Langevin-Informed Transfer Learning: Replacing Target Samples by Black-Box Feedback
This study addresses the challenge of extracting low-dimensional slow dynamics in stochastic dynamical systems where target trajectories are inaccessible and only biased samples are available. To this end, we propose the LITL framework, which relies solely on black-box feedback. By leveraging Dirichlet representation learning, the method captures the spectral structure and projected drift of the target infinitesimal generator, while introducing spherical variants to optimize the guided control of normalized latent representations, thereby achieving Langevin dynamics reconstruction via spectral operator learning. Experimental results demonstrate that the proposed approach successfully recovers physical timescales and spherical symmetry from biased simulations, establishes a dynamical structure for generative models, and enables post-hoc guided control within the latent space.