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

NeurIPS 2026 · Probabilistic and scientific modeling › Variational and generative sampling · approach: Hamiltonian Monte Carlo · 0 citations (OpenAlex)

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Frames MCMC trajectory termination as a learned stopping policy within non-acyclic GFlowNets, training state-dependent stop classifiers with prefix trajectory balance and a multilevel extension for sampling unnormalized densities.

Problem

MCMC samplers use fixed or hand-tuned trajectory lengths, leading to slow mixing and high cost, and existing stopping rules are diagnostics that do not give reliable stopping guarantees.

Approach

Treat trajectory termination as learnable: state-dependent forward and backward classifiers decide when to stop, and the sampling dynamics are cast as a non-acyclic continuous GFlowNet trained with prefix trajectory balance plus flow regularization; a multilevel scheme interpolates between initial and target densities.

Key results

• On GMM9 (d=2), ULA w/ clf & corr reduces Sinkhorn distance to 0.221 vs 0.463 for ULA, with mean trajectory length 29.6 vs 10^4 for ULA.
• On Funnel (d=2), ULA w/ clf & corr achieves SD 4.947 vs 14.101 for ULA and ELBO -0.392 vs EUBO 1.005.
• Multilevel (L=5) achieves the best SD among proposed methods on GMM9 (d=40) at 152.3, versus DDS 180.2 and PIS 329.4, with mean trajectory length comparable to diffusion baselines (about 45-75 steps).

Surprising findings

• Classifier-based stopping alone improves trajectory length substantially, but sample-quality gains without learned forward corrections are limited.
• Distribution-matching diffusion samplers DDS are reported as slightly better than the proposed multilevel model on GMM9 MMD and ManyWell ELBO/EUBO.

Limitations

• Training uses fixed-length prefix sampling with classifiers disabled and requires a large N_max, adding optimization complexity.
• Assumes finite expected trajectory length, justified only via a lower bound on the classifier (epsilon=1e-5) rather than proven in general.
• Experiments are limited to low-dimensional synthetic targets and a single high-dimensional Digits task; the paper notes added learning components raise optimization difficulty.

Experimental setup

Datasets: GMM9 Funnel ManyWell Digits (NICE flow target on MNIST)

Benchmarks: GMM9 Funnel ManyWell Digits

Metrics: Sinkhorn distance MMD ELBO EUBO mean trajectory length

Baselines: ULA ULA with Gelman-Rubin stopping ULA with Geweke stopping PIS DDS

Builds on: non-acyclic GFlowNets prefix trajectory balance unadjusted Langevin algorithm annealed importance sampling Gelman-Rubin diagnostic

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