发表机构
Istituto Italiano di Tecnologia; University of Novi Sad; CMAP-Ecole Polytechnique; Télécom Sud-Paris; Université Paris Nanterre; University College London（意大利理工学院; 诺维萨德大学; 巴黎综合理工学院应用数学中心; 巴黎南电信学院; 巴黎南泰尔大学; 伦敦大学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出 Langevin 信息迁移学习（LITL），利用黑盒反馈从有偏源样本恢复目标 Langevin 动力学，学习谱结构与投影漂移，具备有限样本保证，并在分子模拟、生成模型和神经网络潜在引导中验证了有效性。
AI 中文摘要
许多科学和机器学习系统，从分子动力学到扩散模型乃至更广泛的领域，都受具有低维结构、在慢时间尺度上演化的随机动力学支配。然而，用于识别和解释此类动力学的目标轨迹往往难以获取：通常只能获得探索底层流形的有偏或静态样本。我们提出了 Langevin 信息迁移学习（LITL），一个仅利用黑盒反馈从有偏源样本恢复目标 Langevin 动力学的框架。LITL 通过 Dirichlet 表示学习学习目标无穷小生成元的主要谱结构和投影漂移，从而能够以谱形式进行动力学重建并估计慢流形梯度场。我们还引入了一个球形变体，非常适合将学习系统中常用的归一化潜在表示引导至期望目标。我们建立了在 Sobolev 范数下特征值、特征函数和投影漂移估计的有限样本保证，从而确保这些量及其一阶导数的泛化性。在实验上，LITL 从有偏分子模拟中恢复了物理转变时间尺度，从生成模型的静态样本中构建了动力学结构，重建了物理系统的球对称性，并在黑盒反馈下实现了对训练好的神经网络的事后潜在引导。这些结果共同将谱算子学习定位为在分布偏移下恢复随机动力学的实用框架，并为机器学习和物理科学中的应用开辟了道路。
英文摘要
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.
