Transport along Local Annealing Paths: Wasserstein Geometry and Multimodal Sampling
arXiv:2611.05605v1 Announce Type: new Abstract: Variational approaches to learning transport maps for multimodal sampling can suffer from mode collapse. One way to mitigate this problem is to learn transport along a prescribed path of intermediate distributions defined by geometric annealing. We show that annealing can take a substantial detour in Wasserstein space: when mass moves between modes, the path can be much longer than the distance between its endpoints. We further link path geometry to transport learning, showing that long annealing paths can slow population optimization, while suff
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