Adaptive Sampling

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Overview

Adaptive sampling studies how to choose which examples, measurements, or computational steps to spend a limited budget on. Common approaches use uncertainty, prediction error, information gain, or difficulty to guide active learning, Bayesian experimental design, bandit allocation, and adaptive numerical solvers; learned policies, including reinforcement learning, are also used. Applications range from scientific experiments and sensor acquisition to diffusion-model sampling and test-time reasoning with language models. A central challenge is ensuring that the signals used to prioritize samples reliably improve the final task without sacrificing coverage, introducing bias, or costing more to compute than they save.

Latest papers

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202 papers37 papers in the last four weeks, up 106% on the four weeks before. 0.2% of all new papers.

Jul 3, 2026

BFMT: Enhancing Search Capabilities of Tree Sampler via Bootstrap Flow-Map Tree

The ability to efficiently navigate high-dimensional spaces to identify optimal candidates-whether designing targeted molecular structures or generating images with preferred attributes-stands as a central pillar of modern scientific progress. Recent tree-based samplers enable highly scalable inference-time search by eliminating the reward-gradient bottleneck inherent to particle-based methods. Despite their potential, existing tree-based samplers are fundamentally constrained by the massive number of function evaluations (NFEs) required for node valuation, crippling their utility in exploration-heavy tasks. Furthermore, their reliance on small, uniform transitions at each depth precludes dynamic, adaptive search capabilities. To address this, we introduce Bootstrap Flow-Map-Tree (a.k.a BFMT), a computationally efficient sampling framework that enables full tree-path construction from any tree depth using a single function evaluation, drastically reducing computational overhead while providing critical foresight for sequential sampling. By enabling dynamic transition time-step scheduling, BFMT efficiently allocates its sampling budget, smoothly transitioning from broad global exploration to fine-grained local refinement of high-utility modes discovered through exploration. Extensive experiments and ablation studies across diverse domains-from high-dimensional images to large-scale molecules-demonstrate BFMT's superiority over baseline approaches in both search and alignment tasks.

Binglin Ji, Anindya Sarkar, Hengchang Lu +4

Department of CSE, Washington University in St.Louis, USA · Department of Information Technology, Uppsala University, Sweden

Inference-Time SearchImage GenerationAdaptive SamplingMolecule Design
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Jul 2, 2026

Adaptive Reparametrized Time for Score-Based Diffusion Sampling

We study timestep allocation for score-based diffusion sampling, where a learned reverse-time dynamics is discretized on a finite grid. Uniform and hand-crafted schedules are standard choices, but they rely on fixed prescriptions and can therefore be suboptimal. To address this limitation, we propose Adaptive Reparameterized Time (ART), a continuous-time control formulation that learns a time change by treating the speed of the sampling clock as the control, so that a uniform grid on the learned clock induces adaptive timesteps in the original diffusion time. Based on a leading-order Euler error surrogate, ART provides a principled objective for allocating timesteps along the sampling trajectory. To solve this deterministic control problem, we introduce ART-RL, an auxiliary randomized formulation with Gaussian policies that turns schedule learning into a continuous-time reinforcement learning problem. We prove that the randomized ART-RL formulation is equivalent to ART at the optimizer level, in the sense that its optimal Gaussian policy recovers the optimal ART time-warping rate through its mean. We further establish policy evaluation and policy improvement characterizations and derive trajectory-based moment identities that yield implementable actor--critic updates for learning the schedule. Across experiments ranging from controlled low-dimensional settings to image generation, ART-RL can be plugged into existing diffusion samplers by changing only the timestep grid, consistently improving sample quality over strong baseline schedules at matched budgets while leaving the rest of the sampling pipeline unchanged. The learned schedules also exhibit broad generalization, transferring without retraining across sampling budgets, datasets, solvers, pipelines, and representation spaces.

Yilie Huang, Wenpin Tang, Xun Yu Zhou

Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong. · Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027, USA. · Department of Industrial Engineering and Operations Research and Data Science Institute, Columbia University, New York, NY 10027, USA.

Diffusion SamplingAdaptive SamplingRL for Diffusion ModelsDiffusion Timestep Scheduling
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Jun 25, 2026

Accelerated sampling using SamAdams variable timesteps and position-adaptive Langevin dynamics

We introduce an accelerated Langevin-based sampling method that is based on two complementary devices: SamAdams adaptive timestepping, which automatically shrinks the effective integration step in stiff regions of phase space using a relaxed stiffness monitor, and position-adaptive Langevin (PAL) dynamics, which concentrates friction along the local force direction while preserving the canonical distribution as the exact invariant measure. The resulting combined scheme (SA-PAL) is implemented in a palindromic integrator which requires only one force evaluation per iteration through suitable organisation of the integration steps and by exploiting the rank-one-plus-scalar structure of the PAL friction tensor. We test the method on various model problems: the Rosenbrock function, a thin entropic channel, the Mueller-Brown potential, and a Bayesian parameterisation problem with a sparsity-inducing shrinkage prior. On the Rosenbrock and Mueller-Brown potentials mixing rates are improved by 1.5-3 times compared to fixed stepsize integration. Efficiency gains of more than an order of magnitude are documented in the other examples.

Benedict Leimkuhler, Peter A. Whalley

School of Mathematics, University of Edinburgh, Edinburgh, UK. · Seminar for Statistics, Department of Mathematics, ETH Zürich, Zürich, Switzerland.

Langevin DynamicsPosterior SamplingAdaptive SamplingNumerical Integration
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Jun 23, 2026

QC-SMOTE: Quality-Controlled SMOTE for Imbalanced Classification

Class imbalance poses a significant challenge in classification, where existing methods such as SMOTE often generate low-quality synthetic samples in regions with noise or class overlap. We propose QC-SMOTE, a quality-controlled oversampling framework that estimates minority sample reliability using a composite neighbourhood trustworthiness score combining local density, safe-level, and isolation from the majority class. Synthetic candidates are generated using an IPQ-guided best-of-K strategy that evaluates midpoint purity and, when required, majority clearance, with allocation guided by sample reliability and boundary informativeness. Generation behaviour adapts across overlap--imbalance regimes, adjusting interpolation range and selection criteria to match local data geometry. Low-quality synthetic samples are replaced with original minority duplicates when neighbourhood purity falls below an adaptive threshold, providing graceful degradation by reverting to duplication in severely noisy regions. Experiments on 30 imbalanced datasets using repeated stratified cross-validation show that QC-SMOTE achieves the strongest average AUC-ROC and Macro F1 among the compared oversampling methods, with particularly clear gains under moderate and severe imbalance. These results demonstrate the importance of quality-aware, geometry-adaptive synthetic sampling for robust imbalanced classification.

Parth Upman, Shreyank N Gowda

School of Computer Science, University of Nottingham, Jubilee Campus, Wollaton Road, Nottingham, NG8 1BB, United Kingdom

Class-Imbalanced LearningSynthetic Data AugmentationAdaptive Sampling
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Jun 22, 2026

Dynamic estimation of slowly varying sequences

We consider the problem of sequentially approximating functions of each element in a slowly-varying sequence, i.e. one where the magnitude αiα_i of the difference between the elements at positions ii and i−1i-1 is small. Recent work on implicit trace estimation shows that when αtα_t is small, reusing queries to past sequence elements can reduce the overall cost [Dharangutte & Musco, NeurIPS2021; Woodruff et al., NeurIPS2022]. We introduce a framework generalizing this to a variety of linear and nonlinear functions on diverse vector spaces, obtaining novel sequential estimation results for matrix powers, spectral densities, Monte Carlo integration, and a boundary value problem from partial differential equations~(PDEs). Furthermore, we develop a novel algorithm for use with this framework that locally scales the estimation budget with αtα_t, obtaining sharper path-length-style variation bounds of form O(∑i=1mαi)\mathcal O(\sum_{i=1}^mα_i) on the cost of estimating a sequence of length mm. This improves upon the previous implicit trace estimation bound of O(m⋅max⁡iαi)\mathcal O(m\cdot\max_iα_i) [Dharangutte & Musco, NeurIPS~2021], which is achieved by fixing the query budget using the worst-case αiα_i and is thus inefficient for stable sequences with rare bursts. Lastly, while all past work assumes a known bound on αiα_i, we show in certain cases how the changes can be estimated on-the-fly with (nearly) no added cost. In summary, our framework makes the sequential approximation toolkit general-purpose and adaptive while improving upon state-of-the-art-guarantees for dynamic trace estimation.

Prashant Gokhale, Mikhail Khodak, Sandeep Silwal

University of Wisconsin–Madison

Adaptive Sampling
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Jun 22, 2026

FPAS: Frontier-Based Path Planning with Adaptive Sampling for Large-Scale Unknown Environments

In this work, we propose Frontier-based Path Planning with Adaptive Sampling (FPAS), a novel framework designed for efficient goal-reaching in large-scale, unknown environments. While existing planners often struggle with computational bottlenecks or inefficient paths during long-range navigation, FPAS overcomes these challenges by reinterpreting the frontier concept for goal-directed tasks. Specifically, our method leverages frontiers to effectively guide forward progression into unobserved regions and to select promising subgoals for backtracking from dead-ends or inefficient paths. Furthermore, FPAS introduces an adaptive sampling mechanism based on a frontier-derived openness metric. This mechanism dynamically adjusts the global graph's density by employing sparse nodes in open areas to alleviate computational burdens, while preserving denser sampling in narrow passages to ensure connectivity. Extensive evaluations demonstrate that FPAS substantially improves computational efficiency over baseline methods while maintaining highly competitive goal-reaching performance.

Jinwoo Choi, Yeonkyu Lee, Jung-Taak Kim +2

Department of Electrical and Computer Engineering, Seoul National University, Seoul, South Korea

Robot NavigationAdaptive SamplingRobot Motion PlanningSampling-Based Motion Planning
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Jun 20, 2026

Ranking-and-Selection with Multiple Correct Answers and Non-Answerable Estimates

We study fixed-precision ranking-and-selection in structured settings where the answer may be non-unique and where noisy estimates may temporarily admit no valid answer at all. This phenomenon arises naturally in problems such as multi-fidelity ranking-and-selection and identifying a Condorcet winner from pairwise comparisons. To address this, we propose a unified framework based on answer-wise acceptance sets, restricted generalized likelihood ratio stopping, and an answer-pitfall decomposition that yields a max-max-min characteristic value and a common sampling principle. We introduce ENDS, a general procedure that combines estimation, nomination, pitfall detection, and cost-aware information-directed selection. We instantiate ENDS for various problems by deriving explicit formulas. Extensive numerical experiments show that this unified recipe performs well across a broad range of pure-exploration problems and offers a practical framework and proof-of-concept algorithmic recipe.

Qiaoqiao Wang, Wei You

Dept. of Industrial Engineering and Decision Analytics, The Hong Kong University of Science and Technology, Hong Kong, China

Best-Arm IdentificationAdaptive SamplingSequential Hypothesis Testing
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Jun 19, 2026

Adaptive Beam Selection for Efficient Scanning Probe Tomography

In X-ray tomography, reconstruction quality generally improves with larger numbers of projections. However, more projections increase experiment costs, acquisition time and the radiation dose imparted to the sample. One mitigation to these trade-offs is to adopt a sequential design of experiments, in which each subsequent measurement is determined as a function of previously acquired data in order to maximize information gain. In practice, a widely used heuristic to maximize information is to align beams with the edges of the sample. A key challenge, however, is that the true sample is unknown, so identifying edge-aligned beams typically requires reconstructing the sample based on available measurements. This work proposes a novel sequential design method that identifies edge-aligned measurements directly from the sinogram, bypassing any reconstruction, thereby improving computational efficiency and reducing the experimental design's susceptibility to reconstruction errors. Our method dynamically selects the next set of measurement beams by maximizing an acquisition function that balances exploration and exploitation over the domain of all possible measurements, improving reconstruction quality while reducing measurement redundancy.

San Dinh, Zichao Wendy Di, Matt Menickelly

Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, IL, 60439, USA

Image ReconstructionSequential Experimental DesignAdaptive SamplingBayesian Experimental DesignComputed Tomography
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Jun 19, 2026

Subsampling for supervised learning in reproducing kernel Hilbert spaces

In the era of big data, subsampling became a common practice in statistical learning. By selecting a subgroup of individuals based on which the learner is trained, subsampling aims at reducing the computational cost and time of the estimation step, and ideally leads to a decrease of its energy consumption and carbon footprint. This work focuses on a nonparametric setting, in which the hypotheses set lies in a reproducing kernel Hilbert space, and the estimator is a minimizer of an empirical risk reweighted à la Horvitz-Thompson. By studying the asymptotic properties of this estimator, we reveal an optimal subsampling scheme (regarding the trace of the covariance operator) and show that it can be used via plug-in. A numerical study on synthetic and real-world datasets shows the practicability and the benefit of the proposed approach.

Eyal Vayness, Maxime Sangnier

Sorbonne Universit´e, LPSM, Paris, France

Importance SamplingAdaptive SamplingReproducing Kernel Hilbert SpacesStatistical Learning Theory
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Jun 18, 2026

CELEUS: Certifiable and Efficient LLM Evaluation via E-Processes

Can we trust evaluation scores to capture an LLM's true real-world performance? Certifiable evaluation answers this question by providing guarantee for LLM evaluation. In particular, existing methods sequentially curate evaluation samples and keep updating confidence intervals (CIs) that cover the true performance with high probability (e.g., 95%) until some conditions are satisfied, e.g., the CI width reaches a target precision. However, existing methods are not generally anytime-valid: the claimed coverage (e.g., 95%) may fail when CIs are repeatedly updated and used to decide when to stop, leaving a gap between theoretical rigor and practice. This paper bridges this gap by proposing Celeus, a Certifiable framework for Efficient LLM evaluation, which leverages E-processes to build anytime-valid CIs. Concretely, we propose signals that combine two ingredients: (i) Uncertainty-guided sampling to select informative samples for evaluation, and (ii) Surrogate-assisted approximations for unevaluated samples. We prove that such signals remain unbiased for the evaluation score conditional on the past, enabling statistically-grounded and anytime-valid ee-process CIs. More importantly, the two ingredients reduce estimation variance and help reach the target precision with fewer evaluated samples. We also prove that CIs obtained by Celeus can shrink at a near-parametric rate up to logarithmic factors and analyze the oracle variance-optimal sampling rule that motivates the empirical uncertainty-guided one. Experiments show that Celeus reaches the target precision using 54-62% fewer evaluated samples than baselines, while preserving anytime-valid coverage.

Zhijian Zhou, Zesheng Ye, Zhaorun Chen +2

The University of Melbourne · Department of Computer Science, University of Chicago · Department of Computer Science, University of Illinois Urbana-Champaign

LLM EvaluationAnytime-Valid InferenceAdaptive SamplingUncertainty Sampling
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Jun 16, 2026

Video2Code: Generating Interactive Webpages from UI Videos via Action-Aware Revisit

UI videos provide a natural input for generating interactive webpages, as they capture both webpage appearance and action-triggered state transitions. However, directly applying video-capable vision-language models to this task remains insufficient. Existing models typically rely on sparse sampling or compressed temporal representations, which may miss short action boundaries and break the state-action-state transitions needed to implement webpage behavior. We formulate UI video-to-code generation as executable state-transition recovery from interaction videos, and identify this failure mode as state-transition misalignment. We introduce Video2Code, an action-aware video-to-code approach for recovering executable UI state transitions. Rather than allocating the visual budget uniformly across the video, Video2Code first performs coarse video understanding to locate action-critical regions, then invokes a temporal clipping tool to revisit these regions at higher temporal resolution before generating HTML/CSS/JavaScript code. We instantiate Video2Code with action-aligned video-code supervision and evaluate it under both visual and functional criteria. Experiments show that Video2Code substantially strengthens the underlying open-source model for UI video-to-code generation, improving functional correctness over direct video observation, especially on dense multi-step interactions.

Mingde Xu, Zhen Yang, Yan Wang +7

University of Waterloo · Tsinghua University · Zhipu AI +1

Web Application GenerationAdaptive SamplingAdaptive Video Frame Sampling
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Jun 15, 2026

Uncertainty Quantification of Engineering Structures by Polynomial Chaos Expansion and Multivariate Active Learning

In many engineering applications, a single high-fidelity model produces multiple quantities of interest (QoIs) under the same input parameters, e.g. finite element models of complex physical systems. To alleviate the high computational cost of direct model evaluations, surrogate models are widely used to construct efficient approximations of model responses. Naturally, the accuracy of surrogates strongly depends on the quality of the experimental design (ED). However, a single ED may not provide an adequate representation for all outputs simultaneously, especially when different outputs exhibit varying sensitivities to the input variables. A straightforward solution is to perform separate sampling for each output, but this results in increased sampling complexity and computational cost. From a statistical perspective, such an approach also ignores potential correlations among all outputs and may compromise data consistency. To address this issue, an adaptive sequential sampling method for constructing polynomial chaos expansion surrogate models is generalized for vector valued QoIs. The method sequentially selects new samples from a candidate pool based on their local contribution to the output variance, while balancing distance-based exploration of the input space and exploitation of aggregated variance information across all outputs. Its performance is compared with non-sequential Latin Hypercube Sampling through several numerical examples from engineering problems. Numerical results demonstrate that the proposed strategy improves both surrogate accuracy and stability, and provides a more reliable estimation of second-order statistics.

Qitian Lu, Jafar Jafari-Asl, Panagiotis Spyridis +1

Brno University of Technology, Brno, Czech Republic · University of Rostock, Rostock, Germany

Surrogate ModelingUncertainty QuantificationAdaptive Sampling
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Jun 15, 2026

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

Sampling from complex, unnormalized probability densities is a fundamental challenge in Bayesian inference and probabilistic modeling. While Markov chain Monte Carlo (MCMC) methods provide asymptotic guarantees, they often suffer from slow mixing and high computational costs due to fixed or manually tuned trajectory lengths. In this work, we propose a novel framework that treats trajectory termination as a learnable component of the sampling dynamics. By framing MCMC within the theory of non-acyclic generative flow networks (GFlowNets), we train state-dependent neural classifiers to decide when a trajectory has reached a high-density region and should terminate. We theoretically establish the connection between optimal classifiers and the target density via detailed balance conditions and introduce a multilevel training scheme to facilitate exploration in complex geometries. Experimental results across various benchmark densities demonstrate that our approach significantly reduces average trajectory lengths while improving mode coverage and mixing compared to standard MCMC baselines.

Kirill Korolev, Nikita Morozov, Stepan Pavlenko +2

1HSE University · University of Edinburgh · 3CIFAR Fellow.

Markov Chain Monte CarloBayesian InferenceAdaptive Sampling
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Jun 12, 2026

A Complexity Measure for Active Learning in Multi-group Mean Estimation

We study a max-risk objective for active learning in a multi-group mean estimation dd-armed bandits: a learner adaptively allocates a budget of TT samples across dd groups to minimize the worst-case uncertainty index max⁡k∈[d]σk2/nk\max_{k\in[d]}σ_k^2/n_k, where σkσ_k is the standard deviation of the distribution of arm dd, and nkn_k is the number of times arm dd is sampled. We develop a local minimax framework and prove the first general lower bound for this objective, valid for any finite-variance hypothesis class. The bound separates difficulty into three orthogonal factors: a budget term, a heteroscedasticity index measuring how unevenly the uncertainty is spread across arms, and a model-dependent complexity measure, the Variance Local Curvature (VLC\mathrm{VLC}), which captures how much information a local change of variance creates inside the hypothesis class. For smooth classes, the VLC\mathrm{VLC} is a reparametrization of a variance--Fisher information, with closed-form values for common families. Benchmarking against the strongest available upper bound shows near-optimality up to logarithmic factors in broad regimes, and pinpoints a systematic gap in highly heterogeneous instances. Our proof introduces two key ingredients: a loss-induced ℓ1\ell_1 geometry on the decision space, and a representation-based instance generator that reduces hard-instance construction to an explicit random matrix calculation.

Abdellah Aznag, Rachel Cummings, Adam N. Elmachtoub

Department of Industrial Engineering and Operations Research & Data Science Institute, Columbia University

Multi-Armed BanditsActive LearningMinimax EstimationAdaptive Sampling
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Jun 12, 2026

Adaptive Nucleus Truncation for Long-Form Reasoning

Sampling plays an important role in long-form language-model reasoning. Over thousands of decoding steps, small changes in the candidate token set can compound into different reasoning trajectories, stability profiles, and final answers. Existing truncation methods such as top-pp, min-pp, and fixed top-nσnσ sampling improve over unrestricted sampling, but they rely on fixed thresholds that cannot adapt to changes in entropy, task difficulty, training stage, or generation budget. We introduce Adaptive Nucleus Truncation Sampling (ANTS), which extends top-nσnσ sampling from a fixed decoding rule into an adaptive rollout-control mechanism for long-form generation. ANTS selects standardized neighborhoods around the maximum logit before temperature scaling, adapts the truncation width using an entropy-conditioned controller, and retains a no-truncation fallback arm to stabilize training when truncation becomes unsafe. On a 33B-total / 4B-active sparse Mixture-of-Experts reasoning model, ANTS improves average performance over percentage-based benchmarks by +1.9, +3.8, and +5.2 points at 8K, 16K, and 32K generation budgets, respectively. The strongest gains appear on instruction following and mathematical reasoning, with IFBench improving by more than 10 points at 32K and AIME 2025 improving by 7 points. Code generation reveals an important budget interaction. On Codeforces, ANTS trails the baseline at 8K, but reverses this gap and substantially improves ELO at 16K and 32K. These results suggest that sampler design should be treated not just as a decoding hyperparameter, but as part of how we stabilize and scale long-budget reasoning.

Ousmane Amadou Dia

Language Model DecodingAdaptive SamplingLLM ReasoningLarge Reasoning Models
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Jun 10, 2026

RCAP: Robust, Class-Aware, Probabilistic Dynamic Dataset Pruning

Dynamic data pruning techniques aim to reduce computational cost while minimizing information loss by periodically selecting representative subsets of input data during model training. However, existing methods often struggle to maintain strong worst-group accuracy, particularly at high pruning rates, across balanced and imbalanced datasets. To address this challenge, we propose RCAP, a Robust, Class-Aware, Probabilistic dynamic dataset pruning algorithm for classification tasks. RCAP applies a closed-form solution to estimate the fraction of samples to be included in the training subset for each individual class. This fraction is adaptively adjusted in every epoch using class-wise aggregated loss. Thereafter, it employs an adaptive sampling strategy that prioritizes samples having high loss for populating the class-wise subsets. We evaluate RCAP on six diverse datasets ranging from class-balanced to highly imbalanced using five distinct models across three training paradigms: training from scratch, transfer learning, and fine-tuning. Our approach consistently outperforms state-of-the-art dataset pruning methods, achieving superior worst-group accuracy at all pruning rates. Remarkably, with only 10%10\% data, RCAP delivers >1%>1\% improvement in performance on class-imbalanced datasets compared to full data training while providing an average 8.69×8.69\times speedup. The code can be accessed at https://github.com/atif-hassan/RCAP-dynamic-dataset-pruning

Atif Hassan, Swanand Khare, Jiaul H. Paik

Department of Artificial Intelligence, IIT Kharagpur, Kharagpur, West Bengal, India · Department of Mathematics, IIT Kharagpur, Kharagpur, West Bengal, India

Dataset PruningTraining Data SelectionAdaptive Sampling
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Jun 9, 2026

Annealed Entropic Allocation for Ranking and Selection

We propose annealed entropic allocation, an adaptive sampling policy based on an annealed, weighted soft-min formulation of static budget allocation. We replace the maximin large-deviation rate objective with a weighted log-sum-exp surrogate that blends challenger-specific pairwise scores through soft-min weights, avoiding hard switching when several challengers are nearly active. To capture tail behavior beyond the leading exponent, the surrogate incorporates saddlepoint prefactors from refined pairwise tail asymptotics. Because these corrections are subexponential, decreasing the annealing temperature with the budget preserves the same first-order target allocation. For the static problem, we prove uniform convergence to the hard minimum, concentration of soft-min weights on active challengers, and continuity of the induced target-allocation map under fixed weights. Experiments show that the proposed methods are consistently competitive: the no-saddlepoint ablation performs best in symmetric Gaussian and exponential slippage settings, while saddlepoint weighting can help in heterogeneous or asymmetric cases.

Xin Fei, Juergen Branke

Business School · The University of Edinburgh, Edinburgh, UK · Warwick Business School +1

Multi-Armed BanditsAdaptive SamplingLarge Deviation Principles
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Jun 9, 2026

Provenance-Grounded Gating and Adaptive Recovery in Synthetic Post-Training Data Curation

Synthetic post-training pipelines commonly filter generated samples with reward models or holistic LLM judges, yet two practices remain rarely examined together: whether the filtering signal is grounded in the source evidence that induced each generation, and whether rejected samples can be systematically recovered rather than permanently discarded. We present a controlled study of both questions across gate configurations, recovery strategies, and generator scales, using adversarially injected corpora to provide ground-truth failure labels. We find that exact source provenance improves faithfulness gating for stronger judges, that hallucination and reward gates reject largely disjoint sample populations making both necessary, and that an adaptive recovery pipeline combining failure diagnosis with targeted regeneration achieves higher yield, recovery rate, and injection recall than naive resampling. Downstream fine-tuning quality is driven primarily by generator scale, with filtration and recovery conditions contributing meaningfully but secondarily.

Soham Bhattacharjee, Karun Sharma, Vinay Kumar Sankarapu +1

Lexsi Labs

Adaptive SamplingLLM Post-TrainingSynthetic Data EvaluationSynthetic Data Selection
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Jun 8, 2026

Learning Where to Simulate: Generative Active Sampling for Online PDE Surrogate Training

Data-driven PDE surrogates are trained with data produced by numerical PDE solvers. However, when the surrogate's goal is to generalize across a wide range of PDE configurations (e.g., initial conditions and physical coefficients), generating a representative training set is non-trivial. Uniform sampling of configuration parameters often under-represents trajectories exhibiting challenging dynamics, leading to high prediction errors and large error variance in the trained surrogate. Online training, where data generation and surrogate training are coupled, offers a natural advantage by allowing solver parameters to be steered on-the-fly. To efficiently exploit this capability, we introduce Online Generative Active Sampling (OGAS), an active learning method that reactively learns the relationship between configuration parameters and surrogate performance to control the sampling distribution. OGAS trains a fast diffusion model in parallel to the surrogate to act as a conditional sampler, mapping a surrogate-derived difficulty signal (e.g., loss or uncertainty) to configuration parameters. By actively drawing target signals from a prior biased toward high difficulty, OGAS continuously steers data generation toward challenging regimes without delaying the training workflow. We evaluate OGAS across 2D PDEs with distinct challenging dynamics (Kuramoto-Sivashinsky, Navier-Stokes, Gray-Scott) and up to 308 parameters, using multiple surrogate architectures. Across all settings, OGAS consistently improves tail statistics, yielding substantial reductions in errors above the 99th percentile and overall error dispersion compared to uniform sampling. While prioritizing challenging trajectories introduces a trade-off with average error, OGAS effectively ensures worst-case reliability of trained surrogates with negligible wall-time overhead.

Pierre Cesar, Sofya Dymchenko, Abhishek Purandare +1

DATAMOVE · Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LIG, Grenoble, France

PDE Surrogate ModelingActive LearningAdaptive Sampling
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Jun 7, 2026

sGPO: Trading Inference FLOPs for Training Efficiency in RLVR

Standard Reinforcement Learning with Verifiable Rewards (RLVR) training allocates a fixed rollout budget to every query, without regard for what each query's difficulty means for the current policy. This leads to two symmetric failure modes: easy queries produce near-zero advantage because the policy already solves them, while unsolvable queries produce no signal because the policy never solves them. Both regimes waste training FLOPs without contributing to a learning gradient. We introduce sorted Group Policy Optimization (sGPO), a compute-efficient strategy that trades a small budget of inference FLOPs for a large reduction in wasted training FLOPs. The key insight is that cheap inference compute can serve as a single offline proxy for query difficulty. By generating a small batch of parallel samples per query under the initial policy, we obtain a model-aware empirical success rate. This motivates setting the training rollout group size to the inverse of this success rate, a practical rule that maximizes sample efficiency by extracting the most advantage per generated rollout. This single profiling pass simultaneously drives data filtering (removing trivial queries and sub-sampling unsolvable ones), adaptive group size allocation, and curriculum construction (scheduling queries from easy to hard). sGPO matches or exceeds baseline performance while reducing total training compute by a factor of three, with the upfront inference profiling cost included.

Shivchander Sudalairaj, Kai Xu, Akash Srivastava +1

AI Innovation, Red Hat · Core AI, IBM

Group Relative Policy OptimizationAdaptive SamplingReinforcement Learning with Verifiable RewardsSample-Efficient RL
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Jun 7, 2026

Sample Where You Struggle: Sharpening Base Model Reasoning via Entropy-Guided Power Sampling

Sampling from the sequence-level power distribution pαp^α elicits RL-level reasoning from base language models without any parameter updates, but the standard Metropolis--Hastings (MH), a Markov Chain Monte Carlo (MCMC) sampler, is both expensive and slow-mixing. We trace both to a structural mismatch: pαp^α mainly departs from pp at a sparse, spatially clustered set of high-entropy decision points, yet MH proposes resampling positions uniformly along the prefix -- wasting compute on near-degenerate conditionals while under-mixing precisely where modes diverge. We propose Entropy-Guided Power Sampling (EGPS), a training-free and verifier-free sampler that re-derives its proposal from token-level entropy already in the forward pass. EGPS skips deterministic blocks, localizes each MCMC move to a high-entropy neighborhood, and applies Multiple-Try Metropolis at decision points -- making sampling cost scale with entropy mass rather than sequence length. On Qwen2.5-Math-7B, EGPS reaches best or tied-best accuracy on all three benchmarks (MATH500 75.8%75.8\%, HumanEval 62.2%62.2\%, GPQA 42.4%42.4\%) at up to a 12.6×12.6\times wall-clock speedup over the MH baseline.

Hong Guo, Nianhui Guo, Christoph Meinel +1

Hasso Plattner Institut · German University of Digital Science

Markov Chain Monte CarloInference-Time ScalingEfficient Language Model ReasoningLLM Inference AccelerationAdaptive Sampling
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Jun 6, 2026

Generative Frontier Planning for Adaptive Peer-Referral Recruitment under Covariate-Dependent Arrivals

Peer-referral recruitment systems such as respondent-driven sampling are critical for studying and intervening on hidden populations affected by infectious diseases. To accelerate recruitment, public health agencies must adaptively allocate limited referral resources across multiple rounds, where current decisions shape both the number and the covariates of future recruits. Prior work makes this problem tractable by assuming that referrals are drawn i.i.d.\ from a homogeneous population, an assumption that ignores the homophily and shared context that drive real peer recruitment. We instead consider a more realistic model in which both referral capacity and the covariates of newly referred individuals are conditioned on the referrer, learned from data with a censored count model and a conditional generative model. The resulting planning problem is challenging because each candidate allocation induces a different distribution over future recruits. We propose Generative Frontier Planning (GFP), a model-based planner that replaces per-step Monte-Carlo sampling with a deterministic backup over a latent covariate-coverage value surrogate. The surrogate is designed so that the expected value of the next frontier depends on the offspring generative model only through finite-dimensional summaries that are amortized offline, and so that the resulting per-round objective is monotone with diminishing returns. Together, these two properties make planning tractable: the deterministic backup eliminates Monte-Carlo sampling, and the diminishing-returns structure lets a marginal greedy allocation achieve a (1−1/e)(1-1/e)-approximation for the per-round problem. On a simulation environment calibrated to a real respondent-driven sampling dataset, GFP outperforms random, reinforcement-learning, and i.i.d.\ dynamic-programming baselines across four discount factors.

Lingkai Kong, Hezi Jiang, Andrew Ma +3

Harvard University

Adaptive SamplingModel-Based Planning
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Jun 4, 2026

DAS-PINNs for high-dimensional partial differential equations: extending deep adaptive sampling to spacetime domains

Time-dependent high-dimensional partial differential equations (PDEs) with spatially localised and dynamically evolving solutions pose a fundamental challenge for physics-informed neural networks (PINNs), as uniform collocation sampling becomes increasingly ineffective in high-dimensional spatiotemporal domains. In this work, a deep adaptive sampling framework for PINNs is extended to the time-dependent setting by treating space and time as a unified domain without any explicit time marching. A normalising flow neural network model effectively learns the distribution induced by the PDE residual and generates new collocation points concentrated in regions where the solution is most difficult to learn. Unlike conventional adaptive strategies that require explicit time stepping or moving meshes, high-residual regions are automatically identified and tracked across both space and time, driven purely by the PDE residual distribution. The effectiveness of the proposed strategy is assessed on a range of benchmark problems, from sharp and moving features in two spatial dimensions to localised structures in up to eight spatial dimensions.

Anshima Singh, David J. Silvester

Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK

PDE SolvingAdaptive SamplingPhysics-Informed ML
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Jun 4, 2026

Reactive Flux Matching: Mechanism Discovery and Adaptive Sampling of Rare Events

Path sampling methods generate ensembles of reactive trajectories connecting metastable states, but extracting mechanistic insight from these data remains nontrivial. We introduce Flux Matching, a framework that learns two complementary objects directly from reactive trajectory data: a current velocity u(z)u(z), whose streamlines trace the dominant reaction pathways, and a scalar potential h(z)h(z), obtained from a weighted Helmholtz-Hodge decomposition of the reactive current, that serves as a data-driven reaction coordinate. Both minimize quadratic functionals over the reactive path ensemble, analogous to the flow matching loss in generative modeling, and require no knowledge of the underlying dynamics or stationary distribution. Unlike committor-based methods, uu and hh remain well-defined under projection onto non-Markovian collective variables, and their level sets in turn provide adaptive interfaces for improved sampling with enhanced sampling methods. Flux Matching is validated through the generation of current velocity trajectories and rate constant calculations on molecular systems.

Rishal Aggarwal, David Ryan Koes, Nicholas M. Boffi +1

CMU-Pitt Program in Computational Biology Dept. of Computational & Systems Biology University of Pittsburgh · Machine Learning Department Dept. of Mathematical Sciences Carnegie Mellon University · Courant Institute, New York University Machine Learning Lab +1

Adaptive SamplingMolecular Dynamics Simulation
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Jun 4, 2026

Revisiting Prototype Rehearsal for Exemplar-Free Continual Learning: Manifold-Aware Boundary Sampling with Adaptive Class-Balanced Loss

Exemplar-free class-incremental learning (EFCIL) aims to acquire new classes over time without storing raw data. Historically, prototype rehearsal, which samples around stored class prototypes and mixes them with current-task data, has been a popular strategy to reduce catastrophic forgetting. However, recent drift-compensation methods that explicitly realign prototypes in the evolving feature space consistently outperform prototype-based rehearsal, raising the question of whether rehearsal itself is fundamentally limited. We argue that the performance gap stems not from the idea of prototype rehearsal per se, but from how it is typically instantiated: existing approaches treat prototypes as isolated class summaries that ignore information from nearby enemy classes, and fail to correct the emerging class imbalance between a handful of synthetic old-class samples and hundreds of real instances from newly introduced classes. Building on this hypothesis, we revisit prototype rehearsal and propose a manifold-aware variant that restores its competitiveness in EFCIL. First, we introduce Constrained Expansive Over-Sampling, which interpolates each old-class prototype toward its nearest enemy features from new classes, generating boundary-aware rehearsal samples that better follow the underlying data manifold while preserving inter-class separation. Second, we design an Adaptive Class-Balanced loss that performs time-based class weighting, amplifying gradients from older prototypes when they are most informative and gradually annealing their influence as richer supervision from later tasks accumulates. Together, these components turn prototype rehearsal into a drift-resilient, imbalance-aware mechanism that closes, and often reverses, the gap to recent drift-compensation methods, achieving state-of-the-art performance across multiple EFCIL benchmarks.

Hongye Xu, Bartosz Krawczyk

Chester F. Carlson Center for Imaging Science Rochester Institute of Technology

Class-Incremental LearningPrototype-Based ClassificationAdaptive Sampling
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Jun 2, 2026

Stein Kernelized Molecular Dynamics for Active Learning of Interatomic Potentials

Machine learning interatomic potentials (MLIPs) enable efficient and accurate atomistic simulations but depend critically on the quality and diversity of the training data. We introduce Stein kernelized molecular dynamics (SKMD), an enhanced sampling method that uses interacting particle dynamics to acquire informative training configurations for the active learning and fine-tuning of MLIPs. SKMD corresponds to a stochastic variant of Stein variational gradient descent that is adapted for molecular dynamics by incorporating asynchronous particle updates and a kernel of global atomic descriptors, which provides a symmetry-aware measure of configurational similarity. Unlike other enhanced samplers used in molecular dynamics, SKMD preserves the Boltzmann distribution as the asymptotic distribution of the dynamics. This property enforces a balance between the exploration of diverse configurations and attraction toward high-probability regions of the energy landscape. We further propose an approach to efficient online data acquisition using an adaptive stopping criterion that selects non-redundant training data over the course of simulation. We demonstrate SKMD for the active learning of a neural network model of the Müller-Brown potential and the fine-tuning of a MACE interatomic potential for alanine dipeptide. Compared to active learning baselines, our method achieves higher model accuracy in fewer training iterations with the same number of acquired training samples.

Joanna Zou, Fraser Birks, Dallas Foster +1

Center for Computational Science & Engineering, Schwarzman College of Computing, MIT · Warwick Centre for Predictive Modelling, School of Engineering, University of Warwick · NVIDIA

Machine Learning Interatomic PotentialsActive LearningAdaptive SamplingKernel MethodsMolecular Dynamics SimulationStein Variational Gradient Descent
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Jun 2, 2026

A Quantitative Approximation Framework for Flow Distillation in Diffusion Models

We develop a quantitative approximation framework for diffusion distillation, viewing few-step sampling as error propagation under compositions of learned flow maps. Focusing on trajectory distillation for the probability-flow ODE, we show that local approximation errors can be strongly amplified in low-noise multimodal regimes, where the underlying dynamics become stiff. In an analytically tractable Gaussian-mixture Ornstein--Uhlenbeck setting, we separate two core difficulties: approximating the time-dependent score field and controlling the dynamical amplification governed by the time-integrated Jacobian bound of the probability-flow ODE. On the approximation side, we prove constructive L^p(p_t) guarantees showing that ReLU--ReQU networks approximate the Gaussian-mixture score uniformly over time, with depth and width scaling polylogarithmically in the target accuracy and explicitly with the mixture geometry. On the stability side, we derive an explicit bound L(t) for the spatial Lipschitz constant of the probability-flow velocity and convert it into a flow map stability estimate governed by \int_s^t L(u),du, making late-time amplification in stiff regimes computable. Building on these estimates, we prove that deep residual compositions efficiently approximate the long-horizon transport, with global error controlled by the stability amplification factor, and identify a Lipschitz-mismatch regime in which one-step distillation is structurally unfavorable. The resulting theory yields a stability-balanced non-uniform time grid obtained by uniform partitioning in the cumulative stability coordinate. Experiments support the prediction and reduce end-to-end relative MSE by up to 51.9% with 8 segments compared with uniform grids.

Weiguo Gao, Ming Li, Lei Shi +1

School of Mathematical Sciences, Fudan University, Shanghai, 200433, China · Shanghai Key Laboratory of Contemporary Applied Mathematics, Fudan University, Shanghai, 200433, China

Diffusion Model DistillationFew-Step Diffusion SamplingAdaptive Sampling
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Jun 2, 2026

Small RL Controller, Large Language Model: RL-Guided Adaptive Sampling for Test-Time Scaling

Test-time scaling improves the reasoning performance of large language models but incurs substantial cost in both total computation and latency. Existing adaptive sampling methods partially mitigate this issue by dynamically deciding when to stop sampling, yet they typically rely on heuristic rules or rely on distribution assumptions. In this work, we formulate adaptive sampling as a Markov decision process (MDP). We train a lightweight sampling controller with reinforcement learning (RL) to jointly balance answer correctness, latency, and computation cost. At each round, the controller decides to stop sampling or to acquire additional samples. Our method is lightweight which only relies on statistics of final answers, and can be trained and deployed on CPU. We further show that the resulting framework admits an interpretation as the Lagrangian relaxation of a constrained optimization problem with explicit budget constraints. Experiments against strong baselines such as ASC and ESC show that our method achieves improved trade-offs among answer correctness, sampling rounds, and total samples required.

Runpeng Dai, Tong Zheng, Rui Liu +2

University of North Carolina at Chapel Hill · University of Maryland, College Park · Washington University in St. Louis

Reinforcement LearningTest-Time ScalingLLM Inference AccelerationAdaptive Sampling
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Jun 1, 2026

Mitigating Spurious Correlations with Memorization-Guided Dataset De-Biasing

Real-world datasets often contain spurious correlations that are not causally related to the target label. When such correlations dominate the majority of training samples, models tend to rely on them, leading to misclassification of minority samples that do not exhibit the same spurious patterns. While a potential approach is to select subsets of data to better represent the minority samples, this may require access to group labels, which are typically unknown. Furthermore, as we demonstrate, widely used sample scoring functions in the invariant subset or coreset selection literature largely depend on spurious features and therefore fail to accurately capture the importance or difficulty of core, causally relevant features. Accordingly, we propose to mitigate spurious correlations by developing a two-stage sample scoring function that disentangles the learning dynamics of core and spurious features and evaluates their difficulty separately. Based on our proposed metric, we introduce a new algorithm to find and prioritize informative samples both with and without spurious correlations. Extensive experiments demonstrate that a standard ERM model trained on our selected samples achieves superior performance compared to state-of-the-art debiasing techniques, while requiring as little as 10% of the original training data.

Arda Fazla, Abolfazl Hashemi

School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907, USA.

Debiased MLTraining Data SelectionAdaptive SamplingCoreset SelectionSpurious Correlation RobustnessSpurious Correlation+1
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Jun 1, 2026

Doing well with less! On Sampling Techniques for Empirical Pairwise Loss Estimation/Minimization

Many machine learning problems, including similarity learning, ranking, and clustering, rely on empirical pairwise loss functions whose quadratic computational cost quickly becomes prohibitive at scale. We demonstrate how a frugal approach that retains only a fraction of the available information on pairs can achieve estimation or optimization performance comparable to that obtained by using all pairs, by leveraging survey sampling techniques. A central finding, supported by both theory and experiments, is that such sampling plans must target pairs directly rather than individual observations. In particular, for pairwise losses between high-dimensional vectors such as embeddings in vision or graph learning, assigning higher inclusion probabilities to informative pairs using suitable auxiliary information yields performance close to full pairwise evaluation, providing a principled and theoretically grounded trade-off between accuracy and computational cost.

Louise Davy, Stephan Clémençon, Charlotte Laclau

IDS, LTCI Télécom Paris Palaiseau, France

Pairwise ComparisonImportance SamplingAdaptive Sampling
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