Why Can Latent Dynamics Models Adapt to Visual Shifts from a Few Examples?

Latent dynamics models built on pretrained foundation representations often adapt to dynamics-preserving visual shifts from only a few target-domain episodes. We explain this sample efficiency through the structure of the required functional correction. Much of this correction is globally shared across inputs and both statistically and optimization-wise accessible through low cross-episode latent variability and low-dimensional parameter updates. The state-dependent remainder is learned more gradually but concentrates in a substantially lower-dimensional subspace than under source-specific representations. Transport analysis link these structures to the interaction between representation geometry and pretrained dynamics. These findings show that foundation representations facilitate adaptation not merely through transferable features, but by structuring the functional change required to reuse source-trained dynamics across domains.