Stop the Sampler! Classifier-Based Adaptive Stopping for Sampling Kernels

2026-06-16 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, extended

Summary

The article proposes a novel framework for adaptive MCMC sampling, addressing the slow mixing and high computational costs associated with fixed or manually tuned trajectory lengths. It leverages non-acyclic Generative Flow Networks (GFlowNets) to train state-dependent neural classifiers that dynamically decide when a sampling trajectory has reached a high-density region and should terminate. The authors theoretically connect optimal classifiers to the target density through detailed balance conditions and introduce a multilevel training scheme to enhance exploration in complex geometries. Experimental evaluations on benchmark densities like GMM9, Funnel, ManyWell, and Digits (d=196) demonstrate that this approach significantly reduces average trajectory lengths while improving mode coverage and mixing compared to standard MCMC baselines such as ULA, ULA RG, and ULA Geweke. The full model, incorporating learned forward kernels, further boosts approximation quality, achieving lower Sinkhorn distance and MMD.

Key takeaway

For Machine Learning Engineers optimizing MCMC sampling, consider integrating GFlowNet-based adaptive stopping. This approach dynamically shortens trajectories in high-density regions, significantly reducing computational costs and improving mode coverage compared to fixed-length methods. You should explore the multilevel scheme for complex, high-dimensional distributions to stabilize learning and enhance exploration, potentially outperforming traditional diffusion samplers.

Key insights

Adaptive MCMC stopping can be learned via GFlowNet-trained neural classifiers, dynamically optimizing trajectory lengths for efficiency.

Principles

• MCMC trajectory termination can be a learnable component.
• Optimal stopping policies connect to target density via detailed balance.
• Minimizing total flow reduces expected trajectory lengths.

Method

Train state-dependent neural classifiers using a non-acyclic GFlowNet framework with a prefix trajectory balance objective and flow regularization. Employ a multilevel scheme for complex geometries.

In practice

• Implement neural classifiers to dynamically stop MCMC trajectories.
• Apply flow regularization to encourage shorter sampling paths.
• Use a multilevel approach for high-dimensional or multimodal targets.

Topics

• Markov Chain Monte Carlo
• Generative Flow Networks
• Adaptive Sampling
• Neural Classifiers
• Bayesian Inference
• Multimodal Distributions

Code references

• kkorolev1/stop-the-sampler
• DenisBless/variational_sampling_methods

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

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