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Langevin-Informed Transfer Learning: Replacing the Target Samples by Black-Box Feedback

NeurIPS 2026 · Probabilistic and scientific modeling › Dynamical systems · approach: State-space inference for stochastic systems

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Proposes Langevin-Informed Transfer Learning (LITL), which recovers the spectrum and projected drift of a target Langevin generator from biased or static source samples using importance weighting, Dirichlet/Sobolev representation learning, and generalized eigendecomposition, with a spherical variant for steering normalized latent representations.

Problem

Recovering target stochastic (Langevin) dynamics, including slow spectral structure and drift, from biased or static source samples without target trajectories, gradients, or retraining.

Approach

Learns the leading eigenspace of the resolvent of the target generator via a Dirichlet-energy HS loss with importance weights, then solves a generalized eigenproblem on the learned slow subspace to get eigenpairs and projected drift; the spherical variant uses uniform-measure source dynamics for gradient-free latent steering.

Key results

• On the double well, LITL eigenvalues match ground truth closely (e.g., 15.315 vs 15.37, 46.9 vs 47.31) while the compared baseline deviates more.
• Alanine dipeptide slowest eigenvalue changes from -0.56 (no reweighting) to -0.029 (reweighted), giving a physically meaningful timescale of about 350 versus about 2.
• Adult Income fairness experiment reduces TPR gap by about 94% (relative TPR gap 94.16%) at about 97% relative accuracy, comparable to retraining baseline.

Surprising findings

• Retraining and fine-tuning baselines achieve similar TPR gap reduction to LITL, despite LITL requiring no retraining or sensitive features.
• Removing audit feedback still yields roughly 50-60% TPR gap improvement.

Limitations

• Restricted to reversible Langevin dynamics
• Requires informative black-box evaluations and identifiable low-dimensional slow structure
• Fairness experiment is a proof-of-concept

Experimental setup

Datasets: Chignolin MD trajectories BioEmu samples Adult Income

Benchmarks: double well eigenvalues alanine dipeptide transition timescales Chignolin kinetics cobalt nanoparticle spectrum Adult Income fairness (TPR gap)

Metrics: eigenvalue error eigenfunction L2 error relative accuracy relative TPR gap

Baselines: prior generator-learning method (double well comparison) retraining baseline fine-tuning baseline latent correction baseline

Builds on: transfer operator methods Koopman operator learning TICA importance reweighting

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