Daily Papers

The long-tail distribution of the visual world poses great challenges for deep learning based classification models on how to handle the class imbalance problem. Existing solutions usually involve class-balancing strategies, e.g., by loss re-weighting, data re-sampling, or transfer learning from head- to tail-classes, but most of them adhere to the scheme of jointly learning representations and classifiers. In this work, we decouple the learning procedure into representation learning and classification, and systematically explore how different balancing strategies affect them for long-tailed recognition. The findings are surprising: (1) data imbalance might not be an issue in learning high-quality representations; (2) with representations learned with the simplest instance-balanced (natural) sampling, it is also possible to achieve strong long-tailed recognition ability by adjusting only the classifier. We conduct extensive experiments and set new state-of-the-art performance on common long-tailed benchmarks like ImageNet-LT, Places-LT and iNaturalist, showing that it is possible to outperform carefully designed losses, sampling strategies, even complex modules with memory, by using a straightforward approach that decouples representation and classification. Our code is available at https://github.com/facebookresearch/classifier-balancing.

White blood cell (WBC) classification is fundamental for hematology applications such as infection assessment, leukemia screening, and treatment monitoring. However, real-world WBC datasets present substantial appearance variations caused by staining and scanning conditions, as well as severe class imbalance in which common cell types dominate while rare but clinically important categories are underrepresented. To address these challenges, we propose a stain-normalized, decoupled training framework that first learns transferable representations using instance-balanced sampling, and then rebalances the classifier with class-aware sampling and a hybrid loss combining effective-number weighting and focal modulation. In inference stage, we further enhance robustness by ensembling various trained backbones with test-time augmentation. Our approach achieved the top rank on the leaderboard of the WBCBench 2026: Robust White Blood Cell Classification Challenge at ISBI 2026.

In domains ranging from computer vision to natural language processing, machine learning models have been shown to exhibit stark disparities, often performing worse for members of traditionally underserved groups. One factor contributing to these performance gaps is a lack of representation in the data the models are trained on. It is often unclear, however, how to operationalize representativeness in specific applications. Here we formalize the problem of creating equitable training datasets, and propose a statistical framework for addressing this problem. We consider a setting where a model builder must decide how to allocate a fixed data collection budget to gather training data from different subgroups. We then frame dataset creation as a constrained optimization problem, in which one maximizes a function of group-specific performance metrics based on (estimated) group-specific learning rates and costs per sample. This flexible approach incorporates preferences of model-builders and other stakeholders, as well as the statistical properties of the learning task. When data collection decisions are made sequentially, we show that under certain conditions this optimization problem can be efficiently solved even without prior knowledge of the learning rates. To illustrate our approach, we conduct a simulation study of polygenic risk scores on synthetic genomic data -- an application domain that often suffers from non-representative data collection. We find that our adaptive sampling strategy outperforms several common data collection heuristics, including equal and proportional sampling, demonstrating the value of strategic dataset design for building equitable models.

We investigate imbalanced regression with tabular data that have an imbalance ratio larger than 1,000 ("highly imbalanced"). Accurately estimating the target values of rare instances is important in applications such as forecasting the intensity of rare harmful Solar Energetic Particle (SEP) events. For regression, the MSE loss does not consider the correlation between predicted and actual values. Typical inverse importance functions allow only convex functions. Uniform sampling might yield mini-batches that do not have rare instances. We propose CISIR that incorporates correlation, Monotonically Decreasing Involution (MDI) importance, and stratified sampling. Based on five datasets, our experimental results indicate that CISIR can achieve lower error and higher correlation than some recent methods. Also, adding our correlation component to other recent methods can improve their performance. Lastly, MDI importance can outperform other importance functions. Our code can be found in https://github.com/Machine-Earning/CISIR.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula (1-β^{n})/(1-β), where n is the number of samples and βin [0,1) is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.

Class imbalance is a fundamental challenge in medical image segmentation, where frequent classes typically dominate training at the expense of rare classes. Loss-based approaches mitigate imbalance by reweighting the per-pixel loss within the batch, while sampling strategies control which images enter the batch. Yet neither explicitly controls which classes appear within the batch, leaving rare-class exposure only partially rebalanced. In this work, we adopt episodic sampling from few-shot learning to promote class-balanced batch construction in a fully supervised setting. We decouple episodic sampling from its conventional metric-learning context and evaluate it in body composition segmentation in CT. We compare episodic sampling against random and weighted sampling on nine muscle and adipose tissues, derived from 210 scans of the public SAROS dataset. Training is performed under full- and low-data regimes, with additional comparisons under matched training iteration budgets. Under full-data training, all three strategies performed comparably (mean Dice 0.882 for episodic, 0.878 for random and weighted). Under low-data training, episodic sampling outperformed random and weighted (0.787 vs. 0.758 and 0.762), driven by a 12-fold difference in training iterations. Under matched training budgets, random and weighted overfit earlier, while episodic improved for approximately three times more iterations before plateauing. Our findings identify the training iteration budget as under-recognized confound in sampling strategies, motivating iteration-aware evaluation protocols for small datasets. Furthermore, the residual advantage of episodic sampling is consistent with an implicit regularization effect of class-balanced batches, offering a low-cost, model-agnostic strategy for class-imbalanced medical image segmentation. Code is available at https://github.com/iasonsky/episodic-sampling.

Sampling is ubiquitous in machine learning methodologies. Due to the growth of large datasets and model complexity, we want to learn and adapt the sampling process while training a representation. Towards achieving this grand goal, a variety of sampling techniques have been proposed. However, most of them either use a fixed sampling scheme or adjust the sampling scheme based on simple heuristics. They cannot choose the best sample for model training in different stages. Inspired by "Think, Fast and Slow" (System 1 and System 2) in cognitive science, we propose a reward-guided sampling strategy called Adaptive Sample with Reward (ASR) to tackle this challenge. To the best of our knowledge, this is the first work utilizing reinforcement learning (RL) to address the sampling problem in representation learning. Our approach optimally adjusts the sampling process to achieve optimal performance. We explore geographical relationships among samples by distance-based sampling to maximize overall cumulative reward. We apply ASR to the long-standing sampling problems in similarity-based loss functions. Empirical results in information retrieval and clustering demonstrate ASR's superb performance across different datasets. We also discuss an engrossing phenomenon which we name as "ASR gravity well" in experiments.

We present a novel approach for generating minority samples that live on low-density regions of a data manifold. Our framework is built upon diffusion models, leveraging the principle of guided sampling that incorporates an arbitrary energy-based guidance during inference time. The key defining feature of our sampler lies in its self-contained nature, \ie, implementable solely with a pretrained model. This distinguishes our sampler from existing techniques that require expensive additional components (like external classifiers) for minority generation. Specifically, we first estimate the likelihood of features within an intermediate latent sample by evaluating a reconstruction loss w.r.t. its posterior mean. The generation then proceeds with the minimization of the estimated likelihood, thereby encouraging the emergence of minority features in the latent samples of subsequent timesteps. To further improve the performance of our sampler, we provide several time-scheduling techniques that properly manage the influence of guidance over inference steps. Experiments on benchmark real datasets demonstrate that our approach can greatly improve the capability of creating realistic low-likelihood minority instances over the existing techniques without the reliance on costly additional elements. Code is available at https://github.com/soobin-um/sg-minority.

Repeated Sampling (RS) is a simple inference-time algorithm that has been shown to improve model performance on complex tasks. Although it is an effective way of scaling inference time, it often struggles to generate diverse solution candidates, frequently relying on the same underlying approach to solve the problem and thus producing redundant samples. To address this limitation, we propose a new inference algorithm, GuidedSampling, which decouples the exploration and generation phases during inference, increasing diversity of generated candidate solutions. The exploration phase identifies multiple concepts that can be utilized to solve the problem, while the generation phase applies a specific concept to provide final solution candidates. We first define the theoretical bounds of GuidedSampling and then empirically demonstrate that it improves the performance of base model at pass@50 by on an average ~21.6% across various benchmarks compared to RS. Furthermore, models trained on trajectories of GuidedSampling exhibit substantial performance improvements at pass@5 by on an average ~9.7%, compared to models trained on traditional RS. Additionally, models trained with GuidedSampling increases the average number of concepts per instance (1.67 -> 3.03), yielding a diverse set of candidates than traditional RS.

Rejection sampling is a technique for sampling from difficult distributions. However, its use is limited due to a high rejection rate. Common adaptive rejection sampling methods either work only for very specific distributions or without performance guarantees. In this paper, we present pliable rejection sampling (PRS), a new approach to rejection sampling, where we learn the sampling proposal using a kernel estimator. Since our method builds on rejection sampling, the samples obtained are with high probability i.i.d. and distributed according to f. Moreover, PRS comes with a guarantee on the number of accepted samples.

Polar slice sampling (Roberts & Rosenthal, 2002) is a Markov chain approach for approximate sampling of distributions that is difficult, if not impossible, to implement efficiently, but behaves provably well with respect to the dimension. By updating the directional and radial components of chain iterates separately, we obtain a family of samplers that mimic polar slice sampling, and yet can be implemented efficiently. Numerical experiments in a variety of settings indicate that our proposed algorithm outperforms the two most closely related approaches, elliptical slice sampling (Murray et al., 2010) and hit-and-run uniform slice sampling (MacKay, 2003). We prove the well-definedness and convergence of our methods under suitable assumptions on the target distribution.

An approach to the construction of classifiers from imbalanced datasets is described. A dataset is imbalanced if the classification categories are not approximately equally represented. Often real-world data sets are predominately composed of "normal" examples with only a small percentage of "abnormal" or "interesting" examples. It is also the case that the cost of misclassifying an abnormal (interesting) example as a normal example is often much higher than the cost of the reverse error. Under-sampling of the majority (normal) class has been proposed as a good means of increasing the sensitivity of a classifier to the minority class. This paper shows that a combination of our method of over-sampling the minority (abnormal) class and under-sampling the majority (normal) class can achieve better classifier performance (in ROC space) than only under-sampling the majority class. This paper also shows that a combination of our method of over-sampling the minority class and under-sampling the majority class can achieve better classifier performance (in ROC space) than varying the loss ratios in Ripper or class priors in Naive Bayes. Our method of over-sampling the minority class involves creating synthetic minority class examples. Experiments are performed using C4.5, Ripper and a Naive Bayes classifier. The method is evaluated using the area under the Receiver Operating Characteristic curve (AUC) and the ROC convex hull strategy.

Self-supervised features are the cornerstone of modern machine learning systems. They are typically pre-trained on data collections whose construction and curation typically require extensive human effort. This manual process has some limitations similar to those encountered in supervised learning, e.g., the crowd-sourced selection of data is costly and time-consuming, preventing scaling the dataset size. In this work, we consider the problem of automatic curation of high-quality datasets for self-supervised pre-training. We posit that such datasets should be large, diverse and balanced, and propose a clustering-based approach for building ones satisfying all these criteria. Our method involves successive and hierarchical applications of k-means on a large and diverse data repository to obtain clusters that distribute uniformly among data concepts, followed by a hierarchical, balanced sampling step from these clusters. Extensive experiments on three different data domains including web-based images, satellite images and text show that features trained on our automatically curated datasets outperform those trained on uncurated data while being on par or better than ones trained on manually curated data.

We explore the problem of generating minority samples using diffusion models. The minority samples are instances that lie on low-density regions of a data manifold. Generating a sufficient number of such minority instances is important, since they often contain some unique attributes of the data. However, the conventional generation process of the diffusion models mostly yields majority samples (that lie on high-density regions of the manifold) due to their high likelihoods, making themselves ineffective and time-consuming for the minority generating task. In this work, we present a novel framework that can make the generation process of the diffusion models focus on the minority samples. We first highlight that Tweedie's denoising formula yields favorable results for majority samples. The observation motivates us to introduce a metric that describes the uniqueness of a given sample. To address the inherent preference of the diffusion models w.r.t. the majority samples, we further develop minority guidance, a sampling technique that can guide the generation process toward regions with desired likelihood levels. Experiments on benchmark real datasets demonstrate that our minority guidance can greatly improve the capability of generating high-quality minority samples over existing generative samplers. We showcase that the performance benefit of our framework persists even in demanding real-world scenarios such as medical imaging, further underscoring the practical significance of our work. Code is available at https://github.com/soobin-um/minority-guidance.

Sampling-based search, a simple paradigm for utilizing test-time compute, involves generating multiple candidate responses and selecting the best one -- typically by verifying each response for correctness. In this paper, we study the scaling trends governing sampling-based search. Among our findings is that simply scaling up a minimalist implementation that uses only random sampling and direct self-verification results in sustained performance improvements that, for example, elevate the Gemini v1.5 Pro model's reasoning capabilities past that of o1-Preview on popular benchmarks. We partially attribute the scalability of sampling-based search to a phenomenon of implicit scaling, where sampling a larger pool of responses in turn improves verification accuracy. We further identify two useful principles for improving self-verification capabilities with test-time compute: (1) comparing across responses provides helpful signals about the locations of errors and hallucinations, and (2) different model output styles are useful for different contexts -- chains of thought are useful for reasoning but harder to verify. We also find that, though accurate verification can be elicited, frontier models demonstrate remarkably weak out-of-box verification capabilities and introduce a benchmark to measure progress on these deficiencies.

We propose an embarrassingly simple method -- instance-aware repeat factor sampling (IRFS) to address the problem of imbalanced data in long-tailed object detection. Imbalanced datasets in real-world object detection often suffer from a large disparity in the number of instances for each class. To improve the generalization performance of object detection models on rare classes, various data sampling techniques have been proposed. Repeat factor sampling (RFS) has shown promise due to its simplicity and effectiveness. Despite its efficiency, RFS completely neglects the instance counts and solely relies on the image count during re-sampling process. However, instance count may immensely vary for different classes with similar image counts. Such variation highlights the importance of both image and instance for addressing the long-tail distributions. Thus, we propose IRFS which unifies instance and image counts for the re-sampling process to be aware of different perspectives of the imbalance in long-tailed datasets. Our method shows promising results on the challenging LVIS v1.0 benchmark dataset over various architectures and backbones, demonstrating their effectiveness in improving the performance of object detection models on rare classes with a relative +50% average precision (AP) improvement over counterpart RFS. IRFS can serve as a strong baseline and be easily incorporated into existing long-tailed frameworks.

Data plays a fundamental role in the training of Large Language Models (LLMs). While attention has been paid to the collection and composition of datasets, determining the data sampling strategy in training remains an open question. Most LLMs are trained with a simple strategy, random sampling. However, this sampling strategy ignores the unbalanced nature of training data distribution, which can be sub-optimal. In this paper, we propose ClusterClip Sampling to balance the text distribution of training data for better model training. Specifically, ClusterClip Sampling utilizes data clustering to reflect the data distribution of the training set and balances the common samples and rare samples during training based on the cluster results. A repetition clip operation is introduced to mitigate the overfitting issue led by samples from certain clusters. Extensive experiments validate the effectiveness of ClusterClip Sampling, which outperforms random sampling and other cluster-based sampling variants under various training datasets and large language models.

Thompson sampling is an algorithm for online decision problems where actions are taken sequentially in a manner that must balance between exploiting what is known to maximize immediate performance and investing to accumulate new information that may improve future performance. The algorithm addresses a broad range of problems in a computationally efficient manner and is therefore enjoying wide use. This tutorial covers the algorithm and its application, illustrating concepts through a range of examples, including Bernoulli bandit problems, shortest path problems, product recommendation, assortment, active learning with neural networks, and reinforcement learning in Markov decision processes. Most of these problems involve complex information structures, where information revealed by taking an action informs beliefs about other actions. We will also discuss when and why Thompson sampling is or is not effective and relations to alternative algorithms.

Standard continuous-time generative models rely on monolithic architectures that must navigate vastly different signal regimes, from isotropic noise to intricate data distributions. While scaling model capacity improves performance, deploying a massive network uniformly across the entire generative timeline is inherently inefficient. In this work, we propose Complexity-Balanced Splitting (CBS), a principled framework for temporal capacity allocation that distributes the generative workload across multiple specialized sub-networks. Grounded in function approximation theory and de Boor's equidistribution principle, CBS partitions the diffusion timeline into segments of equal approximation burden, allocating more representational capacity to regions where the generative dynamics are more difficult to model. To estimate this local complexity, we introduce two complementary and tractable monitor functions: a spatial measure based on the flow's Dirichlet energy, and a geometric measure based on the acceleration of the sampling trajectories. Using a lightweight auxiliary model to estimate these complexity profiles, our approach eliminates the need for heuristic temporal splits or computationally expensive search procedures. Extensive evaluation across multiple architectures (SiT, JiT, and UNet) and datasets demonstrates that CBS consistently improves synthesis quality without increasing per-step inference cost. In particular, CBS improves FID by ~35% on SiT-XL with CFG relative to naive temporal partitioning. Project page is available at https://noamissachar.github.io/CBS/.

The rise in internet usage has led to the generation of massive amounts of data, resulting in the adoption of various supervised and semi-supervised machine learning algorithms, which can effectively utilize the colossal amount of data to train models. However, before deploying these models in the real world, these must be strictly evaluated on performance measures like worst-case recall and satisfy constraints such as fairness. We find that current state-of-the-art empirical techniques offer sub-optimal performance on these practical, non-decomposable performance objectives. On the other hand, the theoretical techniques necessitate training a new model from scratch for each performance objective. To bridge the gap, we propose SelMix, a selective mixup-based inexpensive fine-tuning technique for pre-trained models, to optimize for the desired objective. The core idea of our framework is to determine a sampling distribution to perform a mixup of features between samples from particular classes such that it optimizes the given objective. We comprehensively evaluate our technique against the existing empirical and theoretically principled methods on standard benchmark datasets for imbalanced classification. We find that proposed SelMix fine-tuning significantly improves the performance for various practical non-decomposable objectives across benchmarks.

Large language models show great potential in generating and optimizing code. Widely used sampling methods such as Nucleus Sampling increase the diversity of generation but often produce repeated samples for low temperatures and incoherent samples for high temperatures. Furthermore, the temperature coefficient has to be tuned for each task, limiting its usability. We present Priority Sampling, a simple and deterministic sampling technique that produces unique samples ordered by the model's confidence. Each new sample expands the unexpanded token with the highest probability in the augmented search tree. Additionally, Priority Sampling supports generation based on regular expression that provides a controllable and structured exploration process. Priority Sampling outperforms Nucleus Sampling for any number of samples, boosting the performance of the original model from 2.87% to 5% improvement over -Oz. Moreover, it outperforms the autotuner used for the generation of labels for the training of the original model in just 30 samples.

Finetuning large language models on instruction data is crucial for enhancing pre-trained knowledge and improving instruction-following capabilities. As instruction datasets proliferate, selecting optimal data for effective training becomes increasingly important. This work addresses the question: How can we determine the optimal subset of data for effective training? While existing research often emphasizes local criteria like instance quality for subset selection, we argue that a global approach focused on data diversity is more critical. Our method employs k-means clustering to ensure the selected subset effectively represents the full dataset. We propose an iterative refinement method inspired by active learning techniques to resample instances from clusters, reassessing each cluster's importance and sampling weight in every training iteration. This approach reduces the effect of outliers and automatically filters out clusters containing low-quality data. Through extensive evaluation across natural language reasoning, general world knowledge, code and math reasoning tasks, and by fine-tuning models from various families, we observe consistent improvements, achieving a 7% increase over random selection and a 3.8% improvement over state-of-the-art sampling methods. Our work highlights the significance of diversity-first sampling when finetuning LLMs to enhance performance across a broad array of evaluation tasks. Our code is available at https://github.com/for-ai/iterative-data-selection.

We investigate the extent to which offline demonstration data can improve online learning. It is natural to expect some improvement, but the question is how, and by how much? We show that the degree of improvement must depend on the quality of the demonstration data. To generate portable insights, we focus on Thompson sampling (TS) applied to a multi-armed bandit as a prototypical online learning algorithm and model. The demonstration data is generated by an expert with a given competence level, a notion we introduce. We propose an informed TS algorithm that utilizes the demonstration data in a coherent way through Bayes' rule and derive a prior-dependent Bayesian regret bound. This offers insight into how pretraining can greatly improve online performance and how the degree of improvement increases with the expert's competence level. We also develop a practical, approximate informed TS algorithm through Bayesian bootstrapping and show substantial empirical regret reduction through experiments.

Existing pretraining data mixing methods for large language models (LLMs) typically follow a domain-wise methodology, a top-down process that first determines domain weights and then performs uniform data sampling across each domain. However, these approaches neglect significant inter-domain overlaps and commonalities, failing to control the global diversity of the constructed training dataset. Further, uniform sampling within domains ignores fine-grained sample-specific features, potentially leading to suboptimal data distribution. To address these shortcomings, we propose a novel sample-wise data mixture approach based on a bottom-up paradigm. This method performs global cross-domain sampling by systematically evaluating the quality and diversity of each sample, thereby dynamically determining the optimal domain distribution. Comprehensive experiments across multiple downstream tasks and perplexity assessments demonstrate that SampleMix surpasses existing domain-based methods. Meanwhile, SampleMix requires 1.4x to 2.1x training steps to achieves the baselines' performance, highlighting the substantial potential of SampleMix to optimize pre-training data.

Assessing the capabilities and risks of frontier AI systems is a critical area of research, and recent work has shown that repeated sampling from models can dramatically increase both. For instance, repeated sampling has been shown to increase their capabilities, such as solving difficult math and coding problems, but it has also been shown to increase their potential for harm, such as being jailbroken. Such results raise a crucial question for both capability and safety forecasting: how can one accurately predict a model's behavior when scaled to a massive number of attempts, given a vastly smaller sampling budget? This question is directly relevant to model providers, who serve hundreds of millions of users daily, and to governmental regulators, who seek to prevent harms. To answer this questions, we make three contributions. First, we find that standard methods for fitting these laws suffer from statistical shortcomings that hinder predictive accuracy, especially in data-limited scenarios. Second, we remedy these shortcomings by introducing a robust estimation framework, which uses a beta-binomial distribution to generate more accurate predictions from limited data. Third, we propose a dynamic sampling strategy that allocates a greater budget to harder problems. Combined, these innovations enable more reliable prediction of rare risks and capabilities at a fraction of the computational cost.

Self-improvement methods enable large language models (LLMs) to generate solutions themselves and iteratively train on filtered, high-quality rationales. This process proves effective and reduces the reliance on human supervision in LLMs' reasoning, but the performance soon plateaus. We delve into the process and find that models tend to over-sample on easy queries and under-sample on queries they have yet to master. As iterations proceed, this imbalance in sampling is exacerbated, leading to a long-tail distribution where solutions to difficult queries almost diminish. This phenomenon limits the performance gain of self-improving models. A straightforward solution is brute-force sampling to balance the distribution, which significantly raises computational costs. In this paper, we introduce Guided Self-Improvement (GSI), a strategy aimed at improving the efficiency of sampling challenging heavy-tailed data. It leverages Socratic-style guidance signals to help LLM reasoning with complex queries, reducing the exploration effort and minimizing computational overhead. Experiments on four models across diverse mathematical tasks show that GSI strikes a balance between performance and efficiency, while also being effective on held-out tasks.

Model customization necessitates high-quality and diverse datasets, but acquiring such data remains time-consuming and labor-intensive. Despite the great potential of large language models (LLMs) for data synthesis, current approaches are constrained by limited seed data, model biases, and low-variation prompts, resulting in limited diversity and biased distributions with the increase of data scales. To tackle this challenge, we introduce TREESYNTH, a tree-guided subspace-based data synthesis approach inspired by decision trees. It constructs a spatial partitioning tree to recursively divide a task-specific full data space (i.e., root node) into numerous atomic subspaces (i.e., leaf nodes) with mutually exclusive and exhaustive attributes to ensure both distinctiveness and comprehensiveness before synthesizing samples within each atomic subspace. This globally dividing-and-synthesizing method finally collects subspace samples into a comprehensive dataset, effectively circumventing repetition and space collapse to ensure the diversity of large-scale data synthesis. Furthermore, the spatial partitioning tree enables sample allocation into atomic subspaces, allowing the rebalancing of existing datasets for more balanced and comprehensive distributions. Empirically, extensive experiments across diverse benchmarks consistently demonstrate the superior data diversity, model performance, and robust scalability of TREESYNTH compared to both human-crafted datasets and peer data synthesis methods, with an average performance gain reaching 10%. Besides, the consistent improvements of TREESYNTH-balanced datasets highlight its efficacious application to redistribute existing datasets for more comprehensive coverage and the induced performance enhancement. The code is available at https://github.com/cpa2001/TreeSynth.

Fairness in graph neural networks has been actively studied recently. However, existing works often do not explicitly consider the role of message passing in introducing or amplifying the bias. In this paper, we first investigate the problem of bias amplification in message passing. We empirically and theoretically demonstrate that message passing could amplify the bias when the 1-hop neighbors from different demographic groups are unbalanced. Guided by such analyses, we propose BeMap, a fair message passing method, that leverages a balance-aware sampling strategy to balance the number of the 1-hop neighbors of each node among different demographic groups. Extensive experiments on node classification demonstrate the efficacy of BeMap in mitigating bias while maintaining classification accuracy. The code is available at https://github.com/xiaolin-cs/BeMap.

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.

Data quality and diversity are key to the construction of effective instruction-tuning datasets. % With the increasing availability of open-source instruction-tuning datasets, it is advantageous to automatically select high-quality and diverse subsets from a vast amount of data. % Existing methods typically prioritize instance quality and use heuristic rules to maintain diversity. % However, this absence of a comprehensive view of the entire collection often leads to suboptimal results. % Moreover, heuristic rules generally focus on distance or clustering within the embedding space, which fails to accurately capture the intent of complex instructions in the semantic space. % To bridge this gap, we propose a unified method for quantifying the information content of datasets. This method models the semantic space by constructing a label graph and quantifies diversity based on the distribution of information within the graph. % Based on such a measurement, we further introduce an efficient sampling method that selects data samples iteratively to Maximize the Information Gain (MIG) in semantic space. % Experiments on various datasets and base models demonstrate that MIG consistently outperforms state-of-the-art methods. % Notably, the model fine-tuned with 5\% Tulu3 data sampled by MIG achieves comparable performance to the official SFT model trained on the full dataset, with improvements of +5.73\% on AlpacaEval and +6.89\% on Wildbench.

Experience replay is a key component in reinforcement learning for stabilizing learning and improving sample efficiency. Its typical implementation samples transitions with replacement from a replay buffer. In contrast, in supervised learning with a fixed dataset, it is a common practice to shuffle the dataset every epoch and consume data sequentially, which is called random reshuffling (RR). RR enjoys theoretically better convergence properties and has been shown to outperform with-replacement sampling empirically. To leverage the benefits of RR in reinforcement learning, we propose sampling methods that extend RR to experience replay, both in uniform and prioritized settings. We evaluate our sampling methods on Atari benchmarks, demonstrating their effectiveness in deep reinforcement learning.

Generative processes that involve solving differential equations, such as diffusion models, frequently necessitate balancing speed and quality. ODE-based samplers are fast but plateau in performance while SDE-based samplers deliver higher sample quality at the cost of increased sampling time. We attribute this difference to sampling errors: ODE-samplers involve smaller discretization errors while stochasticity in SDE contracts accumulated errors. Based on these findings, we propose a novel sampling algorithm called Restart in order to better balance discretization errors and contraction. The sampling method alternates between adding substantial noise in additional forward steps and strictly following a backward ODE. Empirically, Restart sampler surpasses previous SDE and ODE samplers in both speed and accuracy. Restart not only outperforms the previous best SDE results, but also accelerates the sampling speed by 10-fold / 2-fold on CIFAR-10 / ImageNet 64 times 64. In addition, it attains significantly better sample quality than ODE samplers within comparable sampling times. Moreover, Restart better balances text-image alignment/visual quality versus diversity than previous samplers in the large-scale text-to-image Stable Diffusion model pre-trained on LAION 512 times 512. Code is available at https://github.com/Newbeeer/diffusion_restart_sampling

Sampling is a basic operation in many inference-time algorithms of large language models (LLMs). To scale up inference efficiently with a limited compute, it is crucial to find an optimal allocation for sample compute budgets: Which sampling configurations (model, temperature, language, etc.) do we use? How many samples do we generate in each configuration? We formulate these choices as a learning problem and propose OSCA, an algorithm that Optimizes Sample Compute Allocation by finding an optimal mix of different inference configurations. Our experiments show that with our learned mixed allocation, we can achieve accuracy better than the best single configuration with 128x less compute on code generation and 25x less compute on 4 reasoning tasks. OSCA is also shown to be effective in agentic workflows beyond single-turn tasks, achieving a better accuracy on SWE-Bench with 3x less compute than the default configuration. Our code and generations are released at https://github.com/LeiLiLab/OSCA.

Large language models (LLMs) are often equipped with multi-sample decoding strategies. An LLM implicitly defines an arithmetic code book, facilitating efficient and embarrassingly parallelizable arithmetic sampling to produce multiple samples using quasi-random codes. Traditional text generation methods, such as beam search and sampling-based techniques, have notable limitations: they lack parallelizability or diversity of sampled sequences. This study explores the potential of arithmetic sampling, contrasting it with ancestral sampling across two decoding tasks that employ multi-sample inference: chain-of-thought reasoning with self-consistency and machine translation with minimum Bayes risk decoding. Our results demonstrate that arithmetic sampling produces more diverse samples, significantly improving reasoning and translation performance as the sample size increases. We observe a 3text{-5%} point increase in accuracy on the GSM8K dataset and a 0.45text{-0.89%} point increment in COMET score for WMT19 tasks using arithmetic sampling without any significant computational overhead.

The training of large language models (LLMs) is expensive. In this paper, we study data-efficient approaches for pre-training LLMs, i.e., techniques that aim to optimize the Pareto frontier of model quality and training resource/data consumption. We seek to understand the tradeoffs associated with data selection routines based on (i) expensive-to-compute data-quality estimates, and (ii) maximization of coverage and diversity-based measures in the feature space. Our first technique, Ask-LLM, leverages the zero-shot reasoning capabilities of instruction-tuned LLMs to directly assess the quality of a training example. To target coverage, we propose Density sampling, which models the data distribution to select a diverse sample. In our comparison of 19 samplers, involving hundreds of evaluation tasks and pre-training runs, we find that Ask-LLM and Density are the best methods in their respective categories. Coverage sampling can recover the performance of the full data, while models trained on Ask-LLM data consistently outperform full-data training -- even when we reject 90% of the original dataset, while converging up to 70% faster.

The task of mixture proportion estimation (MPE) is to estimate the weight of a component distribution in a mixture, given observations from both the component and mixture. Previous work on MPE adopts the irreducibility assumption, which ensures identifiablity of the mixture proportion. In this paper, we propose a more general sufficient condition that accommodates several settings of interest where irreducibility does not hold. We further present a resampling-based meta-algorithm that takes any existing MPE algorithm designed to work under irreducibility and adapts it to work under our more general condition. Our approach empirically exhibits improved estimation performance relative to baseline methods and to a recently proposed regrouping-based algorithm.

Consider a fixed universe of N=2^n elements and the uniform distribution over elements of some subset of size K. Given samples from this distribution, the task of complement sampling is to provide a sample from the complementary subset. We give a simple quantum algorithm that uses only a single quantum sample -- a single copy of the uniform superposition over elements of the subset. When K=N/2, we show that the quantum algorithm succeeds with probability 1, whereas any classical algorithm that succeeds with bounded probability of error requires a number of samples of the order of N. This shows that in a sample-to-sample setting, quantum computation can achieve the largest possible separation over classical computation. We show that the same bound can be lifted to prove average-case hardness, paving the way for demonstrations on noisy intermediate-scale quantum (NISQ) computers. It follows that under the assumption of the existence of one-way functions, complement sampling gives provable, verifiable and NISQable quantum advantage in a sample complexity setting.

We consider the task of evaluating policies of algorithmic resource allocation through randomized controlled trials (RCTs). Such policies are tasked with optimizing the utilization of limited intervention resources, with the goal of maximizing the benefits derived. Evaluation of such allocation policies through RCTs proves difficult, notwithstanding the scale of the trial, because the individuals' outcomes are inextricably interlinked through resource constraints controlling the policy decisions. Our key contribution is to present a new estimator leveraging our proposed novel concept, that involves retrospective reshuffling of participants across experimental arms at the end of an RCT. We identify conditions under which such reassignments are permissible and can be leveraged to construct counterfactual trials, whose outcomes can be accurately ascertained, for free. We prove theoretically that such an estimator is more accurate than common estimators based on sample means -- we show that it returns an unbiased estimate and simultaneously reduces variance. We demonstrate the value of our approach through empirical experiments on synthetic, semi-synthetic as well as real case study data and show improved estimation accuracy across the board.

Large Language Models (LLMs) are increasingly being used to simulate human-like decision making in agent-based financial market models (ABMs). As models become more powerful and accessible, researchers can now incorporate individual LLM decisions into ABM environments. However, integration may introduce inherent biases that need careful evaluation. In this paper we test three state-of-the-art GPT models for bias using two model sampling approaches: one-shot and few-shot API queries. We observe significant variations in distributions of outputs between specific models, and model sub versions, with GPT-4o-Mini-2024-07-18 showing notably better performance (32-43% yes responses) compared to GPT-4-0125-preview's extreme bias (98-99% yes responses). We show that sampling methods and model sub-versions significantly impact results: repeated independent API calls produce different distributions compared to batch sampling within a single call. While no current GPT model can simultaneously achieve a uniform distribution and Markovian properties in one-shot testing, few-shot sampling can approach uniform distributions under certain conditions. We explore the Temperature parameter, providing a definition and comparative results. We further compare our results to true random binary series and test specifically for the common human bias of Negative Recency - finding LLMs have a mixed ability to 'beat' humans in this one regard. These findings emphasise the critical importance of careful LLM integration into ABMs for financial markets and more broadly.

In large scale machine learning, random sampling is a popular way to approximate datasets by a small representative subset of examples. In particular, sensitivity sampling is an intensely studied technique which provides provable guarantees on the quality of approximation, while reducing the number of examples to the product of the VC dimension d and the total sensitivity mathfrak S in remarkably general settings. However, guarantees going beyond this general bound of mathfrak S d are known in perhaps only one setting, for ell_2 subspace embeddings, despite intense study of sensitivity sampling in prior work. In this work, we show the first bounds for sensitivity sampling for ell_p subspace embeddings for pneq 2 that improve over the general mathfrak S d bound, achieving a bound of roughly mathfrak S^{2/p} for 1leq p<2 and mathfrak S^{2-2/p} for 2<p<infty. For 1leq p<2, we show that this bound is tight, in the sense that there exist matrices for which mathfrak S^{2/p} samples is necessary. Furthermore, our techniques yield further new results in the study of sampling algorithms, showing that the root leverage score sampling algorithm achieves a bound of roughly d for 1leq p<2, and that a combination of leverage score and sensitivity sampling achieves an improved bound of roughly d^{2/p}mathfrak S^{2-4/p} for 2<p<infty. Our sensitivity sampling results yield the best known sample complexity for a wide class of structured matrices that have small ell_p sensitivity.

This paper derives confidence intervals (CI) and time-uniform confidence sequences (CS) for the classical problem of estimating an unknown mean from bounded observations. We present a general approach for deriving concentration bounds, that can be seen as a generalization and improvement of the celebrated Chernoff method. At its heart, it is based on a class of composite nonnegative martingales, with strong connections to testing by betting and the method of mixtures. We show how to extend these ideas to sampling without replacement, another heavily studied problem. In all cases, our bounds are adaptive to the unknown variance, and empirically vastly outperform existing approaches based on Hoeffding or empirical Bernstein inequalities and their recent supermartingale generalizations. In short, we establish a new state-of-the-art for four fundamental problems: CSs and CIs for bounded means, when sampling with and without replacement.

Mixture-of-Experts (MoE) large language models (LLMs), which leverage dynamic routing and sparse activation to enhance efficiency and scalability, have achieved higher performance while reducing computational costs. However, these models face significant memory overheads, limiting their practical deployment and broader adoption. Post-training quantization (PTQ), a widely used method for compressing LLMs, encounters severe accuracy degradation and diminished generalization performance when applied to MoE models. This paper investigates the impact of MoE's sparse and dynamic characteristics on quantization and identifies two primary challenges: (1) Inter-expert imbalance, referring to the uneven distribution of samples across experts, which leads to insufficient and biased calibration for less frequently utilized experts; (2) Intra-expert imbalance, arising from MoE's unique aggregation mechanism, which leads to varying degrees of correlation between different samples and their assigned experts. To address these challenges, we propose MoEQuant, a novel quantization framework tailored for MoE LLMs. MoE-Quant includes two novel techniques: 1) Expert-Balanced Self-Sampling (EBSS) is an efficient sampling method that efficiently constructs a calibration set with balanced expert distributions by leveraging the cumulative probabilities of tokens and expert balance metrics as guiding factors. 2) Affinity-Guided Quantization (AGQ), which incorporates affinities between experts and samples into the quantization process, thereby accurately assessing the impact of individual samples on different experts within the MoE layer. Experiments demonstrate that MoEQuant achieves substantial performance gains (more than 10 points accuracy gain in the HumanEval for DeepSeekMoE-16B under 4-bit quantization) and boosts efficiency.

Dataset distillation aims to synthesize small datasets with little information loss from original large-scale ones for reducing storage and training costs. Recent state-of-the-art methods mainly constrain the sample synthesis process by matching synthetic images and the original ones regarding gradients, embedding distributions, or training trajectories. Although there are various matching objectives, currently the strategy for selecting original images is limited to naive random sampling. We argue that random sampling overlooks the evenness of the selected sample distribution, which may result in noisy or biased matching targets. Besides, the sample diversity is also not constrained by random sampling. These factors together lead to optimization instability in the distilling process and degrade the training efficiency. Accordingly, we propose a novel matching strategy named as Dataset distillation by REpresentAtive Matching (DREAM), where only representative original images are selected for matching. DREAM is able to be easily plugged into popular dataset distillation frameworks and reduce the distilling iterations by more than 8 times without performance drop. Given sufficient training time, DREAM further provides significant improvements and achieves state-of-the-art performances.

Determinantal point processes (DPPs) are a useful probabilistic model for selecting a small diverse subset out of a large collection of items, with applications in summarization, stochastic optimization, active learning and more. Given a kernel function and a subset size k, our goal is to sample k out of n items with probability proportional to the determinant of the kernel matrix induced by the subset (a.k.a. k-DPP). Existing k-DPP sampling algorithms require an expensive preprocessing step which involves multiple passes over all n items, making it infeasible for large datasets. A naïve heuristic addressing this problem is to uniformly subsample a fraction of the data and perform k-DPP sampling only on those items, however this method offers no guarantee that the produced sample will even approximately resemble the target distribution over the original dataset. In this paper, we develop an algorithm which adaptively builds a sufficiently large uniform sample of data that is then used to efficiently generate a smaller set of k items, while ensuring that this set is drawn exactly from the target distribution defined on all n items. We show empirically that our algorithm produces a k-DPP sample after observing only a small fraction of all elements, leading to several orders of magnitude faster performance compared to the state-of-the-art.

Data balancing across multiple modalities and sources appears in various forms in foundation models in machine learning and AI, e.g. in CLIP and DINO. We show that data balancing across modalities and sources actually offers an unsuspected benefit: variance reduction. We present a non-asymptotic statistical bound that quantifies this variance reduction effect and relates it to the eigenvalue decay of Markov operators. Furthermore, we describe how various forms of data balancing in contrastive multimodal learning and self-supervised clustering can be better understood, and even improved upon, owing to our variance reduction viewpoint.

The k-means++ seeding algorithm (Arthur & Vassilvitskii, 2007) is widely used in practice for the k-means clustering problem where the goal is to cluster a dataset X subset R ^d into k clusters. The popularity of this algorithm is due to its simplicity and provable guarantee of being O(log k) competitive with the optimal solution in expectation. However, its running time is O(|X|kd), making it expensive for large datasets. In this work, we present a simple and effective rejection sampling based approach for speeding up k-means++. Our first method runs in time O(nnz (X) + beta k^2d) while still being O(log k ) competitive in expectation. Here, beta is a parameter which is the ratio of the variance of the dataset to the optimal k-means cost in expectation and O hides logarithmic factors in k and |X|. Our second method presents a new trade-off between computational cost and solution quality. It incurs an additional scale-invariant factor of k^{-Omega( m/beta)} Var (X) in addition to the O(log k) guarantee of k-means++ improving upon a result of (Bachem et al, 2016a) who get an additional factor of m^{-1}Var(X) while still running in time O(nnz(X) + mk^2d). We perform extensive empirical evaluations to validate our theoretical results and to show the effectiveness of our approach on real datasets.

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.

Machine learning (ML) holds great potential for accurately forecasting treatment outcomes over time, which could ultimately enable the adoption of more individualized treatment strategies in many practical applications. However, a significant challenge that has been largely overlooked by the ML literature on this topic is the presence of informative sampling in observational data. When instances are observed irregularly over time, sampling times are typically not random, but rather informative -- depending on the instance's characteristics, past outcomes, and administered treatments. In this work, we formalize informative sampling as a covariate shift problem and show that it can prohibit accurate estimation of treatment outcomes if not properly accounted for. To overcome this challenge, we present a general framework for learning treatment outcomes in the presence of informative sampling using inverse intensity-weighting, and propose a novel method, TESAR-CDE, that instantiates this framework using Neural CDEs. Using a simulation environment based on a clinical use case, we demonstrate the effectiveness of our approach in learning under informative sampling.

Large Language Models (LLMs) have advanced rapidly but face significant memory demands. While quantization has shown promise for LLMs, current methods typically require lengthy training to alleviate the performance degradation from quantization loss. However, deploying LLMs across diverse scenarios with different resource constraints, e.g., servers and personal computers, requires repeated training per application, which amplifies the lengthy training problem. Given that, it is advantageous to train a once-for-all (OFA) supernet capable of yielding diverse optimal subnets for downstream applications through one-shot training. Nonetheless, the scale of current language models impedes efficiency and amplifies interference from weight sharing between subnets. We make an initial attempt to extend the once-for-all framework to large language models. Specifically, we decouple shared weights to eliminate the interference and incorporate Low-Rank adapters for training efficiency. Furthermore, we observe the imbalance allocation of training resources from the traditional uniform sampling. A non-parametric scheduler is introduced to adjust the sampling rate for each quantization configuration, achieving a more balanced allocation among subnets with varying demands. We validate the approach on LLaMA2 families, and downstream evaluation confirms our ability to maintain high performance while significantly reducing deployment time faced with multiple scenarios.

General-purpose open-domain dense retrieval systems are usually trained with a large, eclectic mix of corpora and search tasks. How should these diverse corpora and tasks be sampled for training? Conventional approaches sample them uniformly, proportional to their instance population sizes, or depend on human-level expert supervision. It is well known that the training data sampling strategy can greatly impact model performance. However, how to find the optimal strategy has not been adequately studied in the context of embedding models. We propose Inf-DDS, a novel reinforcement learning driven sampling framework that adaptively reweighs training datasets guided by influence-based reward signals and is much more lightweight with respect to GPU consumption. Our technique iteratively refines the sampling policy, prioritizing datasets that maximize model performance on a target development set. We evaluate the efficacy of our sampling strategy on a wide range of text retrieval tasks, demonstrating strong improvements in retrieval performance and better adaptation compared to existing gradient-based sampling methods, while also being 1.5x to 4x cheaper in GPU compute. Our sampling strategy achieves a 5.03 absolute NDCG@10 improvement while training a multilingual bge-m3 model and an absolute NDCG@10 improvement of 0.94 while training all-MiniLM-L6-v2, even when starting from expert-assigned weights on a large pool of training datasets.

Timestep sampling p(t) is a central design choice in Flow Matching models, yet common practice increasingly favors static middle-biased distributions (e.g., Logit-Normal). We show that this choice induces a speed--quality trade-off: middle-biased sampling accelerates early convergence but yields worse asymptotic fidelity than Uniform sampling. By analyzing per-timestep training losses, we identify a U-shaped difficulty profile with persistent errors near the boundary regimes, implying that under-sampling the endpoints leaves fine details unresolved. Guided by this insight, we propose Curriculum Sampling, a two-phase schedule that begins with middle-biased sampling for rapid structure learning and then switches to Uniform sampling for boundary refinement. On CIFAR-10, Curriculum Sampling improves the best FID from 3.85 (Uniform) to 3.22 while reaching peak performance at 100k rather than 150k training steps. Our results highlight that timestep sampling should be treated as an evolving curriculum rather than a fixed hyperparameter.

Recent advancements in generative models, particularly large language models (LLMs) and diffusion models, have been driven by extensive pretraining on large datasets followed by post-training. However, current post-training methods such as reinforcement learning from human feedback (RLHF) and direct alignment from preference methods (DAP) primarily utilize single-sample comparisons. These approaches often fail to capture critical characteristics such as generative diversity and bias, which are more accurately assessed through multiple samples. To address these limitations, we introduce a novel approach that extends post-training to include multi-sample comparisons. To achieve this, we propose Multi-sample Direct Preference Optimization (mDPO) and Multi-sample Identity Preference Optimization (mIPO). These methods improve traditional DAP methods by focusing on group-wise characteristics. Empirically, we demonstrate that multi-sample comparison is more effective in optimizing collective characteristics~(e.g., diversity and bias) for generative models than single-sample comparison. Additionally, our findings suggest that multi-sample comparisons provide a more robust optimization framework, particularly for dataset with label noise.

We study the problem of learning a neural sampler to generate samples from discrete state spaces where the target probability mass function piproptoe^{-U} is known up to a normalizing constant, which is an important task in fields such as statistical physics, machine learning, combinatorial optimization, etc. To better address this challenging task when the state space has a large cardinality and the distribution is multi-modal, we propose Masked Diffusion Neural Sampler (MDNS), a novel framework for training discrete neural samplers by aligning two path measures through a family of learning objectives, theoretically grounded in the stochastic optimal control of the continuous-time Markov chains. We validate the efficiency and scalability of MDNS through extensive experiments on various distributions with distinct statistical properties, where MDNS learns to accurately sample from the target distributions despite the extremely high problem dimensions and outperforms other learning-based baselines by a large margin. A comprehensive study of ablations and extensions is also provided to demonstrate the efficacy and potential of the proposed framework.

Hands are essential to human interaction, and understanding contact between hands and the world can promote comprehensive understanding of their function. Recently, there have been growing number of hand interaction datasets that cover interaction with object, other hand, scene, and body. Despite the significance of the task and increasing high-quality data, how to effectively learn dense hand contact estimation remains largely underexplored. There are two major challenges for learning dense hand contact estimation. First, there exists class imbalance issue from hand contact datasets where majority of samples are not in contact. Second, hand contact datasets contain spatial imbalance issue with most of hand contact exhibited in finger tips, resulting in challenges for generalization towards contacts in other hand regions. To tackle these issues, we present a framework that learns dense HAnd COntact estimation (HACO) from imbalanced data. To resolve the class imbalance issue, we introduce balanced contact sampling, which builds and samples from multiple sampling groups that fairly represent diverse contact statistics for both contact and non-contact samples. Moreover, to address the spatial imbalance issue, we propose vertex-level class-balanced (VCB) loss, which incorporates spatially varying contact distribution by separately reweighting loss contribution of each vertex based on its contact frequency across dataset. As a result, we effectively learn to predict dense hand contact estimation with large-scale hand contact data without suffering from class and spatial imbalance issue. The codes will be released.

Selecting appropriate training data is crucial for effective instruction fine-tuning of large language models (LLMs), which aims to (1) elicit strong capabilities, and (2) achieve balanced performance across a diverse range of tasks. Influence-based methods show promise in achieving (1) by estimating the contribution of each training example to the model's predictions, but often struggle with (2). Our systematic investigation reveals that this underperformance can be attributed to an inherent bias where certain tasks intrinsically have greater influence than others. As a result, data selection is often biased towards these tasks, not only hurting the model's performance on others but also, counterintuitively, harms performance on these high-influence tasks themselves. As a remedy, we propose BIDS, a Balanced and Influential Data Selection algorithm. BIDS first normalizes influence scores of the training data, and then iteratively balances data selection by choosing the training example with the highest influence on the most underrepresented task. Experiments with both Llama-3 and Mistral-v0.3 on seven benchmarks spanning five diverse capabilities show that BIDS consistently outperforms both state-of-the-art influence-based algorithms and other non-influence-based selection frameworks. Surprisingly, training on a 15% subset selected by BIDS can even outperform full-dataset training with a much more balanced performance. Our analysis further highlights the importance of both instance-level normalization and iterative optimization of selected data for balanced learning of diverse capabilities.

Large language models (LLMs), despite their impressive performance across a wide range of tasks, often struggle to balance two competing objectives in open-ended text generation: fostering diversity and creativity while preserving logical coherence. Existing truncated sampling techniques, including temperature scaling, top-\p (nucleus) sampling, and min-\p sampling, aim to manage this trade-off. However, they exhibit limitations, particularly in the effective incorporation of the confidence of the model into the corresponding sampling strategy. For example, min-\p sampling relies on a single top token as a heuristic for confidence, eventually underutilizing the information of the probability distribution. Toward effective incorporation of the confidence of the model, in this paper, we present **top-H** decoding. We first establish the theoretical foundation of the interplay between creativity and coherence in truncated sampling by formulating an **entropy-constrained minimum divergence** problem. We then prove this minimization problem to be equivalent to an **entropy-constrained mass maximization** (ECMM) problem, which is NP-hard. Finally, we present top-H decoding, a computationally efficient greedy algorithm to solve the ECMM problem. Extensive empirical evaluations demonstrate that top-H outperforms the state-of-the-art (SoTA) alternative of min-\p sampling by up to **25.63%** on creative writing benchmarks, while maintaining robustness on question-answering datasets such as GPQA, GSM8K, and MT-Bench. Additionally, an *LLM-as-judge* evaluation confirms that top-H indeed produces coherent outputs even at higher temperatures, where creativity is especially critical. In summary, top-H advances SoTA in open-ended text generation and can be *easily integrated* into creative writing applications. The code is available at https://github.com/ErfanBaghaei/Top-H-Decoding.

Client selection strategies are widely adopted to handle the communication-efficient problem in recent studies of Federated Learning (FL). However, due to the large variance of the selected subset's update, prior selection approaches with a limited sampling ratio cannot perform well on convergence and accuracy in heterogeneous FL. To address this problem, in this paper, we propose a novel stratified client selection scheme to reduce the variance for the pursuit of better convergence and higher accuracy. Specifically, to mitigate the impact of heterogeneity, we develop stratification based on clients' local data distribution to derive approximate homogeneous strata for better selection in each stratum. Concentrating on a limited sampling ratio scenario, we next present an optimized sample size allocation scheme by considering the diversity of stratum's variability, with the promise of further variance reduction. Theoretically, we elaborate the explicit relation among different selection schemes with regard to variance, under heterogeneous settings, we demonstrate the effectiveness of our selection scheme. Experimental results confirm that our approach not only allows for better performance relative to state-of-the-art methods but also is compatible with prevalent FL algorithms.

Sampling-based algorithms, which eliminate ''unimportant'' computations during forward and/or back propagation (BP), offer potential solutions to accelerate neural network training. However, since sampling introduces approximations to training, such algorithms may not consistently maintain accuracy across various tasks. In this work, we introduce a variance-controlled adaptive sampling (VCAS) method designed to accelerate BP. VCAS computes an unbiased stochastic gradient with fine-grained layerwise importance sampling in data dimension for activation gradient calculation and leverage score sampling in token dimension for weight gradient calculation. To preserve accuracy, we control the additional variance by learning the sample ratio jointly with model parameters during training. We assessed VCAS on multiple fine-tuning and pre-training tasks in both vision and natural language domains. On all the tasks, VCAS can preserve the original training loss trajectory and validation accuracy with an up to 73.87% FLOPs reduction of BP and 49.58% FLOPs reduction of the whole training process. The implementation is available at https://github.com/thu-ml/VCAS .

To train accurate deep object detectors under the extreme foreground-background imbalance, heuristic sampling methods are always necessary, which either re-sample a subset of all training samples (hard sampling methods, \eg biased sampling, OHEM), or use all training samples but re-weight them discriminatively (soft sampling methods, \eg Focal Loss, GHM). In this paper, we challenge the necessity of such hard/soft sampling methods for training accurate deep object detectors. While previous studies have shown that training detectors without heuristic sampling methods would significantly degrade accuracy, we reveal that this degradation comes from an unreasonable classification gradient magnitude caused by the imbalance, rather than a lack of re-sampling/re-weighting. Motivated by our discovery, we propose a simple yet effective Sampling-Free mechanism to achieve a reasonable classification gradient magnitude by initialization and loss scaling. Unlike heuristic sampling methods with multiple hyperparameters, our Sampling-Free mechanism is fully data diagnostic, without laborious hyperparameters searching. We verify the effectiveness of our method in training anchor-based and anchor-free object detectors, where our method always achieves higher detection accuracy than heuristic sampling methods on COCO and PASCAL VOC datasets. Our Sampling-Free mechanism provides a new perspective to address the foreground-background imbalance. Our code is released at https://github.com/ChenJoya/sampling-free.

In ecology, psychometrics, and the analysis of social and financial networks, binary matrices are often analyzed conditional on their observed row and column sums, which restricts the problem to a finite sample space of matrices with the same margins. Two fundamental problems are to count this space and to sample uniformly from it. Sequential importance sampling (SIS) addresses both with independent weighted samples and an unbiased count estimator, but its efficiency depends critically on the proposal distribution. Existing proposals are analytically designed, and their accuracy can vary substantially with the margins. We show that the ideal SIS proposal, under which every weight equals the count and the variance vanishes, is exactly the policy of a generative flow network (GFlowNet) with unit reward on every matrix that has the given margins. We therefore propose MarginFlow, a framework that turns the design of the proposal into a learning problem and amortizes it across margins by exploiting their self-similarity. Every partial matrix is itself an instance with reduced margins, so one set transformer that reads the remaining margins serves every margin. We train MarginFlow on a pool of 1904 margins and evaluate it zero-shot on 1190 held-out margins, synthetic and real, from 3times3 to 870times6. On 1187 of the 1190 margins it matches or beats the best of 31 analytically designed configurations, chosen post hoc for each margin, and its median effective sample fraction is 99.8%. On the 56 margins where that best loses more than one nat of effective sample size, MarginFlow wins every one and raises the median effective sample fraction from 10.3% to 94.1%.

Inference-time scaling has emerged as a powerful technique for enhancing the reasoning performance of Large Language Models (LLMs). However, existing approaches often rely on heuristic strategies for parallel sampling, lacking a principled foundation. To address this gap, we propose a probabilistic framework that formalizes the optimality of inference-time scaling under the assumption that parallel samples are independently and identically distributed (i.i.d.), and where the Best-of-N selection strategy follows a probability distribution that can be estimated. Within this framework, we derive a theoretical lower bound on the required number of samples to achieve a target performance level, providing the first principled guidance for compute-efficient scaling. Leveraging this insight, we develop OptScale, a practical algorithm that dynamically determines the optimal number of sampled responses. OptScale employs a language model-based predictor to estimate probabilistic prior parameters, enabling the decision of the minimal number of samples needed that satisfy predefined performance thresholds and confidence levels. Extensive experiments on representative reasoning benchmarks (including MATH-500, GSM8K, AIME, and AMC) demonstrate that OptScale significantly reduces sampling overhead while remaining better or on par with state-of-the-art reasoning performance. Our work offers both a theoretical foundation and a practical solution for principled inference-time scaling, addressing a critical gap in the efficient deployment of LLMs for complex reasoning.

Machine learning has opened up new tools for financial fraud detection. Using a sample of annotated transactions, a machine learning classification algorithm learns to detect frauds. With growing credit card transaction volumes and rising fraud percentages there is growing interest in finding appropriate machine learning classifiers for detection. However, fraud data sets are diverse and exhibit inconsistent characteristics. As a result, a model effective on a given data set is not guaranteed to perform on another. Further, the possibility of temporal drift in data patterns and characteristics over time is high. Additionally, fraud data has massive and varying imbalance. In this work, we evaluate sampling methods as a viable pre-processing mechanism to handle imbalance and propose a data-driven classifier selection strategy for characteristic highly imbalanced fraud detection data sets. The model derived based on our selection strategy surpasses peer models, whilst working in more realistic conditions, establishing the effectiveness of the strategy.

Allocating more computation during inference time (test-time scaling) improves language model performance, especially for reasoning tasks. However, popular methods like Best-of-N sampling often show diminishing returns as N increases. To address this inefficiency, we introduce a general test-time calibration framework that adaptively modifies the model toward high-reward reasoning paths, with theoretical guarantees of improving the lower bound of expected reward under finite sampling, all without large language model (LLM) retraining. Within this framework, we propose CarBoN (Calibrated Best-of-N), a two-phase method that first explores the solution space and then learns a calibration of the logits via an input-specific temperature T and additive shift vector delta, guiding generation toward more reliable reasoning. Experiments on MATH-500 and AIME-2024 show that CarBoN improves efficiency, with up to 4times fewer rollouts to reach the same accuracy, while often achieving higher accuracy under fixed budgets. We also analyze the complementary roles of T and delta in balancing output diversity and correctness, and demonstrate that the framework also generalizes to step-level sampling strategies such as beam search. For more information, please refer to our project page at huggingface.co/spaces/TrustSafeAI/Test-Time-Calibration.

We analyse linear ensemble sampling (ES) with standard Gaussian perturbations in stochastic linear bandits. We show that for ensemble size m=Θ(dlog n), ES attains tilde O(d^{3/2}sqrt n) high-probability regret, closing the gap to the Thompson sampling benchmark while keeping computation comparable. The proof brings a new perspective on randomized exploration in linear bandits by reducing the analysis to a time-uniform exceedance problem for m independent Brownian motions. Intriguingly, this continuous-time lens is not forced; it appears natural--and perhaps necessary: the discrete-time problem seems to be asking for a continuous-time solution, and we know of no other way to obtain a sharp ES bound.

We study the complexity of sampling from a distribution over all index subsets of the set {1,...,n} with the probability of a subset S proportional to the determinant of the submatrix L_S of some ntimes n p.s.d. matrix L, where L_S corresponds to the entries of L indexed by S. Known as a determinantal point process, this distribution is used in machine learning to induce diversity in subset selection. In practice, we often wish to sample multiple subsets S with small expected size k = E[|S|] ll n from a very large matrix L, so it is important to minimize the preprocessing cost of the procedure (performed once) as well as the sampling cost (performed repeatedly). For this purpose, we propose a new algorithm which, given access to L, samples exactly from a determinantal point process while satisfying the following two properties: (1) its preprocessing cost is n cdot poly(k), i.e., sublinear in the size of L, and (2) its sampling cost is poly(k), i.e., independent of the size of L. Prior to our results, state-of-the-art exact samplers required O(n^3) preprocessing time and sampling time linear in n or dependent on the spectral properties of L. We also give a reduction which allows using our algorithm for exact sampling from cardinality constrained determinantal point processes with ncdotpoly(k) time preprocessing.

Coreset selection picks a representative subset of the labeled training set to make training cheaper. However, it is usually evaluated by downstream accuracy at a fixed subset size, ignoring both the time spent selecting the subset and the training recipe behind each reported number. We introduce an end-to-end benchmark that standardizes downstream training and charges selection and training to the same auditable wall-clock budget, spanning 4 datasets from CIFAR-10 to ImageNet-1K, 11 selectors, 5 fractions, and 3 seeds, with over 1,500 released runs. Repeated-sampling work has shown that budget-aware evaluation already favors random strategies. Our two budget studies test whether that verdict survives when every selector is granted its most favorable operating point. Across eight wall-clock budget anchors on each of CIFAR-10 and Tiny ImageNet, no anchor is won by a sophisticated selector: every winner is class-balanced random sampling, repeated random sampling, or full-data training. In fixed-budget duels on ImageNet-1K, training on all data for fewer epochs beats every selection strategy we probe while also costing the least. A per-dataset cost audit shows that selection cost is dominated at every scale by a fixed full-dataset scan, so it cannot be amortized away by selecting a smaller fraction, and its absolute size does not extrapolate from one dataset to another. We further quantify when selection does pay back through subset reuse, and document 9 correctness fixes to a widely used codebase, one of which shifts a standard Herding baseline by nearly 6 points. Selection time is not free preprocessing, and an evaluation that ignores it measures the wrong quantity.

Is the same data equally useful to every learner? The question is whether the value of a training sample belongs to the sample or arises in its interaction with the learner. We test it with a selection experiment. Under a per-class budget, two kinds of samples compete for the slots: easy samples, which a short training run learns first, and coverage samples, which spread over the class in feature space. Easy samples win at small budgets and coverage samples at large ones, and the budget at which the winner flips, the crossover m0, can be measured. We ask whether m0 is set by the data or by the learner. To separate the two, we freeze the selected subsets and change only the learner that trains on them. On low-resolution ImageNet-100, doubling the width of a ResNet-18 moves the crossover from 57 to 85 samples per class on the same subsets. Enlarging the input grid from 32 to 64 pixels at fixed image information moves it from 85 to 57, and a single stride change reproduces or removes this shift. The grid shift shrinks as width grows. Under the native ImageNet-1k protocol, a 4x range of width moves the boundary by at most a few samples per class. On a Vision Transformer, coverage wins at every measured budget, even with easy subsets that work on the convolutional learner. The budget at which one kind of sample stops being the more useful kind therefore belongs to the learner, and the preferred regime of a selection strategy has to be read against the learner that will use the data.

Selecting high-quality and diverse training samples from extensive datasets plays a crucial role in reducing training overhead and enhancing the performance of Large Language Models (LLMs). However, existing studies fall short in assessing the overall value of selected data, focusing primarily on individual quality, and struggle to strike an effective balance between ensuring diversity and minimizing data point traversals. Therefore, this paper introduces a novel choice-based sample selection framework that shifts the focus from evaluating individual sample quality to comparing the contribution value of different samples when incorporated into the subset. Thanks to the advanced language understanding capabilities of LLMs, we utilize LLMs to evaluate the value of each option during the selection process. Furthermore, we design a greedy sampling process where samples are incrementally added to the subset, thereby improving efficiency by eliminating the need for exhaustive traversal of the entire dataset with the limited budget. Extensive experiments demonstrate that selected data from our method not only surpass the performance of the full dataset but also achieves competitive results with state-of-the-art (SOTA) studies, while requiring fewer selections. Moreover, we validate our approach on a larger medical dataset, highlighting its practical applicability in real-world applications.

Diffusion models have demonstrated impressive generative capabilities, but their exposure bias problem, described as the input mismatch between training and sampling, lacks in-depth exploration. In this paper, we systematically investigate the exposure bias problem in diffusion models by first analytically modelling the sampling distribution, based on which we then attribute the prediction error at each sampling step as the root cause of the exposure bias issue. Furthermore, we discuss potential solutions to this issue and propose an intuitive metric for it. Along with the elucidation of exposure bias, we propose a simple, yet effective, training-free method called Epsilon Scaling to alleviate the exposure bias. We show that Epsilon Scaling explicitly moves the sampling trajectory closer to the vector field learned in the training phase by scaling down the network output (Epsilon), mitigating the input mismatch between training and sampling. Experiments on various diffusion frameworks (ADM, DDPM/DDIM, EDM, LDM), unconditional and conditional settings, and deterministic vs. stochastic sampling verify the effectiveness of our method. Remarkably, our ADM-ES, as a SOTA stochastic sampler, obtains 2.17 FID on CIFAR-10 under 100-step unconditional generation. The code is available at https://github.com/forever208/ADM-ES and https://github.com/forever208/EDM-ES.

We study the data selection problem, whose aim is to select a small representative subset of data that can be used to efficiently train a machine learning model. We present a new data selection approach based on k-means clustering and sensitivity sampling. Assuming access to an embedding representation of the data with respect to which the model loss is H\"older continuous, our approach provably allows selecting a set of ``typical'' k + 1/varepsilon^2 elements whose average loss corresponds to the average loss of the whole dataset, up to a multiplicative (1pmvarepsilon) factor and an additive varepsilon lambda Phi_k, where Phi_k represents the k-means cost for the input embeddings and lambda is the H\"older constant. We furthermore demonstrate the performance and scalability of our approach on fine-tuning foundation models and show that it outperforms state-of-the-art methods. We also show how it can be applied on linear regression, leading to a new sampling strategy that surprisingly matches the performances of leverage score sampling, while being conceptually simpler and more scalable.

Effective implementations of sampling-based probabilistic inference often require manually constructed, model-specific proposals. Inspired by recent progresses in meta-learning for training learning agents that can generalize to unseen environments, we propose a meta-learning approach to building effective and generalizable MCMC proposals. We parametrize the proposal as a neural network to provide fast approximations to block Gibbs conditionals. The learned neural proposals generalize to occurrences of common structural motifs across different models, allowing for the construction of a library of learned inference primitives that can accelerate inference on unseen models with no model-specific training required. We explore several applications including open-universe Gaussian mixture models, in which our learned proposals outperform a hand-tuned sampler, and a real-world named entity recognition task, in which our sampler yields higher final F1 scores than classical single-site Gibbs sampling.

Recent research has generated hope that inference scaling could allow weaker language models to match or exceed the accuracy of stronger models, such as by repeatedly sampling solutions to a coding problem until it passes unit tests. The central thesis of this paper is that there is no free lunch for inference scaling: indefinite accuracy improvement through resampling can only be realized if the "verifier" (in this case, a set of unit tests) is perfect. When the verifier is imperfect, as it almost always is in domains such as reasoning or coding (for example, unit tests have imperfect coverage), there is a nonzero probability of false positives: incorrect solutions that pass the verifier. Resampling cannot decrease this probability, so it imposes an upper bound to the accuracy of resampling-based inference scaling even with an infinite compute budget. We find that there is a very strong correlation between the model's single-sample accuracy (i.e. accuracy without unit tests) and its false positive rate on coding benchmarks HumanEval and MBPP, whose unit tests have limited coverage. Therefore, no amount of inference scaling of weaker models can enable them to match the single-sample accuracy of a sufficiently strong model (Fig. 1a). When we consider that false positives have a negative utility compared to abstaining from producing a solution, it bends the inference scaling curve further downward. Empirically, we find that the optimal number of samples can be less than 10 under realistic assumptions (Fig. 1b). Finally, we show that beyond accuracy, false positives may have other undesirable qualities, such as poor adherence to coding style conventions.

Parallel thinking enhances LLM reasoning by multi-path sampling and aggregation. In system-level evaluations, a global parallelism level N is allocated to all samples, typically set large to maximize overall dataset accuracy. However, due to sample heterogeneity, some samples can achieve comparable performance with a smaller N'< N, causing budget redundancy. This incompatibility between system-level efficacy and sample-level efficiency constitutes the overscaling curse. In this paper, we formalize and quantify the overscaling curse, showing its universality and severity in practice, and analyze its trigger mechanism. We then propose a lightweight method, T2, to break the overscaling curse, which utilizes latent representations to estimate the optimal parallelism level for each sample before decoding. Experiments show that T2 significantly reduces cost while maintaining comparable performance, enabling more efficient parallel thinking.

This paper studies active regression for single-index models under general ell_p-loss with an unknown 1-Lipschitz link function f, formulated as min_{f,x} |f(Ax)-b|_p^p with full access to A but coordinate-query access to b. Prior work established upper bounds for known link functions for all pgeq 1 and for unknown link functions only in the p=2 case, together with lower bounds for pleq 2. This work addresses the more challenging setting of unknown link functions and general p geq 1. A non-adaptive sampling algorithm is presented that achieves a (1+ε)-approximation using O(d^{p/2vee 1}/ε^{pvee 2}polylog(n/ε)) queries. Nearly tight lower bounds are also established for p>2. These results close much of the remaining gap in active ell_p-regression for single-index models.

Incrementally fine-tuning foundational models on new tasks or domains is now the de facto approach in NLP. A known pitfall of this approach is the catastrophic forgetting of prior knowledge that happens during fine-tuning. A common approach to alleviate such forgetting is to rehearse samples from prior tasks during fine-tuning. Several existing works assume a fixed memory buffer to store prior task examples, while relying on inferences (forward passes) with the model at hand for choosing examples for rehearsal from the buffer. However, given the increasing computational cost of model inference, and decreasing cost of data storage, we focus on the setting to rehearse samples with a fixed computational budget instead of a fixed memory budget. We propose a sampling scheme, \bf mix-cd, that prioritizes rehearsal of ``collateral damage'' samples, which are samples predicted correctly by the prior model but forgotten by the incrementally tuned one. The crux of our scheme is a procedure to efficiently estimate the density of collateral damage samples without incurring additional model inferences. Our approach is computationally efficient, easy to implement, and outperforms several leading continual learning methods in compute-constrained settings. All the code will be publicly available at https://github.com/jybai/mix-cd-rehearsal.

Reinforcement learning (RL) is a central approach for improving reasoning capabilities in large language models (LLMs), where training efficiency depends critically on how problems are sampled during optimization. Existing adaptive curriculum learning methods typically prioritize prompts of intermediate difficulty, treating problem selection as a standard bandit problem with independent arms and overlooking the structured, heterogeneous nature of the task space. In this work, we frame problem sampling as a manifold-structured bandit problem with endogenous non-stationarity: problems are related through the model's latent representation space, and sampling decisions can steer how learning signals evolve across that space. To operationalize this perspective, we introduce Bayesian Manifold Curriculum (BMC), a structure-aware framework that organizes problems into a hierarchical task tree and applies Bayesian learning to guide sampling. Empirically, we find that different sampling strategies induce non-trivial tradeoffs between productivity (learning signal), diversity (coverage of the task manifold), and utility (evaluation relevance). These results show that prioritizing difficulty alone is insufficient for strong downstream performance, highlighting the importance of incorporating structure and type-awareness into problem sampling.

Can we learn more from data than existed in the generating process itself? Can new and useful information be constructed from merely applying deterministic transformations to existing data? Can the learnable content in data be evaluated without considering a downstream task? On these questions, Shannon information and Kolmogorov complexity come up nearly empty-handed, in part because they assume observers with unlimited computational capacity and fail to target the useful information content. In this work, we identify and exemplify three seeming paradoxes in information theory: (1) information cannot be increased by deterministic transformations; (2) information is independent of the order of data; (3) likelihood modeling is merely distribution matching. To shed light on the tension between these results and modern practice, and to quantify the value of data, we introduce epiplexity, a formalization of information capturing what computationally bounded observers can learn from data. Epiplexity captures the structural content in data while excluding time-bounded entropy, the random unpredictable content exemplified by pseudorandom number generators and chaotic dynamical systems. With these concepts, we demonstrate how information can be created with computation, how it depends on the ordering of the data, and how likelihood modeling can produce more complex programs than present in the data generating process itself. We also present practical procedures to estimate epiplexity which we show capture differences across data sources, track with downstream performance, and highlight dataset interventions that improve out-of-distribution generalization. In contrast to principles of model selection, epiplexity provides a theoretical foundation for data selection, guiding how to select, generate, or transform data for learning systems.

Exposure bias poses a common challenge in numerous natural language processing tasks, particularly in the dialog generation. In response to this issue, researchers have devised various techniques, among which scheduled sampling has proven to be an effective method for mitigating exposure bias. However, the existing state-of-the-art scheduled sampling methods solely consider the current sampling words' quality for threshold truncation sampling, which overlooks the importance of sentence-level information and the method of threshold truncation warrants further discussion. In this paper, we propose a bilevel scheduled sampling model that takes the sentence-level information into account and incorporates it with word-level quality. To enhance sampling diversity and improve the model's adaptability, we propose a smooth function that maps the combined result of sentence-level and word-level information to an appropriate range, and employ probabilistic sampling based on the mapped values instead of threshold truncation. Experiments conducted on the DailyDialog and PersonaChat datasets demonstrate the effectiveness of our proposed methods, which significantly alleviate the exposure bias problem and outperform state-of-the-art scheduled sampling methods.

Diverse outputs in text generation are necessary for effective exploration in complex reasoning tasks, such as code generation and mathematical problem solving. Such Pass@k problems benefit from distinct candidates covering the solution space. However, traditional sampling approaches often waste computational resources on repetitive failure modes. While Diffusion Language Models have emerged as a competitive alternative to the prevailing Autoregressive paradigm, they remain susceptible to this redundancy, with independent samples frequently collapsing into similar modes. To address this, we propose a training free, low cost intervention to enhance generative diversity in Diffusion Language Models. Our approach modifies intermediate samples in a batch sequentially, where each sample is repelled from the feature space of previous samples, actively penalising redundancy. Unlike prior methods that require retraining or beam search, our strategy incurs negligible computational overhead, while ensuring that each sample contributes a unique perspective to the batch. We evaluate our method on the HumanEval and GSM8K benchmarks using the LLaDA-8B-Instruct model. Our results demonstrate significantly improved diversity and Pass@k performance across various temperature settings. As a simple modification to the sampling process, our method offers an immediate, low-cost improvement for current and future Diffusion Language Models in tasks that benefit from diverse solution search. We make our code available at https://github.com/sean-lamont/odd.

Thompson Sampling is one of the oldest heuristics for multi-armed bandit problems. It is a randomized algorithm based on Bayesian ideas, and has recently generated significant interest after several studies demonstrated it to have better empirical performance compared to the state-of-the-art methods. However, many questions regarding its theoretical performance remained open. In this paper, we design and analyze a generalization of Thompson Sampling algorithm for the stochastic contextual multi-armed bandit problem with linear payoff functions, when the contexts are provided by an adaptive adversary. This is among the most important and widely studied versions of the contextual bandits problem. We provide the first theoretical guarantees for the contextual version of Thompson Sampling. We prove a high probability regret bound of O(d^{3/2}T) (or O(dT log(N))), which is the best regret bound achieved by any computationally efficient algorithm available for this problem in the current literature, and is within a factor of d (or log(N)) of the information-theoretic lower bound for this problem.

Mixture-of-Experts (MoE) models have shown remarkable capability in instruction tuning, especially when the number of tasks scales. However, previous methods simply merge all training tasks (e.g. creative writing, coding, and mathematics) and apply fixed sampling weights, without considering the importance of different tasks as the model training state changes. In this way, the most helpful data cannot be effectively distinguished, leading to suboptimal model performance. To reduce the potential redundancies of datasets, we make the first attempt and propose a novel dynamic data mixture for MoE instruction tuning. Specifically, inspired by MoE's token routing preference, we build dataset-level representations and then capture the subtle differences among datasets. Finally, we propose to dynamically adjust the sampling weight of datasets by their inter-redundancies, thus maximizing global performance under a limited training budget. The experimental results on two MoE models demonstrate the effectiveness of our approach on both downstream knowledge \& reasoning tasks and open-ended queries. Code and models are available at https://github.com/Spico197/MoE-SFT .

This work proposes a procedure for designing algorithms for specific adaptive data collection tasks like active learning and pure-exploration multi-armed bandits. Unlike the design of traditional adaptive algorithms that rely on concentration of measure and careful analysis to justify the correctness and sample complexity of the procedure, our adaptive algorithm is learned via adversarial training over equivalence classes of problems derived from information theoretic lower bounds. In particular, a single adaptive learning algorithm is learned that competes with the best adaptive algorithm learned for each equivalence class. Our procedure takes as input just the available queries, set of hypotheses, loss function, and total query budget. This is in contrast to existing meta-learning work that learns an adaptive algorithm relative to an explicit, user-defined subset or prior distribution over problems which can be challenging to define and be mismatched to the instance encountered at test time. This work is particularly focused on the regime when the total query budget is very small, such as a few dozen, which is much smaller than those budgets typically considered by theoretically derived algorithms. We perform synthetic experiments to justify the stability and effectiveness of the training procedure, and then evaluate the method on tasks derived from real data including a noisy 20 Questions game and a joke recommendation task.

Generalization to out-of-distribution (OOD) data is a critical challenge in machine learning. Ensemble-based methods, like weight space ensembles that interpolate model parameters, have been shown to achieve superior OOD performance. However, the underlying mechanism for their effectiveness remains unclear. In this study, we closely examine WiSE-FT, a popular weight space ensemble method that interpolates between a pre-trained and a fine-tuned model. We observe an unexpected phenomenon, in which WiSE-FT successfully corrects many cases where each individual model makes incorrect predictions, which contributes significantly to its OOD effectiveness. To gain further insights, we conduct theoretical analysis in a multi-class setting with a large number of spurious features. Our analysis predicts the above phenomenon and it further shows that ensemble-based models reduce prediction errors in the OOD settings by utilizing a more diverse set of spurious features. Contrary to the conventional wisdom that focuses on learning invariant features for better OOD performance, our findings suggest that incorporating a large number of diverse spurious features weakens their individual contributions, leading to improved overall OOD generalization performance. Empirically we demonstrate the effectiveness of utilizing diverse spurious features on a MultiColorMNIST dataset, and our experimental results are consistent with the theoretical analysis. Building upon the new theoretical insights into the efficacy of ensemble methods, we further identify an issue of WiSE-FT caused by the overconfidence of fine-tuned models in OOD situations. This overconfidence magnifies the fine-tuned model's incorrect prediction, leading to deteriorated OOD ensemble performance. To remedy this problem, we propose a novel method called BAlaNced averaGing (BANG), which significantly enhances the OOD performance of WiSE-FT.

Methods for carefully selecting or generating a small set of training data to learn from, i.e., data pruning, coreset selection, and data distillation, have been shown to be effective in reducing the ever-increasing cost of training neural networks. Behind this success are rigorously designed strategies for identifying informative training examples out of large datasets. However, these strategies come with additional computational costs associated with subset selection or data distillation before training begins, and furthermore, many are shown to even under-perform random sampling in high data compression regimes. As such, many data pruning, coreset selection, or distillation methods may not reduce 'time-to-accuracy', which has become a critical efficiency measure of training deep neural networks over large datasets. In this work, we revisit a powerful yet overlooked random sampling strategy to address these challenges and introduce an approach called Repeated Sampling of Random Subsets (RSRS or RS2), where we randomly sample the subset of training data for each epoch of model training. We test RS2 against thirty state-of-the-art data pruning and data distillation methods across four datasets including ImageNet. Our results demonstrate that RS2 significantly reduces time-to-accuracy compared to existing techniques. For example, when training on ImageNet in the high-compression regime (using less than 10% of the dataset each epoch), RS2 yields accuracy improvements up to 29% compared to competing pruning methods while offering a runtime reduction of 7x. Beyond the above meta-study, we provide a convergence analysis for RS2 and discuss its generalization capability. The primary goal of our work is to establish RS2 as a competitive baseline for future data selection or distillation techniques aimed at efficient training.

In reinforcement learning, agents collect state information and rewards through environmental interactions, essential for policy refinement. This process is notably time-consuming, especially in complex robotic simulations and real-world applications. Traditional algorithms usually re-engage with the environment after processing a single batch of samples, thereby failing to fully capitalize on historical data. However, frequently observed states, with reliable value estimates, require minimal updates; in contrast, rare observed states necessitate more intensive updates for achieving accurate value estimations. To address uneven sample utilization, we propose Novelty-guided Sample Reuse (NSR). NSR provides extra updates for infrequent, novel states and skips additional updates for frequent states, maximizing sample use before interacting with the environment again. Our experiments show that NSR improves the convergence rate and success rate of algorithms without significantly increasing time consumption. Our code is publicly available at https://github.com/ppksigs/NSR-DDPG-HER.

Thompson Sampling is one of the most widely used and studied bandit algorithms, known for its simple structure, low regret performance, and solid theoretical guarantees. Yet, in stark contrast to most other families of bandit algorithms, the exact mechanism through which posterior sampling (as introduced by Thompson) is able to "properly" balance exploration and exploitation, remains a mystery. In this paper, we show that the core insight to address this question stems from recasting Thompson Sampling as an online optimization algorithm. To distill this, we introduce a suitable time invariant notion of regret that leads to a stationarized bandit problem, and a stationary Bellman-optimal policy. We then show that Thompson Sampling admits an online optimization form that mimics the structure of the aforementioned Bellman-optimal policy, where "greediness" is regularized by a measure of residual uncertainty. This new lens of online optimization allows both a better understanding of Thompson Sampling dynamics, as well as a principled manner for policy improvement that mimics the Bellman-optimal benchmark.

While increasing training compute has significantly improved the performance of large language models (LLMs), similar gains have not been observed when scaling inference compute. We hypothesize that the primary issue lies in the uniformity of LLM outputs, which leads to inefficient sampling as models repeatedly generate similar but inaccurate responses. Motivated by an intriguing relationship between solution accuracy and response diversity, we propose DivSampling -- a novel and versatile sampling technique designed to enhance the diversity of candidate solutions by introducing prompt perturbations.DivSampling incorporates two categories of perturbations: task-agnostic approaches, which are general and not tailored to any specific task, and task-specific approaches, which are customized based on task content. Our theoretical analysis demonstrates that, under mild assumptions, the error rates of responses generated from diverse prompts are significantly lower compared to those produced by stationary prompts. Comprehensive evaluations across various tasks -- including reasoning, mathematics, and code generation -- highlight the effectiveness of DivSampling in improving solution accuracy. This scalable and efficient approach offers a new perspective on optimizing test-time inference, addressing limitations in current sampling strategies.

We introduce UnpredictaBench, an evaluation that tests the ability of large language models (LLMs) to capture true underlying distributions. As LLMs are increasingly used as substitutes for other entities (e.g., for humans in economic simulations), the tendency of many models to collapse towards a single plausible answer means a failure to capture the unpredictability of real systems. Recent work on improving output diversity is insufficient for this setting: simulation requires samples that are calibrated to a target distribution, not merely varied outputs. UnpredictaBench isolates a simplified but fundamental version of this problem: sampling outcomes from individual target distributions, including canonical statistical distributions, distributions induced by stochastic programs, and natural-language scenarios that describe random processes. We introduce 448 such problems together with KS@N, a general-purpose evaluation metric that quantifies how well a model outputs approximate black-box target distributions via the Kolmogorov-Smirnov statistical test. This is the rate at which we fail to reject model samples of size N against ground-truth samples, with larger N indicating greater difficulty. Tested across open and proprietary models, we find a large spread in distributional capabilities. For instance, when models generate samples of size 100 (KS@100, our standard metric), scores range from near 0 to over 20%. No model is able to achieve over 40% at KS@100, showing significant headroom in distributional sampling as a capability. Although adding reasoning can somewhat increase scores, we find no immediate solution for this issue. UnpredictaBench shows that even simple distributional simulation remains challenging, making it a necessary first step toward using LLMs as stand-ins for complex systems.

We consider multi-draft speculative sampling, where the proposal sequences are sampled independently from different draft models. At each step, a token-level draft selection scheme takes a list of valid tokens as input and produces an output token whose distribution matches that of the target model. Previous works have demonstrated that the optimal scheme (which maximizes the probability of accepting one of the input tokens) can be cast as a solution to a linear program. In this work we show that the optimal scheme can be decomposed into a two-step solution: in the first step an importance sampling (IS) type scheme is used to select one intermediate token; in the second step (single-draft) speculative sampling is applied to generate the output token. For the case of two identical draft models we further 1) establish a necessary and sufficient condition on the distributions of the target and draft models for the acceptance probability to equal one and 2) provide an explicit expression for the optimal acceptance probability. Our theoretical analysis also motives a new class of token-level selection scheme based on weighted importance sampling. Our experimental results demonstrate consistent improvements in the achievable block efficiency and token rates over baseline schemes in a number of scenarios.

In online algorithm selection (OAS), instances of an algorithmic problem class are presented to an agent one after another, and the agent has to quickly select a presumably best algorithm from a fixed set of candidate algorithms. For decision problems such as satisfiability (SAT), quality typically refers to the algorithm's runtime. As the latter is known to exhibit a heavy-tail distribution, an algorithm is normally stopped when exceeding a predefined upper time limit. As a consequence, machine learning methods used to optimize an algorithm selection strategy in a data-driven manner need to deal with right-censored samples, a problem that has received little attention in the literature so far. In this work, we revisit multi-armed bandit algorithms for OAS and discuss their capability of dealing with the problem. Moreover, we adapt them towards runtime-oriented losses, allowing for partially censored data while keeping a space- and time-complexity independent of the time horizon. In an extensive experimental evaluation on an adapted version of the ASlib benchmark, we demonstrate that theoretically well-founded methods based on Thompson sampling perform specifically strong and improve in comparison to existing methods.

Large Reasoning Models (LRMs) often overthink easy problems and underthink hard ones, leading to inefficient computation allocation. Existing methods regulate generated computation or select between direct answering and explicit reasoning, but do not jointly control whether}to reason and how much computation to allocate within reasoning. We call the resulting difficulty-dependent loss in accuracy under computation reduction the efficiency tax. We propose When2Think, an RLVR-based post-training framework for instance-adaptive computation allocation. Its core mechanism, Instance-level Difficulty-Aware Control (IDAC), uses cached reference statistics of success and token cost to modulate a correctness-gated efficiency bonus based on generated token count. Importance sampling supports exploration of Think and NoThink, while Batch-Wise Standardization constructs standardized advantages for critic-free optimization. The framework requires neither a learned reward model nor a learned critic, and offline reference caching avoids online reference-model queries during policy updates. On AIME24, When2Think improves Pass@3 by 10.0 percentage points while reducing token usage by 27.9% relative to the backbone.

Recent advances in deep reinforcement learning have made significant strides in performance on applications such as Go and Atari games. However, developing practical methods to balance exploration and exploitation in complex domains remains largely unsolved. Thompson Sampling and its extension to reinforcement learning provide an elegant approach to exploration that only requires access to posterior samples of the model. At the same time, advances in approximate Bayesian methods have made posterior approximation for flexible neural network models practical. Thus, it is attractive to consider approximate Bayesian neural networks in a Thompson Sampling framework. To understand the impact of using an approximate posterior on Thompson Sampling, we benchmark well-established and recently developed methods for approximate posterior sampling combined with Thompson Sampling over a series of contextual bandit problems. We found that many approaches that have been successful in the supervised learning setting underperformed in the sequential decision-making scenario. In particular, we highlight the challenge of adapting slowly converging uncertainty estimates to the online setting.

While Test-Time Scaling (TTS) has proven effective in improving the reasoning ability of large language models (LLMs), low diversity in model outputs often becomes a bottleneck; this is partly caused by the common "one problem, one solution" (1P1S) training practice, which provides a single canonical answer and can push models toward a narrow set of reasoning paths. This homogenization not only limits sampling effectiveness but also restricts the exploration space for subsequent Reinforcement Learning (RL) stages. To address this, we propose a "one problem, multiple solutions" (1PNS) training paradigm that exposes the model to a variety of valid reasoning trajectories and thus increases inference diversity. A core challenge for 1PNS is reliably measuring semantic differences between multi-step chains of thought, so we introduce Reasoning Path Divergence (RPD), a step-level metric that aligns and scores Long Chain-of-Thought solutions to capture differences in intermediate reasoning. Using RPD, we curate maximally diverse solution sets per problem and fine-tune Qwen3-4B-Base. Experiments show that RPD-selected training yields more varied outputs and higher pass@k, with an average +2.80% gain in pass@16 over a strong 1P1S baseline and a +4.99% gain on AIME24, demonstrating that 1PNS further amplifies the effectiveness of TTS. Our code is available at https://github.com/fengjujf/Reasoning-Path-Divergence .

Decoding methods for large language models often trade-off between diversity of outputs and parallelism of computation. Methods such as beam search and Gumbel top-k sampling can guarantee a different output for each element of the beam, but are not easy to parallelize. Alternatively, methods such as temperature sampling and its modifications (top-k sampling, nucleus sampling, typical decoding, and others), are embarrassingly parallel, but have no guarantees about duplicate samples. We present a framework for sampling according to an arithmetic code book implicitly defined by a large language model, compatible with common sampling variations, with provable beam diversity under certain conditions, as well as being embarrassingly parallel and providing unbiased and consistent expectations from the original model. We demonstrate the effectiveness of our approach on WMT machine translation, more than halving the standard deviation when estimating expected BLEU score reward, and closing the BLEU score gap between independent sampling and beam search by up to 63%.

Self-consistency (SC) is a widely used test-time inference technique for improving performance in chain-of-thought reasoning. It involves generating multiple responses, or samples from a large language model (LLM) and selecting the most frequent answer. This procedure can naturally be viewed as a majority vote or empirical mode estimation. Despite its effectiveness, SC is prohibitively expensive at scale when naively applied to datasets, and it lacks a unified theoretical treatment of sample efficiency and scaling behavior. In this paper, we provide the first comprehensive analysis of SC's scaling behavior and its variants, drawing on mode estimation and voting theory. We derive and empirically validate power law scaling for self-consistency across datasets, and analyze the sample efficiency for fixed-allocation and dynamic-allocation sampling schemes. From these insights, we introduce Blend-ASC, a novel variant of self-consistency that dynamically allocates samples to questions during inference, achieving state-of-the-art sample efficiency. Our approach uses 6.8x fewer samples than vanilla SC on average, outperforming both fixed- and dynamic-allocation SC baselines, thereby demonstrating the superiority of our approach in terms of efficiency. In contrast to existing variants, Blend-ASC is hyperparameter-free and can fit an arbitrary sample budget, ensuring it can be easily applied to any self-consistency application.

Class-wise characteristics of training examples affect the performance of deep classifiers. A well-studied example is when the number of training examples of classes follows a long-tailed distribution, a situation that is likely to yield sub-optimal performance for under-represented classes. This class imbalance problem is conventionally addressed by approaches relying on the class-wise cardinality of training examples, such as data resampling. In this paper, we demonstrate that considering solely the cardinality of classes does not cover all issues causing class imbalance. To measure class imbalance, we propose "Class Uncertainty" as the average predictive uncertainty of the training examples, and we show that this novel measure captures the differences across classes better than cardinality. We also curate SVCI-20 as a novel dataset in which the classes have equal number of training examples but they differ in terms of their hardness; thereby causing a type of class imbalance which cannot be addressed by the approaches relying on cardinality. We incorporate our "Class Uncertainty" measure into a diverse set of ten class imbalance mitigation methods to demonstrate its effectiveness on long-tailed datasets as well as on our SVCI-20. Code and datasets will be made available.

Instance selection (IS) is important in machine learning for reducing dataset size while keeping key characteristics. Current IS methods often struggle with capturing complex relationships in high-dimensional spaces and scale with large datasets. This paper introduces a graph attention-based instance selection (GAIS) method that uses attention mechanisms to identify informative instances through their structural relationships in graph representations. We present two approaches for scalable graph construction: a distance-based mini-batch sampling technique that reduces computation through strategic batch processing, and a hierarchical hashing approach that allows for efficient similarity computation through random projections. The mini-batch approach keeps class distributions through stratified sampling, while the hierarchical hashing method captures relationships at multiple granularities through single-level, multi-level, and multi-view variants. Experiments across 39 datasets show that GAIS achieves reduction rates above 96\% while maintaining or improving model performance relative to state-of-the-art IS methods. The findings shows that the distance-based mini-batch approach offers an optimal balance of efficiency and effectiveness for large-scale datasets, while multi-view variants provide superior performance for complex, high-dimensional data, demonstrating that attention-based importance scoring can effectively identify instances crucial for maintaining decision boundaries without requiring exhaustive pairwise comparisons.

Scaling the amount of compute used to train language models has dramatically improved their capabilities. However, when it comes to inference, we often limit the amount of compute to only one attempt per problem. Here, we explore inference compute as another axis for scaling by increasing the number of generated samples. Across multiple tasks and models, we observe that coverage - the fraction of problems solved by any attempt - scales with the number of samples over four orders of magnitude. In domains like coding and formal proofs, where all answers can be automatically verified, these increases in coverage directly translate into improved performance. When we apply repeated sampling to SWE-bench Lite, the fraction of issues solved with DeepSeek-V2-Coder-Instruct increases from 15.9% with one sample to 56% with 250 samples, outperforming the single-attempt state-of-the-art of 43% which uses more capable frontier models. Moreover, using current API pricing, amplifying the cheaper DeepSeek model with five samples is more cost-effective and solves more issues than paying a premium for one sample from GPT-4o or Claude 3.5 Sonnet. Interestingly, the relationship between coverage and the number of samples is often log-linear and can be modelled with an exponentiated power law, suggesting the existence of inference-time scaling laws. Finally, we find that identifying correct samples out of many generations remains an important direction for future research in domains without automatic verifiers. When solving math word problems from GSM8K and MATH, coverage with Llama-3 models grows to over 95% with 10,000 samples. However, common methods to pick correct solutions from a sample collection, such as majority voting or reward models, plateau beyond several hundred samples and fail to fully scale with the sample budget.

Reinforcement Learning (RL) enhances LLM reasoning, yet a paradox emerges as models scale: strong base models saturate standard benchmarks (e.g., MATH), yielding correct but homogeneous solutions. In such environments, the lack of failure cases causes the advantage signal in group-relative algorithms (e.g., GRPO) to vanish, driving policies into mode collapse. To address this, we propose Constrained Uniform Top-K Sampling (CUTS), a parameter-free decoding strategy enforcing structure-preserving exploration. Unlike standard sampling that follows model biases, CUTS flattens the local optimization landscape by sampling uniformly from constrained high-confidence candidates. We integrate this into Mixed-CUTS, a training framework synergizing exploitative and exploratory rollouts to amplify intra-group advantage variance. Experiments on Qwen3 models demonstrate that our approach prevents policy degeneration and significantly boosts out-of-domain generalization. Notably, Mixed-CUTS improves Pass@1 accuracy on the challenging AIME25 benchmark by up to 15.1% over standard GRPO, validating that maintaining diversity within the semantic manifold is critical for rigorous reasoning.

The sampling of probability distributions specified up to a normalization constant is an important problem in both machine learning and statistical mechanics. While classical stochastic sampling methods such as Markov Chain Monte Carlo (MCMC) or Langevin Dynamics (LD) can suffer from slow mixing times there is a growing interest in using normalizing flows in order to learn the transformation of a simple prior distribution to the given target distribution. Here we propose a generalized and combined approach to sample target densities: Stochastic Normalizing Flows (SNF) -- an arbitrary sequence of deterministic invertible functions and stochastic sampling blocks. We show that stochasticity overcomes expressivity limitations of normalizing flows resulting from the invertibility constraint, whereas trainable transformations between sampling steps improve efficiency of pure MCMC/LD along the flow. By invoking ideas from non-equilibrium statistical mechanics we derive an efficient training procedure by which both the sampler's and the flow's parameters can be optimized end-to-end, and by which we can compute exact importance weights without having to marginalize out the randomness of the stochastic blocks. We illustrate the representational power, sampling efficiency and asymptotic correctness of SNFs on several benchmarks including applications to sampling molecular systems in equilibrium.

The increasing adoption of econometric and machine-learning approaches by empirical researchers has led to a widespread use of one data collection method: web scraping. Web scraping refers to the use of automated computer programs to access websites and download their content. The key argument of this paper is that na\"ive web scraping procedures can lead to sampling bias in the collected data. This article describes three sources of sampling bias in web-scraped data. More specifically, sampling bias emerges from web content being volatile (i.e., being subject to change), personalized (i.e., presented in response to request characteristics), and unindexed (i.e., abundance of a population register). In a series of examples, I illustrate the prevalence and magnitude of sampling bias. To support researchers and reviewers, this paper provides recommendations on anticipating, detecting, and overcoming sampling bias in web-scraped data.

The quality of generative models depends on the quality of the data they are trained on. Creating large-scale, high-quality datasets is often expensive and sometimes impossible, e.g. in certain scientific applications where there is no access to clean data due to physical or instrumentation constraints. Ambient Diffusion and related frameworks train diffusion models with solely corrupted data (which are usually cheaper to acquire) but ambient models significantly underperform models trained on clean data. We study this phenomenon at scale by training more than 80 models on data with different corruption levels across three datasets ranging from 30,000 to approx 1.3M samples. We show that it is impossible, at these sample sizes, to match the performance of models trained on clean data when only training on noisy data. Yet, a combination of a small set of clean data (e.g.~10% of the total dataset) and a large set of highly noisy data suffices to reach the performance of models trained solely on similar-size datasets of clean data, and in particular to achieve near state-of-the-art performance. We provide theoretical evidence for our findings by developing novel sample complexity bounds for learning from Gaussian Mixtures with heterogeneous variances. Our theoretical model suggests that, for large enough datasets, the effective marginal utility of a noisy sample is exponentially worse than that of a clean sample. Providing a small set of clean samples can significantly reduce the sample size requirements for noisy data, as we also observe in our experiments.

We show how to obtain improved active learning methods in the agnostic (adversarial noise) setting by combining marginal leverage score sampling with non-independent sampling strategies that promote spatial coverage. In particular, we propose an easily implemented method based on the pivotal sampling algorithm, which we test on problems motivated by learning-based methods for parametric PDEs and uncertainty quantification. In comparison to independent sampling, our method reduces the number of samples needed to reach a given target accuracy by up to 50%. We support our findings with two theoretical results. First, we show that any non-independent leverage score sampling method that obeys a weak one-sided ell_{infty} independence condition (which includes pivotal sampling) can actively learn d dimensional linear functions with O(dlog d) samples, matching independent sampling. This result extends recent work on matrix Chernoff bounds under ell_{infty} independence, and may be of interest for analyzing other sampling strategies beyond pivotal sampling. Second, we show that, for the important case of polynomial regression, our pivotal method obtains an improved bound of O(d) samples.

Class imbalance in binary classification tasks remains a significant challenge in machine learning, often resulting in poor performance on minority classes. This study comprehensively evaluates three widely-used strategies for handling class imbalance: Synthetic Minority Over-sampling Technique (SMOTE), Class Weights tuning, and Decision Threshold Calibration. We compare these methods against a baseline scenario of no-intervention across 15 diverse machine learning models and 30 datasets from various domains, conducting a total of 9,000 experiments. Performance was primarily assessed using the F1-score, although our study also tracked results on additional 9 metrics including F2-score, precision, recall, Brier-score, PR-AUC, and AUC. Our results indicate that all three strategies generally outperform the baseline, with Decision Threshold Calibration emerging as the most consistently effective technique. However, we observed substantial variability in the best-performing method across datasets, highlighting the importance of testing multiple approaches for specific problems. This study provides valuable insights for practitioners dealing with imbalanced datasets and emphasizes the need for dataset-specific analysis in evaluating class imbalance handling techniques.

Recently, the problem of inaccurate learning targets in crowd counting draws increasing attention. Inspired by a few pioneering work, we solve this problem by trying to predict the indices of pre-defined interval bins of counts instead of the count values themselves. However, an inappropriate interval setting might make the count error contributions from different intervals extremely imbalanced, leading to inferior counting performance. Therefore, we propose a novel count interval partition criterion called Uniform Error Partition (UEP), which always keeps the expected counting error contributions equal for all intervals to minimize the prediction risk. Then to mitigate the inevitably introduced discretization errors in the count quantization process, we propose another criterion called Mean Count Proxies (MCP). The MCP criterion selects the best count proxy for each interval to represent its count value during inference, making the overall expected discretization error of an image nearly negligible. As far as we are aware, this work is the first to delve into such a classification task and ends up with a promising solution for count interval partition. Following the above two theoretically demonstrated criterions, we propose a simple yet effective model termed Uniform Error Partition Network (UEPNet), which achieves state-of-the-art performance on several challenging datasets. The codes will be available at: https://github.com/TencentYoutuResearch/CrowdCounting-UEPNet.

Exploiting the recent advancements in artificial intelligence, showcased by ChatGPT and DALL-E, in real-world applications necessitates vast, domain-specific, and publicly accessible datasets. Unfortunately, the scarcity of such datasets poses a significant challenge for researchers aiming to apply these breakthroughs in engineering design. Synthetic datasets emerge as a viable alternative. However, practitioners are often uncertain about generating high-quality datasets that accurately represent real-world data and are suitable for the intended downstream applications. This study aims to fill this knowledge gap by proposing comprehensive guidelines for generating, annotating, and validating synthetic datasets. The trade-offs and methods associated with each of these aspects are elaborated upon. Further, the practical implications of these guidelines are illustrated through the creation of a turbo-compressors dataset. The study underscores the importance of thoughtful sampling methods to ensure the appropriate size, diversity, utility, and realism of a dataset. It also highlights that design diversity does not equate to performance diversity or realism. By employing test sets that represent uniform, real, or task-specific samples, the influence of sample size and sampling strategy is scrutinized. Overall, this paper offers valuable insights for researchers intending to create and publish synthetic datasets for engineering design, thereby paving the way for more effective applications of AI advancements in the field. The code and data for the dataset and methods are made publicly accessible at https://github.com/cyrilpic/radcomp .

Multiple instance learning (MIL) is a variation of supervised learning where a single class label is assigned to a bag of instances. In this paper, we state the MIL problem as learning the Bernoulli distribution of the bag label where the bag label probability is fully parameterized by neural networks. Furthermore, we propose a neural network-based permutation-invariant aggregation operator that corresponds to the attention mechanism. Notably, an application of the proposed attention-based operator provides insight into the contribution of each instance to the bag label. We show empirically that our approach achieves comparable performance to the best MIL methods on benchmark MIL datasets and it outperforms other methods on a MNIST-based MIL dataset and two real-life histopathology datasets without sacrificing interpretability.

Many real-world applications reveal difficulties in learning classifiers from imbalanced data. The rising big data era has been witnessing more classification tasks with large-scale but extremely imbalance and low-quality datasets. Most of existing learning methods suffer from poor performance or low computation efficiency under such a scenario. To tackle this problem, we conduct deep investigations into the nature of class imbalance, which reveals that not only the disproportion between classes, but also other difficulties embedded in the nature of data, especially, noises and class overlapping, prevent us from learning effective classifiers. Taking those factors into consideration, we propose a novel framework for imbalance classification that aims to generate a strong ensemble by self-paced harmonizing data hardness via under-sampling. Extensive experiments have shown that this new framework, while being very computationally efficient, can lead to robust performance even under highly overlapping classes and extremely skewed distribution. Note that, our methods can be easily adapted to most of existing learning methods (e.g., C4.5, SVM, GBDT and Neural Network) to boost their performance on imbalanced data.

We investigate the generation of minority samples using pretrained text-to-image (T2I) latent diffusion models. Minority instances, in the context of T2I generation, can be defined as ones living on low-density regions of text-conditional data distributions. They are valuable for various applications of modern T2I generators, such as data augmentation and creative AI. Unfortunately, existing pretrained T2I diffusion models primarily focus on high-density regions, largely due to the influence of guided samplers (like CFG) that are essential for high-quality generation. To address this, we present a novel framework to counter the high-density-focus of T2I diffusion models. Specifically, we first develop an online prompt optimization framework that encourages emergence of desired properties during inference while preserving semantic contents of user-provided prompts. We subsequently tailor this generic prompt optimizer into a specialized solver that promotes generation of minority features by incorporating a carefully-crafted likelihood objective. Extensive experiments conducted across various types of T2I models demonstrate that our approach significantly enhances the capability to produce high-quality minority instances compared to existing samplers. Code is available at https://github.com/soobin-um/MinorityPrompt.

Rigorous evaluation of large language models (LLMs) relies on comparing models by the prevalence of desirable or undesirable behaviors, such as task pass rates or policy violations. These prevalence estimates are produced by a classifier, either an LLM-as-a-judge or human annotators, making the choice of classifier central to trustworthy evaluation. Common metrics used for this choice, such as Accuracy, Precision, and F1, are sensitive to class imbalance and to arbitrary choices of positive class, and can favor judges that distort prevalence estimates. We show that Youden's J statistic is theoretically aligned with choosing the best judge to compare models, and that Balanced Accuracy is an equivalent linear transformation of J. Through both analytical arguments and empirical examples and simulations, we demonstrate how selecting judges using Balanced Accuracy leads to better, more robust classifier selection.

Underlying data structures, such as symmetries or invariances to transformations, are often exploited to improve the solution of learning tasks. However, embedding these properties in models or learning algorithms can be challenging and computationally intensive. Data augmentation, on the other hand, induces these symmetries during training by applying multiple transformations to the input data. Despite its ubiquity, its effectiveness depends on the choices of which transformations to apply, when to do so, and how often. In fact, there is both empirical and theoretical evidence that the indiscriminate use of data augmentation can introduce biases that outweigh its benefits. This work tackles these issues by automatically adapting the data augmentation while solving the learning task. To do so, it formulates data augmentation as an invariance-constrained learning problem and leverages Monte Carlo Markov Chain (MCMC) sampling to solve it. The result is a practical algorithm that not only does away with a priori searches for augmentation distributions, but also dynamically controls if and when data augmentation is applied. Our experiments illustrate the performance of this method, which achieves state-of-the-art results in automatic data augmentation benchmarks for CIFAR datasets. Furthermore, this approach can be used to gather insights on the actual symmetries underlying a learning task.

Minority samples are underrepresented instances located in low-density regions of a data manifold, and are valuable in many generative AI applications, such as data augmentation, creative content generation, etc. Unfortunately, existing diffusion-based minority generators often rely on computationally expensive guidance dedicated for minority generation. To address this, here we present a simple yet powerful guidance-free approach called Boost-and-Skip for generating minority samples using diffusion models. The key advantage of our framework requires only two minimal changes to standard generative processes: (i) variance-boosted initialization and (ii) timestep skipping. We highlight that these seemingly-trivial modifications are supported by solid theoretical and empirical evidence, thereby effectively promoting emergence of underrepresented minority features. Our comprehensive experiments demonstrate that Boost-and-Skip greatly enhances the capability of generating minority samples, even rivaling guidance-based state-of-the-art approaches while requiring significantly fewer computations. Code is available at https://github.com/soobin-um/BnS.

With local differential privacy (LDP), users can privatize their data and thus guarantee privacy properties before transmitting it to the server (a.k.a. the aggregator). One primary objective of LDP is frequency (or histogram) estimation, in which the aggregator estimates the number of users for each possible value. In practice, when a study with rich content on a population is desired, the interest is in the multiple attributes of the population, that is to say, in multidimensional data (d geq 2). However, contrary to the problem of frequency estimation of a single attribute (the majority of the works), the multidimensional aspect imposes to pay particular attention to the privacy budget. This one can indeed grow extremely quickly due to the composition theorem. To the authors' knowledge, two solutions seem to stand out for this task: 1) splitting the privacy budget for each attribute, i.e., send each value with fracε{d}-LDP (Spl), and 2) random sampling a single attribute and spend all the privacy budget to send it with ε-LDP (Smp). Although Smp adds additional sampling error, it has proven to provide higher data utility than the former Spl solution. However, we argue that aggregators (who are also seen as attackers) are aware of the sampled attribute and its LDP value, which is protected by a "less strict" e^ε probability bound (rather than e^{ε/d}). This way, we propose a solution named Random Sampling plus Fake Data (RS+FD), which allows creating uncertainty over the sampled attribute by generating fake data for each non-sampled attribute; RS+FD further benefits from amplification by sampling. We theoretically and experimentally validate our proposed solution on both synthetic and real-world datasets to show that RS+FD achieves nearly the same or better utility than the state-of-the-art Smp solution.

Thompson Sampling (TS) has attracted a lot of interest due to its good empirical performance, in particular in the computational advertising. Though successful, the tools for its performance analysis appeared only recently. In this paper, we describe and analyze SpectralTS algorithm for a bandit problem, where the payoffs of the choices are smooth given an underlying graph. In this setting, each choice is a node of a graph and the expected payoffs of the neighboring nodes are assumed to be similar. Although the setting has application both in recommender systems and advertising, the traditional algorithms would scale poorly with the number of choices. For that purpose we consider an effective dimension d, which is small in real-world graphs. We deliver the analysis showing that the regret of SpectralTS scales as d*sqrt(T ln N) with high probability, where T is the time horizon and N is the number of choices. Since a d*sqrt(T ln N) regret is comparable to the known results, SpectralTS offers a computationally more efficient alternative. We also show that our algorithm is competitive on both synthetic and real-world data.

The advent of universal time series forecasting models has revolutionized zero-shot forecasting across diverse domains, yet the critical role of data diversity in training these models remains underexplored. Existing large-scale time series datasets often suffer from inherent biases and imbalanced distributions, leading to suboptimal model performance and generalization. To address this gap, we introduce BLAST, a novel pre-training corpus designed to enhance data diversity through a balanced sampling strategy. First, BLAST incorporates 321 billion observations from publicly available datasets and employs a comprehensive suite of statistical metrics to characterize time series patterns. Then, to facilitate pattern-oriented sampling, the data is implicitly clustered using grid-based partitioning. Furthermore, by integrating grid sampling and grid mixup techniques, BLAST ensures a balanced and representative coverage of diverse patterns. Experimental results demonstrate that models pre-trained on BLAST achieve state-of-the-art performance with a fraction of the computational resources and training tokens required by existing methods. Our findings highlight the pivotal role of data diversity in improving both training efficiency and model performance for the universal forecasting task.

A graph homomorphism is a map between two graphs that preserves adjacency relations. We consider the problem of sampling a random graph homomorphism from a graph into a large network. We propose two complementary MCMC algorithms for sampling random graph homomorphisms and establish bounds on their mixing times and the concentration of their time averages. Based on our sampling algorithms, we propose a novel framework for network data analysis that circumvents some of the drawbacks in methods based on independent and neighborhood sampling. Various time averages of the MCMC trajectory give us various computable observables, including well-known ones such as homomorphism density and average clustering coefficient and their generalizations. Furthermore, we show that these network observables are stable with respect to a suitably renormalized cut distance between networks. We provide various examples and simulations demonstrating our framework through synthetic networks. We also demonstrate the performance of our framework on the tasks of network clustering and subgraph classification on the Facebook100 dataset and on Word Adjacency Networks of a set of classic novels.

We investigate the use of a stratified sampling approach for LIME Image, a popular model-agnostic explainable AI method for computer vision tasks, in order to reduce the artifacts generated by typical Monte Carlo sampling. Such artifacts are due to the undersampling of the dependent variable in the synthetic neighborhood around the image being explained, which may result in inadequate explanations due to the impossibility of fitting a linear regressor on the sampled data. We then highlight a connection with the Shapley theory, where similar arguments about undersampling and sample relevance were suggested in the past. We derive all the formulas and adjustment factors required for an unbiased stratified sampling estimator. Experiments show the efficacy of the proposed approach.

We examine a simple stochastic strategy for adapting well-known single-point acquisition functions to allow batch active learning. Unlike acquiring the top-K points from the pool set, score- or rank-based sampling takes into account that acquisition scores change as new data are acquired. This simple strategy for adapting standard single-sample acquisition strategies can even perform just as well as compute-intensive state-of-the-art batch acquisition functions, like BatchBALD or BADGE, while using orders of magnitude less compute. In addition to providing a practical option for machine learning practitioners, the surprising success of the proposed method in a wide range of experimental settings raises a difficult question for the field: when are these expensive batch acquisition methods pulling their weight?

Self-Taught Reasoners (STaR), synonymously known as Rejection sampling Fine-Tuning (RFT), is an integral part of the training pipeline of self-improving reasoning Language Models (LMs). The self-improving mechanism often employs random observation (data) sampling. However, this results in trained observation imbalance; inefficiently over-training on solved examples while under-training on challenging ones. In response, we introduce Adaptive STaR (AdaSTaR), a novel algorithm that rectifies this by integrating two adaptive sampling principles: (1) Adaptive Sampling for Diversity: promoting balanced training across observations, and (2) Adaptive Sampling for Curriculum: dynamically adjusting data difficulty to match the model's evolving strength. Across six benchmarks, AdaSTaR achieves best test accuracy in all instances (6/6) and reduces training FLOPs by an average of 58.6% against an extensive list of baselines. These improvements in performance and efficiency generalize to different pre-trained LMs and larger models, paving the way for more efficient and effective self-improving LMs.

Node classification is an important research topic in graph learning. Graph neural networks (GNNs) have achieved state-of-the-art performance of node classification. However, existing GNNs address the problem where node samples for different classes are balanced; while for many real-world scenarios, some classes may have much fewer instances than others. Directly training a GNN classifier in this case would under-represent samples from those minority classes and result in sub-optimal performance. Therefore, it is very important to develop GNNs for imbalanced node classification. However, the work on this is rather limited. Hence, we seek to extend previous imbalanced learning techniques for i.i.d data to the imbalanced node classification task to facilitate GNN classifiers. In particular, we choose to adopt synthetic minority over-sampling algorithms, as they are found to be the most effective and stable. This task is non-trivial, as previous synthetic minority over-sampling algorithms fail to provide relation information for newly synthesized samples, which is vital for learning on graphs. Moreover, node attributes are high-dimensional. Directly over-sampling in the original input domain could generates out-of-domain samples, which may impair the accuracy of the classifier. We propose a novel framework, GraphSMOTE, in which an embedding space is constructed to encode the similarity among the nodes. New samples are synthesize in this space to assure genuineness. In addition, an edge generator is trained simultaneously to model the relation information, and provide it for those new samples. This framework is general and can be easily extended into different variations. The proposed framework is evaluated using three different datasets, and it outperforms all baselines with a large margin.