz stability in 2-Wasserstein distance (up to log factor) and relative entropy stability for the Kim-Milman flow map w.r.t. target measure perturbations under regularity assumptions, with existence for finite second moment targets.
Stability of optimal transport maps on Riemannian manifolds
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CDOT is introduced as the first convex OT framework that preserves feature correspondence and geometry via operator regularization, proven as a pseudometric with non-asymptotic risk bounds and empirical gains over GW.
Lipschitz L² stability estimates for OT maps in terms of 2-MK distance (and C^{1,α} under Hölder) plus explicit second variation of quadratic MK distance via Monge-Ampère linearization.
The paper characterizes stability of the Kim-Milman flow map with respect to target measure variations measured in relative Fisher information.
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Near-Lipschitz stability of the Kim--Milman flow map
Proves near-Lipschitz stability in 2-Wasserstein distance (up to log factor) and relative entropy stability for the Kim-Milman flow map w.r.t. target measure perturbations under regularity assumptions, with existence for finite second moment targets.
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Convex Distance Operator Transport: A Convex and Geometry-Preserving Formulation
CDOT is introduced as the first convex OT framework that preserves feature correspondence and geometry via operator regularization, proven as a pseudometric with non-asymptotic risk bounds and empirical gains over GW.
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Stability of optimal transport maps and second variation of the 2-Monge-Kantorovich distance
Lipschitz L² stability estimates for OT maps in terms of 2-MK distance (and C^{1,α} under Hölder) plus explicit second variation of quadratic MK distance via Monge-Ampère linearization.
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Stability of the Kim--Milman flow map
The paper characterizes stability of the Kim-Milman flow map with respect to target measure variations measured in relative Fisher information.