Adaptive Sampling

Subsampling is effective in tackling computational challenges for massive data with rare events. Overly aggressive subsampling may adversely affect estimation efficiency, and optimal subsampling is essential to mitigate the information loss. However, existing optimal subsampling probabilities depend on data scales, and some scaling transformations may result in inefficient subsamples. This problem is more significant when there are inactive features, because their influence on the subsampling probabilities can be arbitrarily magnified by inappropriate scaling transformations. We tackle this challenge and introduce a scale-invariant optimal subsampling function in the context of sparse models, where inactive features are commonly assumed. Instead of focusing on estimating model parameters, we define an optimal subsampling function to minimize the prediction error, using adaptive lasso to outline the estimation procedure and study its theoretical guarantee. We first introduce the adaptive lasso estimator for rare-events data and establish its oracle properties, thereby validating the use of subsampling. Then we derive a scale-invariant optimal subsampling function that minimizes the prediction error of the inverse probability weighted (IPW) adaptive lasso. Finally, we present an estimator based on the maximum sampled conditional likelihood (MSCL) to further improve the estimation efficiency. We conduct numerical experiments using both simulated and real-world data sets to demonstrate the performance of the proposed methods.

Anti-amyloid therapies and blood-based biomarkers are changing Alzheimer disease workups into a two-stage measurement workflow: screen broadly with cheaper information, then spend scarce confirmatory amyloid measurements where they support the decision that will be reported. Amyloid positron-emission tomography (PET) remains one such protocol measurement for amyloid burden, but PET slots, trial budgets, and payer-facing evidence packages are finite. This paper asks a deliberately operational question: when is simple transparent PET validation enough, and when is a fitted residual-uncertainty score worth the added complexity? For a weighted protocol target, the first-order value of validating subject i is the product of target influence and residual protocol uncertainty. Generic uncertainty sampling uses only the second factor and can spend PET measurements on subjects that are hard to predict but weak for the scientific, clinical, or commercial claim. We apply this rule to the A4/LEARN PET archive, treating observed PET as a design laboratory for scarce-confirmation studies. For the primary APOE4 carrier versus non-carrier contrast in Centiloid 24-or-higher PET positivity, simple APOE4-balanced validation recovers nearly all of the target-specific gain: at PET budget 200, the confidence-interval width ratio relative to random validation is 0.923 for APOE4 balancing and 0.914 for target-specific scoring, while generic uncertainty sampling is 0.980. Other targets behave differently: target-specific scoring gives larger gains for an age-slope analysis and for cutoff-indexed PET positivity. The practical message is simple: spend scarce protocol measurements according to the claim being validated, not only according to prediction uncertainty.

This paper develops an adaptive surrogate modeling method for problems with very high-dimensional spatio-temporal outputs. The analysis of spatio-temporal multi-physics systems is computationally expensive and consists of a large number of inputs and outputs. Surrogate models are often constructed to replace the physics-based model to achieve computational efficiency in analyses such as uncertainty quantification and optimization that require many function calls. In order to address the challenge introduced by the high dimensionality of spatio-temporal output, a dimension reduction method is first employed to map the high-dimensional output to a low-dimensional latent space. This is followed by the construction of the surrogate model in the low-dimensional space. The prediction error in the original space, which includes both the reconstruction error and surrogate model error, is evaluated using different error metrics. Based on the prediction accuracy of the surrogate model, new training points are identified for adaptive improvement of the surrogate model. We present a novel adaptive sampling technique that combines exploration and exploitation to improve the surrogate model accuracy with the fewest possible runs of the expensive physics-based model. Thermo-mechanical analysis of a gas turbine engine blade is used to analyze the effectiveness of the proposed method.

LLM evaluations often use fixed sampling budgets, testing every item the same number of times even after estimates are precise. We introduce optstop, a precision-based adaptive stopping framework that treats evaluation as a sequential measurement problem: keep sampling where uncertainty remains high, and stop where estimates are precise or stable enough. The framework builds on hierarchical Bayesian inference, supports binary, ordinal, and continuous outcomes, and keeps every benchmark item eligible for sampling, without requiring a calibrated item bank. It runs live or retrospectively, and includes a safeguard that samples more cautiously as measured performance approaches zero, where rare successes matter most. In an illustrative 200-item, 10-epoch evaluation, it removes 57%-97% of planned trials across nine validation settings, with overall conclusions equivalent to the full run. These results show that LLM evaluation compute can be allocated by uncertainty rather than by fixed repetition counts, with the magnitude of savings depending on evaluation design.

Power Sampling sharpens a language model's distribution over complete generation trajectories, offering a verifier-free way to improve reasoning at inference time. It also has the potential to serve as a general-purpose front end for a broad range of downstream sampling methods. However, we uncover a striking paradox: Power Sampling can drive more probability mass toward correct trajectories while degrading the downstream inference it is intended to enhance. Using self-consistency as a representative case, we observe accuracy drops of up to 18.5 percentage points across models and reasoning benchmarks. We trace this paradox to two mismatches. Dose mismatch arises because a fixed exponent induces drastically different amounts of distributional change across problems. Coverage mismatch arises because global sharpening concentrates mass on a narrow set of dominant paths: high pass@k, often interpreted as evidence of preserved diversity, can therefore coexist with the loss of broad reasoning-path support required for downstream aggregation, search, and selection. Guided by this diagnosis, we replace uniform trajectory exponentiation with a deformation-controlled, support-preserving Power target that calibrates sharpening across problems while limiting the suppression of moderate-probability paths. In a same-budget instantiation with weighted self-consistency, the repaired sampler reverses the losses caused by global Power and outperforms standard multi-sample inference across reasoning benchmarks.

Autonomous systems can fail in rare and heterogeneous ways, making real-world failure discovery difficult under limited testing budgets. Although cheaper proxies such as simulators, lower-fidelity systems, or related policies can be sampled extensively to find failures, proxy failures often do not transfer to the real world due to sim-to-real and system-to-system gaps. The key challenge is therefore to effectively leverage proxy system information for accurate prediction of severe target system failures. We propose an adaptive failure discovery method that combines proxy evaluations with limited target system results to guide scenario selection for target system testing. Our method learns a local predictor of target risk by correcting proxy failure signals using control-variate-inspired residual modeling. To find failures that are both likely and diverse, we combine this predictor with a support-aware mutual-information objective that favors realistic, well-supported regions while expanding coverage across failure modes. Across autonomous driving, manipulation, and quadruped velocity-tracking tasks, our method discovers up to 2$\times$ as many failures as random sampling and active-learning baselines, including severe and diverse failures missed by competing methods.

Hamilton-Jacobi (HJ) reachability provides a mathematically rigorous framework for safe control of dynamical systems, but its practical application is bottlenecked by the computational complexity of solving Hamilton-Jacobi-Isaacs variational inequality PDEs in high dimensions. Physics-informed neural networks (PINNs) have recently emerged as a promising alternative to classical mesh-based solvers, yet their performance is highly sensitive to the choice of collocation sampling. In order to learn accurate safety value functions, existing PINNs-based HJ reachability solvers must rely on complex training pipelines and auxiliary supervision. In this work, we propose STEER2REACH (S2R), a PINNs-based HJ reachability solver that requires minimal modification on top of standard PINNs training. S2R's key contribution is a lightweight, low-overhead adaptive collocation sampling distribution constructed by steering forward trajectories using a combination of the optimal control and disturbance signals induced by the current value function, with injected stochastic exploration noise. We demonstrate that despite its simplicity, S2R achieves competitive--and in some cases improved--performance on safety metrics while reducing relative L2 error across a range of reachability benchmarks compared with SoTA MPC-guided HJ reachability solvers, all without requiring multi-stage training or MPC-based supervision.

Test-time scaling improves LLM reasoning by generating and aggregating multiple candidate answers, yet many pipelines use fixed per-query budgets that spend the same compute on easy and difficult prompts. These fixed budgets are also difficult to inspect because they do not explain why a given prompt receives a particular number of samples. We propose adaptive} test-time scaling with a lightweight fuzzy controller that maps interpretable signals, including estimated prompt complexity and model confidence, to a per-query sampling budget. The controller assigns fewer samples to easier or more confident prompts and more samples to harder or less certain prompts, making inference-time compute inspectable rather than fixed or opaque. We evaluate under a fair-alignment protocol with matched decoding settings and controlled answer selection, and compare against best-of-$N$, compute-aware scaling, and self-certainty-based baselines on question-answering and mathematical reasoning tasks. Across models and datasets, adaptive fuzzy control improves over several standard baselines and remains close to a selector-matched full-budget control while reducing the average number of samples. These findings suggest that interpretable adaptive sampling is a practical direction for more efficient test-time reasoning in large language models.

Natural disasters frequently inflict severe damage to the built environment, which demands a rapid, reliable, and cost-effective damage assessment for emergency response. However, traditional methods for post-disaster damage assessment often rely on static, labor-intensive data collection strategies that can be prohibitively expensive and struggle to adapt to dynamic post-disaster conditions. In this study, we propose a cost-aware Bayesian optimization framework combined with level-set estimation that continuously guides autonomous data collectors, e.g., an unmanned aerial vehicle (UAV), toward the most informative regions. By dynamically updating damage estimates across different geographic zones, our approach systematically reduces uncertainty while minimizing operational costs. The proposed framework is first validated using a controlled synthetic toy study, demonstrating the agent's ability to efficiently trace damage boundaries, recover the underlying damage map, and rapidly reduce predictive uncertainty. Furthermore, the approach is evaluated using high-fidelity disaster data generated by the Regional Resilience Determination (R2D) software. The results of the algorithm provide accurate and timely damage estimates that support informative and fast emergency response.

Sequential subset search -- forward selection with floating backtracking and its descendants -- remains the quality reference in feature selection, but every member of the family sweeps the full pool of remaining candidate features at each step, which excludes it from very-high-dimensional problems; there, only individual-feature ranking remains practical, and it models feature interplay weakly or not at all. We introduce a budgeted sampled step operator pair that replaces the full sweeps by a fixed number of candidate evaluations per step. Candidates are drawn by temperature-controlled softmax sampling from dependency-aware per-feature statistics learned online from every criterion evaluation the search performs, guarded by a uniform exploration floor; per-step cost becomes independent of dimensionality. Substituting the operators turns any sequential method into its stochastic counterpart, defining the Stochastic Sequential Search (SSS) family; we study the stochastic counterpart of floating search, sSFFS. On 500-dimensional madelon, sSFFS retains at least 97% of the full-SFFS criterion value at every subset size at about a quarter of its evaluations, while uniform sampling at the same budget collapses on madelon's synergistic features. On 5,000-dimensional gisette, far beyond full-SFFS reach, sSFFS exceeds the saturated criterion level of DAF and BIF ranking at matched budgets; holdout validation shows that at 500 training samples the binding constraint beyond the sequential frontier becomes the criterion, not the search. On 10,105-dimensional reuters, under a trustworthy multinomial filter criterion, sSFFS dominates BIF and DAF on the search objective and on holdout accuracy at every subset size, in about two minutes of single-core evaluation work. A verified standalone implementation accompanies the paper.

Artificial Intelligence is increasingly applied to surgical video analysis for phase segmentation, skill assessment, and workflow optimization. A key challenge is the length of surgical recordings, often one to several hours, creating substantial computational burden. We previously developed Kinematics-Adaptive Frame Recognition (KAFR) for robotic surgery, showing that tracking tool motion effectively identifies informative frames while filtering redundant content. However, laparoscopic surgery introduces additional challenges: manual camera control causes frequent motion artifacts, and image quality is generally lower than robotic systems. This study evaluates whether KAFR generalizes to laparoscopic surgery using the Cholec80 benchmark, comprising 80 laparoscopic cholecystectomy procedures annotated for seven surgical phases. KAFR operates in three stages: a fine-tuned YOLO model detects and segments surgical tools; frames are adaptively selected based on tool displacement or velocity variation; and an X3D model classifies selected frames into surgical phases. KAFR achieved a 91.0% F1 score using only 0.58% of frames for phase classification, representing an approximately seven-fold reduction compared to typical 4% frame sampling, while maintaining performance comparable to LoViT (90.2%) and Trans-SVNet (89.7%). These results demonstrate that kinematics-based frame selection transfers effectively to the challenging laparoscopic environment.

Physics-informed neural networks (PINNs) have emerged as a versatile approach for solving nonlinear partial differential equations (PDEs), yet achieving high accuracy efficiently using these techniques remains challenging for high-dimensional or multiscale systems. Here, we present a hybrid quantum-classical framework that enhances Quantum PINNs (QPINNs) through adaptive collocation point sampling and loss-aware attention mechanisms. By dynamically prioritizing points in regions with large PDE residuals or steep solution gradients, our method mitigates the spectral bias inherent in conventional PINNs. Current Quantum Physics-Informed Neural Networks are commonly assumed to be limited by the expressive power of quantum circuits. In our work, we observed that, across diverse differential equations, optimization - not only expressivity - can be an important bottleneck. Furthermore, a trainable loss-weighting scheme balances contributions from physics residuals, boundary conditions, and data fidelity during training. Integrating these strategies with quantum computing techniques (including variational quantum circuits and quantum gradient estimation) can yield at least a 60% improvement in solution accuracy under specific regimes for benchmark fluid flows and reaction-diffusion systems. Finally, we argue that merely increasing model expressivity is insufficient for resolving complex PDEs via QPINNs, as they remain constrained by the structural optimization limitations of classical PINNs. This framework provides a scalable pathway for quantum-enhanced scientific machine learning, bridging physics-based modeling with emerging quantum computational capabilities.

Machine learning determines which follow-up measurements biological screens collect. In a six-rule Cell Painting battery, the highest-value rule would re-image 96.01% of the library and had a 97.14% false-activation upper bound, showing why predicted value alone cannot justify replacing a fixed plan. We developed OPAL, a held-out decision test that freezes a rule and judges unnecessary measurement, coverage and value after cost against archive-specific criteria fixed before final evaluation. A development-selected sparse Cell Painting rule had 18.2-fold lower added-well burden, but its false-discovery bound exceeded 35%, so the fixed plan remained. LINCS--LJP favored broad acquisition under point-estimate criteria set during development, not selective saving. CTRP required fallback because its frozen score missed measured opportunity. OPAL separates optimization from evidence sufficient to change an experiment.

Evaluating large generative models across benchmarks is time-consuming and computationally expensive. This drives the need for methods that can estimate full benchmark performance by evaluating models on only a subset of items, known as a coreset. Current literature mostly requires the practitioner to input a coreset size. However, when reliable performance estimation takes priority over efficiency, an evaluation method should also be capable of automatically determining a coreset size that reflects this priority. We introduce BayesAME, a sequential Bayesian framework specifically targeting automatic determination of the coreset size. BayesAME models performance as a random variable by defining a latent ability for each group of items sharing the same historical model performances, with a joint prior distribution encoding the belief that the target model behaves similarly to these historical models. The posterior distribution over these abilities is used to derive performance estimators, quantify performance uncertainty, and select items to add to the coreset via an information-gain criterion. The coreset is iteratively augmented until the performance estimate fluctuation and the performance uncertainty fall below their respective user-defined thresholds. We propose a multi-target extension that captures performance correlations across multiple target models to further reduce the coreset size. Through extensive experiments across diverse benchmarks, we demonstrate that BayesAME consistently outperforms sequential adaptations of existing methods. Crucially, our comprehensive analysis addresses recent skepticism in the literature, establishing that non-random coreset selection is advantageous over random selection. Finally, we highlight that leveraging continuous response log-likelihoods over traditional binary scores significantly enhances estimation accuracy.

Two central challenges in diffusion-based sampling are the theoretical one of understanding their remarkable effectiveness even in high-dimensional settings, and the practical one of designing algorithms with certified performance guarantees. We show that these questions are intimately connected via the denoising growth complexity ($\mathsf{DGC}$). It is a geometric measure defined by a log-time weighted integral of the derivative of the denoising mean-squared error along the Gaussian heat flow. We show how the $\mathsf{DGC}$ increments lead to a simple and explicit bound on the KL error of an Euler scheme applied to the stochastic innovations representation. The bound is local along the path: each step is controlled by the corresponding $\mathsf{DGC}$ increment and its relative stepsize. This structure allows us to derive KL sampling guarantees for optimized stepsize schedules, both in a simpler single-block setting and in a more refined $K$-block setting. The $\mathsf{DGC}$ function has a natural martingale structure, which we exploit to develop fully data-certified versions of these algorithms. It also admits information-theoretic upper bounds in terms of covariance, rate distortion, metric entropy, and the Poincar'e constant, thereby recovering and sharpening a range of existing diffusion-sampling guarantees, as well as giving new results. In log heat-time, the fine partition limit is governed by an integral involving the square root of the $\mathsf{DGC}$ density, whereas a single-block schedule depends on its ordinary integral. This comparison precisely characterizes when adaptation to data geometry yields substantial computational gains, including logarithmic-to-constant separations for simple Gaussian mixture models.

Data quality profiling -- computing missing-value rates, duplicate fractions, outlier densities, and functional-dependency violations -- is foundational for data-centric AI pipelines, yet exhaustive scans over millions of rows are prohibitively slow for near-real-time monitoring. Progressive sampling is the standard alternative; the open question is which strategy best preserves profile fidelity at scale. We benchmark nine sampling strategies -- blind (random uniform, geometric, Yamane, cluster) and proxy-guided (Metropolis-Hastings, DAG, stratified by column type or quality score, importance-weighted) -- on three real-world datasets (NYC 311, NYPD arrests, UCI Adult; up to 500K rows), an IoT sensor stream (2.3M rows), two ultra-large real datasets including Ultra-Marathon Running (up to 7.4M rows), and synthetic data scaled to 5x10^6 rows. Contrary to the assumption sharpens estimates, blind representative samplers dominate uniformly. At a 5% budget, random uniform achieves 0.49% mean relative error on NYC 311; DAG-guided MCMC yields 19.5% (approx. 40x worse), and across all real datasets DAG is 11-49x worse (Wilcoxon W=0, p=0.002, n=9 pairs). Cluster sampling matches random uniform (MRE 0.110 vs. 0.111); proxy-guided methods share DAG's failure mode (MRE 0.20-0.35). At scale, random uniform is near-linear (O(N^{0.964})) while DAG is super-linear (O(N^{1.272})), running 28--47x slower on ultra-large data with 6x worse accuracy. The root cause is an IQR proxy mismatch: proxy-guided samplers over-pursue numeric outliers, while quality defects concentrate in categorical columns invisible to the proxy. The actionable finding: representativeness, not domain knowledge, determines sampler quality -- schema-free random uniform or cluster sampling suffices for production-grade quality profiling at scale.

We study streaming federated learning with limited client memory, where newly generated training data incur time-varying sampling costs and must be selectively admitted and retained over time. We consider a joint server-side admission and client-side memory-management framework with the objective of minimizing the cumulative excess population risk under a sampling-cost budget and buffer constraints. We first derive a learning-error bound that explicitly captures the effects of instantaneous training sample size, distinct-sample growth, and reuse imbalance through a characterization of the effective sample size. Through a surrogate penalty obtained from this bound, we develop an Active-Constraint Drift-Plus-Penalty (ACDPP) policy that combines a structured client-side $K$-step retention rule with a server-side online admission rule and a time-varying rectangular admission region. We further present a sequence of comparison arguments, via an auxiliary constant-admission policy, that connects the ACDPP learning bound to a costless oracle benchmark. This yields explicit guarantees in terms of sublinear regret and sampling-cost violation, while the buffer-occupancy violation is controlled through offline selection of the retention horizon. Experiments on multiple datasets demonstrate that the proposed policy remains close to the oracle benchmark while satisfying the sampling-cost and buffer constraints.

Long-tailed learning couples two sources of poor generalization: head classes dominate training exposure, while under-represented classes often converge to sharper regions of the loss landscape. Conventional re-sampling addresses the former without considering geometry, whereas existing long-tailed sharpness-aware minimization (SAM) methods modify losses or perturbations only after biased mini-batches have been drawn. We introduce Sharpness-Guided Equilibrium Sampling (SGS), which treats the sampling distribution as an active control variable for optimization geometry. SGS dynamically adjusts subsequent mini-batches by increasing the sampling probability of less frequently sampled classes while suppressing classes with large SAM-induced loss changes, using only cumulative class counts and EMA sharpness estimates obtained from the standard SAM update, without class-wise perturbations or additional backward passes. We characterize this sampling process through a continuous-time stochastic differential equation and a sampling-dependent PAC-Bayes analysis, explaining how frequency-sharpness feedback can move training toward a more balanced flatness profile. On CIFAR-100 LT with an imbalance ratio of 100, SGS-SAM improves Focal-SAM by 10.85 points in tail accuracy and 3.56 points overall. On ImageNet-LT, it improves ImbSAM by 6.59 points on tail classes and 1.20 points overall. Its training time is only $1.02\times$ that of vanilla SAM. Beyond these gains, SGS establishes a sampling-side route to loss-landscape control, suggesting that future long-tailed methods can jointly regulate data exposure and optimization geometry rather than treating either as fixed.

We introduce Deep Adaptive Bayesian Screening (DABS), a method for performing adaptive factorial screening in high-dimensional discrete design spaces. DABS learns a policy network offline to sequentially select informative experiments, amortizing Bayesian Optimal Experimental Design. It handles binary designs, incorporates sparsity and interactions via a spike-and-slab prior with strong heredity. The model is trained using a contrastive lower bound on information about factor activity with nuisance effect sizes and noise variance analytically integrated out. Unlike prior amortized Bayesian design approaches, DABS also integrates Gibbs posterior inference at deployment, yielding posterior probabilities of factor activity and credible intervals on effect sizes. We demonstrate DABS on screening problems calibrated to real-world benchmarks and show it achieves superior accuracy and scalability over classical and Bayesian baselines under tight experimental budgets.

Magnetic Resonance Imaging (MRI) is often acquired with anisotropic resolution to reduce scan time, producing stair-step artifacts along the through-plane direction. In through-plane MRI super-resolution, an efficiency-fidelity trade-off arises: feed-forward regressors are fast but oversmooth at large slice-thicknesses, while sampling-based methods improve fidelity at high inference cost. We propose DRIFT, a two-stage thickness-conditioned rectified flow framework for through-plane MRI super-resolution with continuous input slice-thickness. Stage 1 employs an Anatomical Projection Network (APN) to map low-resolution patches to a coarse high-resolution manifold, providing a deterministic anatomical initialization that shortens the residual transport of Stage 2 and stabilizes slice-wise refinement. Stage 2 refines details via rectified flow and introduces a Physics-Aware Difficulty (PAD) metric derived from slice-thickness induced through-plane bandwidth deficit to guide an Adaptive Integration Scheduler (AIS), allocating ODE steps by thickness. A Consistent Endpoint Trajectory Alignment (CETA) loss enforces thickness-consistent reconstructions. Experiments show that DRIFT outperforms super-resolution baselines while reducing inference cost. Code, models, and interactive demos are available at https://yoonseokchoi-ai.github.io/drift-eccv2026/.

Real-world optimization problems often involve black-box functions and uncertainties in their evaluation, widely referred to as noisy optimization problems (NOPs). Evolutionary algorithms (EA), including Evolutionary Strategies (ES) and genetic algorithms (GA) have been commonly adopted to solve these problems in the contemporary literature. An ongoing challenge is the computational expense involved, given the number of evaluations required for good fitness estimation and ranking. Two fundamental methods commonly used for fitness estimation for NOPs are implicit averaging and explicit averaging. Explicit averaging uses resampling of solutions to improve the estimates, while implicit averaging typically uses a large population size with low resampling. Implicit averaging has been shown to have theoretical advantages for certain cases, which has motivated some recent approaches to use them. However, a recent study demonstrated that its performance is highly dependent on certain assumptions about the function, such as steepness and constant noise level, which may not apply for majority of the real world problems. Moreover, most existing algorithms have only considered homoscedastic noise, where the amplitude of variation is uniform across the entire search space, as opposed to more generic case of heteroscedastic noise. To address these issues, we introduce a set of heteroscedastic test problems and propose a novel confidence ranking method that employs a computationally efficient explicit averaging strategy with sampling budget adaptation. It is implemented within the Covariance Matrix Adaptation ES (CMA-ES) and GA frameworks to demonstrate its effectiveness and versatility. The resulting algorithm is evaluated on a range of problems with both homoscedastic and heteroscedastic noise, and it demonstrates superior performance compared to state-of-the-art approaches.

We study the problem of efficient online proportional sampling from a high-dimensional domain under a $σ$-smoothed adversary, where the sampling distribution is induced by a dynamically evolving weight function defined over a sequence of piecewise-structured partitions. This setting captures a broad range of applications, including principal-agent games (e.g., pricing and contract design), and algorithm configuration and parameter tuning. The central challenge is maintaining an efficient data structure as the induced partition grows increasingly complex over time -- naively, the number of subregions can grow as $O(t^d)$ by round $t$ in $d$ dimensions. We design a data structure that supports efficient updates and proportional sampling while avoiding the cost of explicitly maintaining this exponential growth, where the discontinuities are structured from axis-parallel hyperplanes. Under a $σ$-smoothed adaptive adversary, we prove a tight $O(\sqrt{σT})$ bound on the depth of our data structure, and an $O(\log T)$ bound under a random-order adversary -- to our knowledge, the first such results for this class of problems. We apply this framework to online learning with piecewise-structured rewards, obtaining efficient no-regret algorithms under both full-information and bandit feedback, with provable sublinear regret guarantees.

Data-driven optimization often requires collecting data to estimate uncertain model parameters before solving the underlying decision problem. In practice, however, data acquisition may incur non-negligible costs, making it critical to determine when to stop additional data collection. In this paper, we study an optimal stopping problem for sequential data collection in stochastic optimization under parameter uncertainty. We propose a benefit-driven stopping framework that balances information gain and sampling cost. We model the unknown distribution parameter within a Bayesian learning framework and update beliefs sequentially as new observations are collected. At each iteration, the decision maker evaluates the expected marginal benefit of additional data relative to the unit sampling cost and determines whether to continue sampling or stop and implement the optimization decision. Based on this framework, we develop several stopping policies. The proposed policies are evaluated through a newsvendor problem with exponentially distributed demand. Numerical experiments compare the policies with fixed-budget and hindsight benchmark strategies. The results show that benefit-driven stopping rules can substantially reduce unnecessary data collection while achieving near-optimal decision performance, demonstrating the effectiveness of adaptive stopping in data-driven optimization.

Subsampling significantly reduces the number of measurements, thereby streamlining data processing and transfer overhead, and shortening acquisition time across diverse real-world applications. The recently introduced Active Deep Probabilistic Subsampling (A-DPS) approach jointly optimizes both the subsampling pattern and the downstream task model, enabling instance- and subject-specific sampling trajectories and effective adaptation to new data at inference time. However, this approach does not fully leverage valuable dataset priors and relies on top-1 sampling, which can impede the optimization process. Herein, we enhance A-DPS by integrating a deterministic (fixed) prior-informed sampling pattern derived from the training dataset, along with group-based sampling via top-k sampling, to achieve more robust optimization, method we call Prior-aware and context-guided Group-based Active DPS (PGA-DPS). We also provide a theoretical analysis supporting improved optimization via group sampling, and validate this with empirical results. We evaluated PGA-DPS on three tasks: classification, image reconstruction, and segmentation, using the MNIST, CIFAR-10, fastMRI knee, and hyperspectral AeroRIT datasets, respectively. In every case, PGA-DPS outperformed A-DPS, DPS, and all other sampling methods.

Eco-acoustic monitoring generates vast volumes of audio data, making active learning a promising approach for reducing annotation effort while efficiently training reliable biodiversity classifiers. This report presents CARE-DPP, a batch active-learning acquisition method submitted to BioDCASE Active Learning for Bioacoustics 2026 challenge. The method combines class-balanced predictive uncertainty with embedding-space novelty, while a determinantal point process (DPP) objective selects a high-quality and non-redundant acquisition batch. The uncertainty-novelty balance is annealed over the annotation budget: early cycles emphasize geometric coverage, whereas later cycles increasingly exploit classifier uncertainty. To mitigate unreliable early scores, the DPP candidate pool mixes top-quality candidates with a decreasing proportion of random exploration. An adaptive acquisition schedule uses smaller batches early and larger batches later. Evaluated over five repeats on the BirdSet HSN, POW and UHH subsets and on ATBFL, CARE-DPP obtains a mean development AULC of 0.50 for macro mAP, compared with 0.46 for the official CoreSet baseline. Ablations identify DPP batch diversification and the adaptive acquisition schedule as the largest contributors.

We present K-ABENA (K-Adaptive Backpropagation with Error-based N-exclusion Algorithm), a selective gradient computation framework that reduces per-iteration training cost by excluding a fraction of low-loss ("minor") observations from the backward pass. Its canonical form (v3) combines a defensive-mixture sampling design over the minor set with Horvitz-Thompson inverse-probability reweighting, yielding a design-unbiased Horvitz-Thompson gradient estimator (Lemma 2) and whose self-normalized practical variant carries a bias of order O(1/m) with an explicit constant (Lemma 3). We prove an O(1/sqrt(T)) non-convex convergence guarantee for SGD under the estimator, with an additive term that quantifies the residual bias (Theorem 1). We further prove that uncompensated loss-based selection - a family that includes OHEM, SBP, and the two earlier K-ABENA variants - admits no stationary point at any minimizer where its selection bias is bounded away from zero (Proposition 2), and we quantify this failure empirically: at 0.17% class imbalance, uncompensated variants reach test AUC 0.53-0.62 versus 0.9998 for full-batch SGD, while the compensated estimator attains 0.9991 at identical 28.4% compute savings. On real datasets (Breast Cancer, Digits, Wine, Diabetes) the compensated estimator is statistically indistinguishable from full-batch SGD (paired permutation tests, p >= 0.5; Section 7) while saving 28-54% of per-epoch gradient computation. A biased "regularized mode" (the earlier half-domain variant) is retained as an option with a proven exact bias decomposition (Lemma 5) and quantified contraindications: it collapses to 0.386 accuracy under 40% label noise (baseline: 0.832) and to 0.53 AUC under extreme imbalance. Every advantage and every limitation reported in this paper is either proved or measured; all experiments are CPU-scale (NumPy/scikit-learn) and their scope is stated explicitly.

Planning under uncertainty in continuous domains is essential for autonomous systems, yet computationally demanding. Tree-based search methods such as Monte Carlo Tree Search (MCTS) remain popular, but their branching structure can require sampling budgets that grow exponentially with lookahead depth in the worst case. From a tree perspective, continuous state or action spaces become especially challenging, since the planner must decide where to search in an infinite branching hierarchy. We propose Graph Sparse Sampling (GSS), an online planning algorithm that shares sampled futures across many candidate decisions, rather than sampling separate successors for each candidate action. This branch-free graph exposes large GPU-friendly batches, while using heuristics to focus computation. We prove finite-sample performance guarantees for GSS covering full-rank or low-rank generative simulators via smoothed backups, and discrete or sampled continuous action spaces. Under suitable overlap, regularity, and action-coverage conditions, these bounds have polynomial dependence on the planning horizon, formalizing when shared futures can avoid the exponential horizon dependence of tree-shaped sparse sampling. We demonstrate continuous-control simulations where GSS substantially outperforms tree-based planners on long horizons or achieves near-optimal performance, supporting no-branching graph planning as a complementary design principle for online control.

Active learning is a promising framework for reducing annotation costs in large-scale bioacoustic monitoring, where expert labeling is expensive and data distributions are highly heterogeneous across environments. However, existing sample selection strategies often rely on static criteria that do not adapt to the evolving reliability of model predictions during training. This limitation can lead to suboptimal exploration-exploitation trade-offs and redundant sample selection. We propose an active learning strategy for multilabel bioacoustic event classification that jointly models predictive uncertainty, embedding-space diversity, and intra-batch redundancy. The method introduces an adaptive weighting scheme that progressively shifts from diversity-driven exploration in high-uncertainty regimes toward uncertainty-driven exploitation as the model becomes more confident, reflecting the increasing reliability of the classifier. To further improve annotation efficiency, a greedy Maximum Marginal Relevance (MMR) procedure is used to enforce diversity among selected samples within each acquisition batch. We evaluate the proposed approach within the BioDCASE 2026 Task 4 active learning framework on terrestrial (BirdSet) and marine (ATBFL) benchmarks using pretrained audio embeddings and a fixed annotation budget. Experimental results show consistent improvements in learning efficiency and competitive in terms of macro mean Average Precision (mAP) and Area Under the Learning Curve (AULC) across heterogeneous acoustic domains. The gains are particularly pronounced on structured terrestrial soundscapes, while performance remains competitive under noisier marine conditions. These findings demonstrate that adaptive acquisition strategies combining uncertainty estimation, embedding-space diversity, and redundancy-aware batch construction provide an effective and robust solution for [...].

Computed Tomography (CT) is indispensable in clinical diagnostics, yet minimizing radiation dose without compromising image quality remains a critical challenge. Conventional low-dose protocols often rely on fixed, uniform angular sampling, independent of the underlying structural complexity of organs of individual patients. We propose ``Stochastic Adaptive Variance-Driven Exploration and Reconstruction'' (SAVER), an adaptive data acquisition framework that selects projection angles in real-time based on the statistical variance of acquired data. Utilizing a Softmax-based stochastic scheduling scheme with simulated annealing, SAVER prioritizes directions with high structural information while maintaining necessary exploration. Numerical experiments across 8 diverse phantoms demonstrate that SAVER achieves consistently higher reconstruction fidelity than conventional random sampling, particularly for objects with high structural anisotropy. Furthermore, the proposed method exhibits robust performance under significant measurement noise. By dynamically reallocating radiation dose to the most informative projections, SAVER provides a mathematically-grounded approach to maximize diagnostic quality per unit of radiation dose, marking a shift toward sample-dependent, data-driven CT acquisition.

The informativeness of a training set is as consequential as its size, yet most sampling strategies remain agnostic to the intrinsic geometry of the data distribution. We introduce CuBAS (Curvature-Based Adaptive Sampling), an information-geometric framework for adaptive data selection in supervised classification, grounded in the q-state Potts Markov random field (MRF) model. The central insight is that a labeled dataset can be viewed as a statistical manifold, on which local curvature, estimated via the ratio of second to first-order observed Fisher information, faithfully encodes the geometric complexity of the data distribution. We construct a k-nearest-neighbor graph over the labeled data and derive a closed-form curvature score at each vertex from the Potts sufficient statistics. This curvature signal partitions the graph into two complementary regimes: low-curvature regions, corresponding to smooth, homogeneous clusters, and high-curvature regions, concentrated around decision boundaries that are disproportionately informative for classification. By selecting nodes from both regimes, CuBAS constructs compact yet maximally informative training subsets. Empirical evaluation across more than 60 benchmark datasets demonstrates consistent and statistically significant improvements over random sampling and uncertainty-based baselines, across a wide range of labeling budgets and classifier architectures. CuBAS is computationally efficient (linear in the number of k-NN graph edges), theoretically grounded in the differential geometry of statistical manifolds, and interpretable in terms of the local shape operator of the data manifold.