Theoretical guidelines for annealed Langevin dynamics in compositional simulation-based inference

2026-05-21 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences, Data Science & Analytics · Depth: Expert, extended

Summary

The paper presents theoretical guidelines for tuning annealed Langevin dynamics hyperparameters in compositional simulation-based inference (SBI). Existing compositional score-based SBI methods, like those by Geffner et al. and Linhart et al., aggregate individual posterior scores, but direct sampling via reverse SDE introduces irreducible bias. Annealed Langevin dynamics offers a principled alternative by sampling from a sequence of tractable bridging densities. Previously, its hyperparameters (step sizes, steps per level, annealing levels) were empirically tuned. This work derives Wasserstein bounds for annealed Langevin with approximate scores, translating them into explicit decision rules for these hyperparameters to guarantee a prescribed sampling accuracy. In a Gaussian setting, closed-form expressions show Linhart's bridging densities consistently allow larger step sizes and fewer total Langevin steps than Geffner's. Empirical results confirm this tuning generalizes to more complex, non-Gaussian problems, demonstrating Linhart's composite score yields a more efficient sampler.

Key takeaway

For Machine Learning Engineers or AI Scientists implementing compositional simulation-based inference, you should adopt the proposed theoretical guidelines for tuning annealed Langevin dynamics. This allows you to achieve a prescribed sampling accuracy without empirical hyperparameter tuning. Specifically, prioritize Linhart's composite score formulation, as it consistently enables larger step sizes and requires fewer total Langevin steps compared to Geffner's, leading to more efficient sampling across various inference tasks, including non-Gaussian settings.

Key insights

Theoretical guidelines for annealed Langevin dynamics hyperparameters ensure sampling accuracy in compositional SBI, favoring Linhart's method.

Principles

• Wasserstein bounds can quantify sampling accuracy for annealed Langevin with approximate scores.
• Log-concavity and smoothness properties of bridging densities are crucial for theoretical guarantees.
• Compositional score choice directly impacts optimal step sizes and total steps in annealed Langevin.

Method

Derive Wasserstein bounds for annealed Langevin with approximate scores. Translate bounds into explicit decision rules for step sizes (h_t) and number of steps (k_t) per annealing level, given a target accuracy γ and bias-variance split ω.

In practice

• Use derived formulas to set annealed Langevin h_t and k_t for guaranteed sampling accuracy.
• Prefer Linhart's composite score for more efficient sampling (larger steps, fewer total steps).
• Apply Gaussian-derived tuning rules as a robust starting point for non-Gaussian SBI problems.

Topics

• Simulation-Based Inference
• Annealed Langevin Dynamics
• Wasserstein Distance
• Score-Based Generative Models
• Hyperparameter Optimization
• Compositional Modeling

Best for: AI Scientist, Machine Learning Engineer, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.