Langevin-Informed Transfer Learning: Replacing Target Samples by Black-Box Feedback
Abstract
Many scientific and machine learning systems, from molecular dynamics to diffusion models and beyond, are governed by stochastic dynamics with low-dimensional structure, evolving on slow timescales. However, target trajectories, used to identify and interpret such dynamics, are often inaccessible: only biased or static samples that explore the underlying manifold are available. We introduce Langevin-Informed Transfer Learning (LITL), a framework for recovering target Langevin dynamics from biased source samples using only black-box feedback. LITL learns the leading spectral structure of the target infinitesimal generator and the projected drift through Dirichlet representation learning, enabling kinetic reconstruction in spectral form and slow-manifold gradient field estimation. We further introduce a spherical variant well suited to steering normalized latent representations commonly used in learning systems toward desired objectives. We establish finite-sample guarantees for eigenvalue, eigenfunction, and projected drift estimation in Sobolev norms, thereby ensuring generalization of these quantities and their first-order derivatives. Empirically, LITL recovers physical transition timescales from biased molecular simulations, builds kinetic structure from static samples of generative models, reconstructs spherical symmetries of physical systems, and enables post-hoc latent steering of trained neural networks under black-box feedback. Together, these results position spectral operator learning as a practical framework for recovering stochastic dynamics under distribution shift and unlock applications across machine learning and the physical sciences.
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BibTeX
@misc{kostic2026langevininformed,
title = {{Langevin-Informed Transfer Learning: Replacing Target Samples by Black-Box Feedback}},
author = {Vladimir R. Kostic and Karim Lounici and Hélène Halconruy and Timothée Devergne and Michele Parrinello and Massimiliano Pontil},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01522},
eprint = {2610.01522},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01522},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Langevin-Informed Transfer Learning: Replacing Target Samples by Black-Box Feedback
AU - Vladimir R. Kostic
AU - Karim Lounici
AU - Hélène Halconruy
AU - Timothée Devergne
AU - Michele Parrinello
AU - Massimiliano Pontil
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01522
UR - https://arxiv.org/abs/2610.01522
AB - Many scientific and machine learning systems, from molecular dynamics to diffusion models and beyond, are governed by stochastic dynamics with low-dimensional structure, evolving on slow timescales. However, target trajectories, used to identify and interpret such dynamics, are often inaccessible: only biased or static samples that explore the underlying manifold are available. We introduce Langevin-Informed Transfer Learning (LITL), a framework for recovering target Langevin dynamics from biased source samples using only black-box feedback. LITL learns the leading spectral structure of the target infinitesimal generator and the projected drift through Dirichlet representation learning, enabling kinetic reconstruction in spectral form and slow-manifold gradient field estimation. We further introduce a spherical variant well suited to steering normalized latent representations commonly used in learning systems toward desired objectives. We establish finite-sample guarantees for eigenvalue, eigenfunction, and projected drift estimation in Sobolev norms, thereby ensuring generalization of these quantities and their first-order derivatives. Empirically, LITL recovers physical transition timescales from biased molecular simulations, builds kinetic structure from static samples of generative models, reconstructs spherical symmetries of physical systems, and enables post-hoc latent steering of trained neural networks under black-box feedback. Together, these results position spectral operator learning as a practical framework for recovering stochastic dynamics under distribution shift and unlock applications across machine learning and the physical sciences.
ER -