Near-Lipschitz stability of the Kim--Milman flow map
Sinho Chewi, Katharina Eichinger, Aram-Alexandre Pooladian
math.PR math.FA stat.ML
Abstract
We prove that the Kim--Milman flow map enjoys favorable stability properties with respect to variations in the target measure, provided that one of the target measures is sufficiently regular. Our results include stability in relative entropy, and more notably, Lipschitz stability in the $2$-Wasserstein distance up to a logarithmic factor. We complement our results with a general existence theorem for these maps for any target measure with finite second moment.
Topics
Classified with taxonomy v2 on Wed, 2 Sept 2026.