Daily Papers

The sparsity of labelled data is an obstacle to the development of Relation Extraction models and the completion of databases in various biomedical areas. While being of high interest in drug-discovery, the natural-products literature, reporting the identification of potential bioactive compounds from organisms, is a concrete example of such an overlooked topic. To mark the start of this new task, we created the first curated evaluation dataset and extracted literature items from the LOTUS database to build training sets. To this end, we developed a new sampler inspired by diversity metrics in ecology, named Greedy Maximum Entropy sampler, or GME-sampler (https://github.com/idiap/gme-sampler). The strategic optimization of both balance and diversity of the selected items in the evaluation set is important given the resource-intensive nature of manual curation. After quantifying the noise in the training set, in the form of discrepancies between the input abstracts text and the expected output labels, we explored different strategies accordingly. Framing the task as an end-to-end Relation Extraction, we evaluated the performance of standard fine-tuning as a generative task and few-shot learning with open Large Language Models (LLaMA 7B-65B). In addition to their evaluation in few-shot settings, we explore the potential of open Large Language Models (Vicuna-13B) as synthetic data generator and propose a new workflow for this purpose. All evaluated models exhibited substantial improvements when fine-tuned on synthetic abstracts rather than the original noisy data. We provide our best performing (f1-score=59.0) BioGPT-Large model for end-to-end RE of natural-products relationships along with all the generated synthetic data and the evaluation dataset. See more details at https://github.com/idiap/abroad-re.

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.

Decoding sits between a language model and everything we do with it, yet it is still treated as a heuristic knob-tuning exercise. We argue decoding should be understood as a principled optimisation layer: at each token, we solve a regularised problem over the probability simplex that trades off model score against structural preferences and constraints. This single template recovers greedy decoding, Softmax sampling, Top-K, Top-P, and Sparsemax-style sparsity as special cases, and explains their common structure through optimality conditions. More importantly, the framework makes it easy to invent new decoders without folklore. We demonstrate this by designing Best-of-K (BoK), a KL-anchored coverage objective aimed at multi-sample pipelines (self-consistency, reranking, verifier selection). BoK targets the probability of covering good alternatives within a fixed K-sample budget and improves empirical performance. We show that such samples can improve accuracy by, for example, +18.6% for Qwen2.5-Math-7B on MATH500 at high sampling temperatures.

Despite significant advances in optimizers for training, most research works use common scheduler choices like Cosine or exponential decay. In this paper, we study GreedyLR, a novel scheduler that adaptively adjusts the learning rate during training based on the current loss. To validate the effectiveness of our proposed scheduler, we conduct experiments on several NLP, CV, and LLM tasks with up to 7B parameters, including both fine-tuning and pre-training experiments. The results show that our approach outperforms several state-of-the-art schedulers in terms of accuracy, speed, and convergence. We also provide a theoretical analysis of the GreedyLR algorithm, including a proof of convergence and derivation of the optimal scaling factor F that maximizes the convergence rate, along with experiments to show robustness of the algorithm to realistic noisy landscapes. Our scheduler is easy to implement, computationally efficient, and could be considered a good default scheduler for training.

The output of Large Language Models (LLMs) are a function of the internal model's parameters and the input provided into the context window. The hypothesis presented here is that under a greedy sampling strategy the variance in the LLM's output is a function of the conceptual certainty embedded in the model's parametric knowledge, as well as the lexical variance in the input. Finetuning the model results in reducing the sensitivity of the model output to the lexical input variations. This is then applied to a classification problem and a probabilistic method is proposed for estimating the certainties of the predicted classes.

Current evaluations of large language models (LLMs) often overlook non-determinism, typically focusing on a single output per example. This limits our understanding of LLM performance variability in real-world applications. Our study addresses this issue by exploring key questions about the performance differences between greedy decoding and sampling, identifying benchmarks' consistency regarding non-determinism, and examining unique model behaviors. Through extensive experiments, we observe that greedy decoding generally outperforms sampling methods for most evaluated tasks. We also observe consistent performance across different LLM sizes and alignment methods, noting that alignment can reduce sampling variance. Moreover, our best-of-N sampling approach demonstrates that smaller LLMs can match or surpass larger models such as GPT-4-Turbo, highlighting the untapped potential of smaller LLMs. This research shows the importance of considering non-determinism in LLM evaluations and provides insights for future LLM development and evaluation.

Ensembles of independently trained neural networks are a state-of-the-art approach to estimate predictive uncertainty in Deep Learning, and can be interpreted as an approximation of the posterior distribution via a mixture of delta functions. The training of ensembles relies on non-convexity of the loss landscape and random initialization of their individual members, making the resulting posterior approximation uncontrolled. This paper proposes a novel and principled method to tackle this limitation, minimizing an f-divergence between the true posterior and a kernel density estimator (KDE) in a function space. We analyze this objective from a combinatorial point of view, and show that it is submodular with respect to mixture components for any f. Subsequently, we consider the problem of greedy ensemble construction. From the marginal gain on the negative f-divergence, which quantifies an improvement in posterior approximation yielded by adding a new component into the KDE, we derive a novel diversity term for ensemble methods. The performance of our approach is demonstrated on computer vision out-of-distribution detection benchmarks in a range of architectures trained on multiple datasets. The source code of our method is made publicly available at https://github.com/Oulu-IMEDS/greedy_ensembles_training.

This paper introduces the counter-intuitive generalization results of overfitting pre-trained large language models (LLMs) on very small datasets. In the setting of open-ended text generation, it is well-documented that LLMs tend to generate repetitive and dull sequences, a phenomenon that is especially apparent when generating using greedy decoding. This issue persists even with state-of-the-art LLMs containing billions of parameters, trained via next-token prediction on large datasets. We find that by further fine-tuning these models to achieve a near-zero training loss on a small set of samples -- a process we refer to as hyperfitting -- the long-sequence generative capabilities are greatly enhanced. Greedy decoding with these Hyperfitted models even outperform Top-P sampling over long-sequences, both in terms of diversity and human preferences. This phenomenon extends to LLMs of various sizes, different domains, and even autoregressive image generation. We further find this phenomena to be distinctly different from that of Grokking and double descent. Surprisingly, our experiments indicate that hyperfitted models rarely fall into repeating sequences they were trained on, and even explicitly blocking these sequences results in high-quality output. All hyperfitted models produce extremely low-entropy predictions, often allocating nearly all probability to a single token.

Masked Diffusion Models (MDMs) offer greater flexibility in decoding order than autoregressive models but require careful planning to achieve high-quality generation. Existing samplers typically adopt greedy heuristics, prioritizing positions with the highest local certainty to decode at each step. Through failure case analysis, we identify a fundamental limitation of this approach: it neglects the downstream impact of current decoding choices on subsequent steps and fails to minimize cumulative uncertainty. In particular, these methods do not fully exploit the non-causal nature of MDMs, which enables evaluating how a decoding decision reshapes token probabilities/uncertainty across all remaining masked positions. To bridge this gap, we propose the Info-Gain Sampler, a principled decoding framework that balances immediate uncertainty with information gain over future masked tokens. Extensive evaluations across diverse architectures and tasks (reasoning, coding, creative writing, and image generation) demonstrate that Info-Gain Sampler consistently outperforms existing samplers for MDMs. For instance, it achieves a 3.6% improvement in average accuracy on reasoning tasks and a 63.1% win-rate in creative writing. Notably, on reasoning tasks it reduces cumulative uncertainty from 78.4 to 48.6, outperforming the best baseline by a large margin. The code will be available at https://github.com/yks23/Information-Gain-Sampler.

Sequence models are a critical component of modern NLP systems, but their predictions are difficult to explain. We consider model explanations though rationales, subsets of context that can explain individual model predictions. We find sequential rationales by solving a combinatorial optimization: the best rationale is the smallest subset of input tokens that would predict the same output as the full sequence. Enumerating all subsets is intractable, so we propose an efficient greedy algorithm to approximate this objective. The algorithm, which is called greedy rationalization, applies to any model. For this approach to be effective, the model should form compatible conditional distributions when making predictions on incomplete subsets of the context. This condition can be enforced with a short fine-tuning step. We study greedy rationalization on language modeling and machine translation. Compared to existing baselines, greedy rationalization is best at optimizing the combinatorial objective and provides the most faithful rationales. On a new dataset of annotated sequential rationales, greedy rationales are most similar to human rationales.

This paper investigates a novel lossy compression framework operating under logarithmic loss, designed to handle situations where the reconstruction distribution diverges from the source distribution. This framework is especially relevant for applications that require joint compression and retrieval, and in scenarios involving distributional shifts due to processing. We show that the proposed formulation extends the classical minimum entropy coupling framework by integrating a bottleneck, allowing for a controlled degree of stochasticity in the coupling. We explore the decomposition of the Minimum Entropy Coupling with Bottleneck (MEC-B) into two distinct optimization problems: Entropy-Bounded Information Maximization (EBIM) for the encoder, and Minimum Entropy Coupling (MEC) for the decoder. Through extensive analysis, we provide a greedy algorithm for EBIM with guaranteed performance, and characterize the optimal solution near functional mappings, yielding significant theoretical insights into the structural complexity of this problem. Furthermore, we illustrate the practical application of MEC-B through experiments in Markov Coding Games (MCGs) under rate limits. These games simulate a communication scenario within a Markov Decision Process, where an agent must transmit a compressed message from a sender to a receiver through its actions. Our experiments highlight the trade-offs between MDP rewards and receiver accuracy across various compression rates, showcasing the efficacy of our method compared to conventional compression baseline.

Large language models (LLMs) typically employ greedy decoding or low-temperature sampling for reasoning tasks, reflecting a perceived trade-off between diversity and accuracy. We challenge this convention by introducing top-nsigma, a novel sampling method that operates directly on pre-softmax logits by leveraging a statistical threshold. Our key insight is that logits naturally separate into a Gaussian-distributed noisy region and a distinct informative region, enabling efficient token filtering without complex probability manipulations. Unlike existing methods (e.g., top-p, min-p) that inadvertently include more noise tokens at higher temperatures, top-nsigma maintains a stable sampling space regardless of temperature scaling. We also provide a theoretical analysis of top-nsigma to better understand its behavior. The extensive experimental results across four reasoning-focused datasets demonstrate that our method not only outperforms existing sampling approaches but also surpasses greedy decoding, while maintaining consistent performance even at high temperatures.

We adapt the greedy Stack-LSTM dependency parser of Dyer et al. (2015) to support a training-with-exploration procedure using dynamic oracles(Goldberg and Nivre, 2013) instead of cross-entropy minimization. This form of training, which accounts for model predictions at training time rather than assuming an error-free action history, improves parsing accuracies for both English and Chinese, obtaining very strong results for both languages. We discuss some modifications needed in order to get training with exploration to work well for a probabilistic neural-network.

Feature selection helps reduce data acquisition costs in ML, but the standard approach is to train models with static feature subsets. Here, we consider the dynamic feature selection (DFS) problem where a model sequentially queries features based on the presently available information. DFS is often addressed with reinforcement learning, but we explore a simpler approach of greedily selecting features based on their conditional mutual information. This method is theoretically appealing but requires oracle access to the data distribution, so we develop a learning approach based on amortized optimization. The proposed method is shown to recover the greedy policy when trained to optimality, and it outperforms numerous existing feature selection methods in our experiments, thus validating it as a simple but powerful approach for this problem.

Top-k decoding is a widely used method for sampling from LLMs: at each token, only the largest k next-token-probabilities are kept, and the next token is sampled after re-normalizing them to sum to unity. Top-k and other sampling methods are motivated by the intuition that true next-token distributions are sparse, and the noisy LLM probabilities need to be truncated. However, to our knowledge, a precise theoretical motivation for the use of top-k decoding is missing. In this work, we develop a theoretical framework that both explains and generalizes top-k decoding. We view decoding at a fixed token as the recovery of a sparse probability distribution. We consider Bregman decoders obtained by minimizing a separable Bregman divergence (for both the primal and dual cases) with a sparsity-inducing ell_0 regularization. Despite the combinatorial nature of the objective, we show how to optimize it efficiently for a large class of divergences. We show that the optimal decoding strategies are greedy, and further that the loss function is discretely convex in k, so that binary search provably and efficiently finds the optimal k. We show that top-k decoding arises as a special case for the KL divergence, and identify new decoding strategies that have distinct behaviors (e.g., non-linearly up-weighting larger probabilities after re-normalization).

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.

Despite their ubiquity in language generation, it remains unknown why truncation sampling heuristics like nucleus sampling are so effective. We provide a theoretical explanation for the effectiveness of the truncation sampling by proving that truncation methods that discard tokens below some probability threshold (the most common type of truncation) can guarantee that all sampled tokens have nonzero true probability. However, thresholds are a coarse heuristic, and necessarily discard some tokens with nonzero true probability as well. In pursuit of a more precise sampling strategy, we show that we can leverage a known source of model errors, the softmax bottleneck, to prove that certain tokens have nonzero true probability, without relying on a threshold. Based on our findings, we develop an experimental truncation strategy and the present pilot studies demonstrating the promise of this type of algorithm. Our evaluations show that our method outperforms its threshold-based counterparts under automatic and human evaluation metrics for low-entropy (i.e., close to greedy) open-ended text generation. Our theoretical findings and pilot experiments provide both insight into why truncation sampling works, and make progress toward more expressive sampling algorithms that better surface the generative capabilities of large language models.

In-context learning is a promising paradigm that utilizes in-context examples as prompts for the predictions of large language models. These prompts are crucial for achieving strong performance. However, since the prompts need to be sampled from a large volume of annotated examples, finding the right prompt may result in high annotation costs. To address this challenge, this paper introduces an influence-driven selective annotation method that aims to minimize annotation costs while improving the quality of in-context examples. The essence of our method is to select a pivotal subset from a large-scale unlabeled data pool to annotate for the subsequent sampling of prompts. Specifically, a directed graph is first constructed to represent unlabeled data. Afterward, the influence of candidate unlabeled subsets is quantified with a diffusion process. A simple yet effective greedy algorithm for unlabeled data selection is lastly introduced. It iteratively selects the data if it provides a maximum marginal gain with respect to quantified influence. Compared with previous efforts on selective annotations, our influence-driven method works in an end-to-end manner, avoids an intractable explicit balance between data diversity and representativeness, and enjoys theoretical support. Experiments confirm the superiority of the proposed method on various benchmarks, achieving better performance under lower time consumption during subset selection. The project page is available at https://skzhang1.github.io/IDEAL/.

In open-ended natural-language generation, existing text decoding methods typically struggle to produce text which is both diverse and high-quality. Greedy and beam search are known to suffer from text degeneration and linguistic diversity issues, while temperature, top-k, and nucleus sampling often yield diverse but low-quality outputs. In this work, we present crowd sampling, a family of decoding methods based on Bayesian risk minimization, to address this diversity-quality trade-off. Inspired by the principle of "the wisdom of the crowd," crowd sampling seeks to select a candidate from a pool of candidates that has the least expected risk (i.e., highest expected reward) under a generative model according to a given utility function. Crowd sampling can be seen as a generalization of numerous existing methods, including majority voting, and in practice, it can be used as a drop-in replacement for existing sampling methods. Extensive experiments show that crowd sampling delivers improvements of 3-7 ROUGE and BLEU points across a wide range of tasks, including summarization, data-to-text, translation, and textual style transfer, while achieving new state-of-the-art results on WebNLG and WMT'16.

Evaluating modern machine learning models has become prohibitively expensive. Benchmarks such as LMMs-Eval and HELM demand thousands of GPU hours per model. Costly evaluation reduces inclusivity, slows the cycle of innovation, and worsens environmental impact. The typical approach follows two steps. First, select an anchor subset of data. Second, train a mapping from the accuracy on this subset to the final test result. The drawback is that anchor selection depends on clustering, which can be complex and sensitive to design choices. We argue that promoting diversity among samples is not essential; what matters is to select samples that maximise diversity in model responses. Our method, Diversifying Sample Condensation (DISCO), selects the top-k samples with the greatest model disagreements. This uses greedy, sample-wise statistics rather than global clustering. The approach is conceptually simpler. From a theoretical view, inter-model disagreement provides an information-theoretically optimal rule for such greedy selection. DISCO shows empirical gains over prior methods, achieving state-of-the-art results in performance prediction across MMLU, Hellaswag, Winogrande, and ARC. Code is available here: https://github.com/arubique/disco-public.

Citizens' assemblies are a form of democratic innovation in which a randomly selected panel of constituents deliberates on questions of public interest. We study a novel goal for the selection of panel members: maximizing the entropy of the distribution over possible panels. We design algorithms that sample from maximum-entropy distributions, potentially subject to constraints on the individual selection probabilities. We investigate the properties of these algorithms theoretically, including in terms of their resistance to manipulation and transparency. We benchmark our algorithms on a large set of real assembly lotteries in terms of their intersectional diversity and the probability of satisfying unseen representation constraints, and we obtain favorable results on both measures. We deploy one of our algorithms on a website for citizens' assembly practitioners.

We study the problem of optimally projecting the transition matrix of a finite ergodic multivariate Markov chain onto a lower-dimensional state space. Specifically, we seek to construct a projected Markov chain that optimizes various information-theoretic criteria under cardinality constraints. These criteria include entropy rate, information-theoretic distance to factorizability, independence, and stationarity. We formulate these tasks as best subset selection problems over multivariate Markov chains and leverage the submodular (or supermodular) structure of the objective functions to develop efficient greedy-based algorithms with theoretical guarantees. We extend our analysis to k-submodular settings and introduce a generalized version of the distorted greedy algorithm, which may be of independent interest. Finally, we illustrate the theory and algorithms through extensive numerical experiments with publicly available code on multivariate Markov chains associated with the Bernoulli-Laplace and Curie-Weiss model.

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.

Recent large-scale neural autoregressive sequence models have shown impressive performances on a variety of natural language generation tasks. However, their generated sequences often exhibit degenerate properties such as non-termination, undesirable repetition, and premature termination, when generated with decoding algorithms such as greedy search, beam search, top-k sampling, and nucleus sampling. In this paper, we focus on the problem of non-terminating sequences resulting from an incomplete decoding algorithm. We first define an incomplete probable decoding algorithm which includes greedy search, top-k sampling, and nucleus sampling, beyond the incomplete decoding algorithm originally put forward by Welleck et al. (2020). We then propose a non-monotonic self-terminating language model, which significantly relaxes the constraint of monotonically increasing termination probability in the originally proposed self-terminating language model by Welleck et al. (2020), to address the issue of non-terminating sequences when using incomplete probable decoding algorithms. We prove that our proposed model prevents non-terminating sequences when using not only incomplete probable decoding algorithms but also beam search. We empirically validate our model on sequence completion tasks with various architectures.

A significant use case of instruction-finetuned Large Language Models (LLMs) is to solve question-answering tasks interactively. In this setting, an LLM agent is tasked with making a prediction by sequentially querying relevant information from the user, as opposed to a single-turn conversation. This paper explores sequential querying strategies that aim to minimize the expected number of queries. One such strategy is Information Pursuit (IP), a greedy algorithm that at each iteration selects the query that maximizes information gain or equivalently minimizes uncertainty. However, obtaining accurate estimates of mutual information or conditional entropy for LLMs is very difficult in practice due to over- or under-confident LLM probabilities, which leads to suboptimal query selection and predictive performance. To better estimate the uncertainty at each iteration, we propose Conformal Information Pursuit (C-IP), an alternative approach to sequential information gain based on conformal prediction sets. More specifically, C-IP leverages a relationship between prediction sets and conditional entropy at each iteration to estimate uncertainty based on the average size of conformal prediction sets. In contrast to conditional entropy, we find that conformal prediction sets are a distribution-free and robust method of measuring uncertainty. Experiments with 20 Questions show that C-IP obtains better predictive performance and shorter query-answer chains compared to previous approaches to IP and uncertainty-based chain-of-thought methods. Furthermore, extending to an interactive medical setting between a doctor and a patient on the MediQ dataset, C-IP achieves competitive performance with direct single-turn prediction while offering greater interpretability.

Byte-Pair Encoding (BPE) is a popular algorithm used for tokenizing data in NLP, despite being devised initially as a compression method. BPE appears to be a greedy algorithm at face value, but the underlying optimization problem that BPE seeks to solve has not yet been laid down. We formalize BPE as a combinatorial optimization problem. Via submodular functions, we prove that the iterative greedy version is a 1{{sigma(mu^star)}}(1-e^{-{sigma(mu^star)}})-approximation of an optimal merge sequence, where {sigma(mu^star)} is the total backward curvature with respect to the optimal merge sequence mu^star. Empirically the lower bound of the approximation is approx 0.37. We provide a faster implementation of BPE which improves the runtime complexity from Oleft(N Mright) to Oleft(N log Mright), where N is the sequence length and M is the merge count. Finally, we optimize the brute-force algorithm for optimal BPE using memoization.

Taking greedy decoding algorithm as it should be, this work focuses on further strengthening the model itself for Chinese word segmentation (CWS), which results in an even more fast and more accurate CWS model. Our model consists of an attention only stacked encoder and a light enough decoder for the greedy segmentation plus two highway connections for smoother training, in which the encoder is composed of a newly proposed Transformer variant, Gaussian-masked Directional (GD) Transformer, and a biaffine attention scorer. With the effective encoder design, our model only needs to take unigram features for scoring. Our model is evaluated on SIGHAN Bakeoff benchmark datasets. The experimental results show that with the highest segmentation speed, the proposed model achieves new state-of-the-art or comparable performance against strong baselines in terms of strict closed test setting.

The performance of acquisition functions for Bayesian optimisation to locate the global optimum of continuous functions is investigated in terms of the Pareto front between exploration and exploitation. We show that Expected Improvement (EI) and the Upper Confidence Bound (UCB) always select solutions to be expensively evaluated on the Pareto front, but Probability of Improvement is not guaranteed to do so and Weighted Expected Improvement does so only for a restricted range of weights. We introduce two novel epsilon-greedy acquisition functions. Extensive empirical evaluation of these together with random search, purely exploratory, and purely exploitative search on 10 benchmark problems in 1 to 10 dimensions shows that epsilon-greedy algorithms are generally at least as effective as conventional acquisition functions (e.g., EI and UCB), particularly with a limited budget. In higher dimensions epsilon-greedy approaches are shown to have improved performance over conventional approaches. These results are borne out on a real world computational fluid dynamics optimisation problem and a robotics active learning problem. Our analysis and experiments suggest that the most effective strategy, particularly in higher dimensions, is to be mostly greedy, occasionally selecting a random exploratory solution.

We consider the stochastic linear contextual bandit problem with high-dimensional features. We analyze the Thompson sampling algorithm using special classes of sparsity-inducing priors (e.g., spike-and-slab) to model the unknown parameter and provide a nearly optimal upper bound on the expected cumulative regret. To the best of our knowledge, this is the first work that provides theoretical guarantees of Thompson sampling in high-dimensional and sparse contextual bandits. For faster computation, we use variational inference instead of Markov Chain Monte Carlo (MCMC) to approximate the posterior distribution. Extensive simulations demonstrate the improved performance of our proposed algorithm over existing ones.

Although Large Vision Language Models (LVLMs) have demonstrated remarkable performance in image understanding tasks, their computational efficiency remains a significant challenge, particularly on resource-constrained devices due to the high cost of processing large numbers of visual tokens. Recently, training-free visual token pruning methods have gained popularity as a low-cost solution to this issue. However, existing approaches suffer from two key limitations: semantic saliency-based strategies primarily focus on high cross-attention visual tokens, often neglecting visual diversity, whereas visual diversity-based methods risk inadvertently discarding semantically important tokens, especially under high compression ratios. In this paper, we introduce GreedyPrune, a training-free plug-and-play visual token pruning algorithm designed to jointly optimize semantic saliency and visual diversity. We formalize the token pruning process as a combinatorial optimization problem and demonstrate that greedy algorithms effectively balance computational efficiency with model accuracy. Extensive experiments validate the effectiveness of our approach, showing that GreedyPrune achieves state-of-the-art accuracy across various multimodal tasks and models while significantly reducing end-to-end inference latency.

Fine-tuned language models use greedy decoding to answer reading comprehension questions with relative success. However, this approach does not ensure that the answer is a span in the given passage, nor does it guarantee that it is the most probable one. Does greedy decoding actually perform worse than an algorithm that does adhere to these properties? To study the performance and optimality of greedy decoding, we present exact-extract, a decoding algorithm that efficiently finds the most probable answer span in the context. We compare the performance of T5 with both decoding algorithms on zero-shot and few-shot extractive question answering. When no training examples are available, exact-extract significantly outperforms greedy decoding. However, greedy decoding quickly converges towards the performance of exact-extract with the introduction of a few training examples, becoming more extractive and increasingly likelier to generate the most probable span as the training set grows. We also show that self-supervised training can bias the model towards extractive behavior, increasing performance in the zero-shot setting without resorting to annotated examples. Overall, our results suggest that pretrained language models are so good at adapting to extractive question answering, that it is often enough to fine-tune on a small training set for the greedy algorithm to emulate the optimal decoding strategy.

Many important optimization problems, such as the minimum spanning tree and minimum-cost flow, can be solved optimally by a greedy method. In this work, we study a learning variant of these problems, where the model of the problem is unknown and has to be learned by interacting repeatedly with the environment in the bandit setting. We formalize our learning problem quite generally, as learning how to maximize an unknown modular function on a known polymatroid. We propose a computationally efficient algorithm for solving our problem and bound its expected cumulative regret. Our gap-dependent upper bound is tight up to a constant and our gap-free upper bound is tight up to polylogarithmic factors. Finally, we evaluate our method on three problems and demonstrate that it is practical.

We address the challenge of exploration in reinforcement learning (RL) when the agent operates in an unknown environment with sparse or no rewards. In this work, we study the maximum entropy exploration problem of two different types. The first type is visitation entropy maximization previously considered by Hazan et al.(2019) in the discounted setting. For this type of exploration, we propose a game-theoretic algorithm that has mathcal{O}(H^3S^2A/varepsilon^2) sample complexity thus improving the varepsilon-dependence upon existing results, where S is a number of states, A is a number of actions, H is an episode length, and varepsilon is a desired accuracy. The second type of entropy we study is the trajectory entropy. This objective function is closely related to the entropy-regularized MDPs, and we propose a simple algorithm that has a sample complexity of order mathcal{O}(poly(S,A,H)/varepsilon). Interestingly, it is the first theoretical result in RL literature that establishes the potential statistical advantage of regularized MDPs for exploration. Finally, we apply developed regularization techniques to reduce sample complexity of visitation entropy maximization to mathcal{O}(H^2SA/varepsilon^2), yielding a statistical separation between maximum entropy exploration and reward-free exploration.

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.

Reinforcement learning (RL) has become a key component in modern large language models, yet the rollout stage remains the key bottleneck in RL training pipelines. Although Multi-Token Prediction (MTP) offers a natural solution to accelerate rollouts through speculative decoding, many studies have observed that MTP acceptance rates degrade significantly during RL training, leading to limited speedup performance. To address this bottleneck, we present Bebop, a systematic study of MTP in LLM post-training, and offer practical recipes to integrate MTP into large-scale RL pipelines. First, we reveal that the MTP acceptance rate is fundamentally bounded by the fluctuation of model entropy, which demonstrates a clear negative linear relationship with the rise of entropy in the RL stage. Second, we show that probabilistic rejection sampling largely alleviates the disturbance introduced by entropy in RL compared to greedy draft sampling. We further identify that the conventional MTP training objectives (cross-entropy or KL) are suboptimal in such settings, and therefore we propose a novel end-to-end TV loss that directly optimizes multi-step rejection sampling acceptance rate, yielding ~10% acceptance rate improvements, achieving up to 95% acceptance rates and up to 25% extra inference throughput gains across mathematical reasoning, code generation, and agentic tasks. Third, we test various online MTP training strategies during RL and show that pre-RL MTP training with e2e TV loss and rejection sampling achieves a consistent acceptance rate and speedup throughout the entire RL, eliminating the need for costly online MTP updating. We provide extensive experiments and analysis that validate our findings. Experimental results show our method achieves up to 1.8x end-to-end acceleration in async RL training of Qwen3.5, Qwen3.6, and Qwen3.7 models.

We propose a class of greedy algorithms for weighted sparse recovery by considering new loss function-based generalizations of Orthogonal Matching Pursuit (OMP). Given a (regularized) loss function, the proposed algorithms alternate the iterative construction of the signal support via greedy index selection and a signal update based on solving a local data-fitting problem restricted to the current support. We show that greedy selection rules associated with popular weighted sparsity-promoting loss functions admit explicitly computable and simple formulas. Specifically, we consider ell^0 - and ell^1 -based versions of the weighted LASSO (Least Absolute Shrinkage and Selection Operator), the Square-Root LASSO (SR-LASSO) and the Least Absolute Deviations LASSO (LAD-LASSO). Through numerical experiments on Gaussian compressive sensing and high-dimensional function approximation, we demonstrate the effectiveness of the proposed algorithms and empirically show that they inherit desirable characteristics from the corresponding loss functions, such as SR-LASSO's noise-blind optimal parameter tuning and LAD-LASSO's fault tolerance. In doing so, our study sheds new light on the connection between greedy sparse recovery and convex relaxation.

This paper presents a novel information-theoretic perspective on generalization in machine learning by framing the learning problem within the context of lossy compression and applying finite blocklength analysis. In our approach, the sampling of training data formally corresponds to an encoding process, and the model construction to a decoding process. By leveraging finite blocklength analysis, we derive lower bounds on sample complexity and generalization error for a fixed randomized learning algorithm and its associated optimal sampling strategy. Our bounds explicitly characterize the degree of overfitting of the learning algorithm and the mismatch between its inductive bias and the task as distinct terms. This separation provides a significant advantage over existing frameworks. Additionally, we decompose the overfitting term to show its theoretical connection to existing metrics found in information-theoretic bounds and stability theory, unifying these perspectives under our proposed framework.

Long samples of text from neural language models can be of poor quality. Truncation sampling algorithms--like top-p or top-k -- address this by setting some words' probabilities to zero at each step. This work provides framing for the aim of truncation, and an improved algorithm for that aim. We propose thinking of a neural language model as a mixture of a true distribution and a smoothing distribution that avoids infinite perplexity. In this light, truncation algorithms aim to perform desmoothing, estimating a subset of the support of the true distribution. Finding a good subset is crucial: we show that top-p unnecessarily truncates high-probability words, for example causing it to truncate all words but Trump for a document that starts with Donald. We introduce eta-sampling, which truncates words below an entropy-dependent probability threshold. Compared to previous algorithms, eta-sampling generates more plausible long English documents according to humans, is better at breaking out of repetition, and behaves more reasonably on a battery of test distributions.

In this work, we present a variety of novel information-theoretic generalization bounds for learning algorithms, from the supersample setting of Steinke & Zakynthinou (2020)-the setting of the "conditional mutual information" framework. Our development exploits projecting the loss pair (obtained from a training instance and a testing instance) down to a single number and correlating loss values with a Rademacher sequence (and its shifted variants). The presented bounds include square-root bounds, fast-rate bounds, including those based on variance and sharpness, and bounds for interpolating algorithms etc. We show theoretically or empirically that these bounds are tighter than all information-theoretic bounds known to date on the same supersample setting.

Decision trees are renowned for their interpretability capability to achieve high predictive performance, especially on tabular data. Traditionally, they are constructed through recursive algorithms, where they partition the data at every node in a tree. However, identifying the best partition is challenging, as decision trees optimized for local segments may not bring global generalization. To address this, we introduce MetaTree, which trains a transformer-based model on filtered outputs from classical algorithms to produce strong decision trees for classification. Specifically, we fit both greedy decision trees and optimized decision trees on a large number of datasets. We then train MetaTree to produce the trees that achieve strong generalization performance. This training enables MetaTree to not only emulate these algorithms, but also to intelligently adapt its strategy according to the context, thereby achieving superior generalization performance.

Test-time scaling evaluates reasoning LLMs by sampling multiple outputs per prompt, but ranking models in this regime remains underexplored. We formalize dense benchmark ranking under test-time scaling and introduce Scorio, a library that implements statistical ranking methods such as paired-comparison models, item response theory (IRT) models, voting rules, and graph- and spectral-based methods. Across 20 reasoning models on four Olympiad-style math benchmarks (AIME'24, AIME'25, HMMT'25, and BrUMO'25; up to N=80 trials), most full-trial rankings agree closely with the Bayesian gold standard Bayes_{U}@80 (mean Kendall's τ_b = 0.93--0.95), and 19--34 methods recover exactly the same ordering. In the single-trial regime, the best methods reach τ_b approx 0.86. Using greedy decoding as an empirical prior (Bayes_{R_0}@N) reduces variance at N=1 by 16--52%, but can bias rankings when greedy and stochastic sampling disagree. These results identify reliable ranking methods for both high- and low-budget test-time scaling. We release Scorio as an open-source library at https://github.com/mohsenhariri/scorio.

We investigate the sets of joint probability distributions that maximize the average multi-information over a collection of margins. These functionals serve as proxies for maximizing the multi-information of a set of variables or the mutual information of two subsets of variables, at a lower computation and estimation complexity. We describe the maximizers and their relations to the maximizers of the multi-information and the mutual information.

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.

Minimum Bayes risk (MBR) decoding outputs the hypothesis with the highest expected utility over the model distribution for some utility function. It has been shown to improve accuracy over beam search in conditional language generation problems and especially neural machine translation, in both human and automatic evaluations. However, the standard sampling-based algorithm for MBR is substantially more computationally expensive than beam search, requiring a large number of samples as well as a quadratic number of calls to the utility function, limiting its applicability. We describe an algorithm for MBR which gradually grows the number of samples used to estimate the utility while pruning hypotheses that are unlikely to have the highest utility according to confidence estimates obtained with bootstrap sampling. Our method requires fewer samples and drastically reduces the number of calls to the utility function compared to standard MBR while being statistically indistinguishable in terms of accuracy. We demonstrate the effectiveness of our approach in experiments on three language pairs, using chrF++ and COMET as utility/evaluation metrics.

We introduce a principled probabilistic framework for reward-guided decoding in large language models, addressing the limitations of standard decoding methods that optimize token-level likelihood rather than sequence-level quality. Our method defines a reward-augmented target distribution over complete sequences by combining model transition probabilities with prefix-dependent reward potentials. Importantly, the approach is training-free: it leaves model weights unchanged and instead modifies the inference distribution via reward potentials, with all gains arising purely from inference-time sampling. To sample from this distribution, we develop Sequential Monte Carlo algorithms, including a computationally efficient prefix-only variant and a lookahead variant whose intermediate targets match the exact marginals of the full sequence distribution. The framework also integrates resample-move updates with Metropolis-Hastings rejuvenation and supports block-wise generation, subsuming common decoding strategies such as temperature sampling and power-tempered objectives. Empirical results across three 7B models show significant gains. On code generation (HumanEval), our method improves base performance by up to 54.9% and surpasses the strongest sampling baselines by 9.1%-15.3%. On mathematical reasoning (MATH500), it achieves gains of up to 8.8%. Notably, it reaches 87.8% on HumanEval and 78.4% on MATH500 with Qwen2.5-7B, consistently outperforming the reinforcement learning method GRPO.

Speculative sampling (SpS) has been successful in accelerating the decoding throughput of auto-regressive large language models by leveraging smaller draft models. SpS strictly enforces the generated distribution to match that of the verifier LLM. This is unnecessarily restrictive as slight variations of the verifier's distribution, such as sampling with top-k or temperature, would also be acceptable. Typical acceptance sampling (TAS) alleviates this issue by accepting more tokens using entropy-based heuristics. However, this approach distorts the verifier distribution, potentially degrading output quality when the verifier encodes critical information. In this work, we formalize the speculative sampling algorithm through the lens of constrained optimization. Based on this formulation, we propose Cactus (constrained acceptance speculative sampling), a method that guarantees controlled divergence from the verifier distribution and increasing acceptance rates. Empirical results across a wide range of benchmarks confirm the effectiveness of our approach.

We present an approach called Q-probing to adapt a pre-trained language model to maximize a task-specific reward function. At a high level, Q-probing sits between heavier approaches such as finetuning and lighter approaches such as few shot prompting, but can also be combined with either. The idea is to learn a simple linear function on a model's embedding space that can be used to reweight candidate completions. We theoretically show that this sampling procedure is equivalent to a KL-constrained maximization of the Q-probe as the number of samples increases. To train the Q-probes we consider either reward modeling or a class of novel direct policy learning objectives based on importance weighted policy gradients. With this technique, we see gains in domains with ground-truth rewards (code generation) as well as implicit rewards defined by preference data, even outperforming finetuning in data-limited regimes. Moreover, a Q-probe can be trained on top of an API since it only assumes access to sampling and embeddings. Code: https://github.com/likenneth/q_probe .

Subsampling is commonly used to mitigate costs associated with data acquisition, such as time or energy requirements, motivating the development of algorithms for estimating the fully-sampled signal of interest x from partially observed measurements y. In maximum-entropy sampling, one selects measurement locations that are expected to have the highest entropy, so as to minimize uncertainty about x. This approach relies on an accurate model of the posterior distribution over future measurements, given the measurements observed so far. Recently, diffusion models have been shown to produce high-quality posterior samples of high-dimensional signals using guided diffusion. In this work, we propose Active Diffusion Subsampling (ADS), a method for performing active subsampling using guided diffusion in which the model tracks a distribution of beliefs over the true state of x throughout the reverse diffusion process, progressively decreasing its uncertainty by choosing to acquire measurements with maximum expected entropy, and ultimately generating the posterior distribution p(x | y). ADS can be applied using pre-trained diffusion models for any subsampling rate, and does not require task-specific retraining - just the specification of a measurement model. Furthermore, the maximum entropy sampling policy employed by ADS is interpretable, enhancing transparency relative to existing methods using black-box policies. Experimentally, we show that ADS outperforms fixed sampling strategies, and study an application of ADS in Magnetic Resonance Imaging acceleration using the fastMRI dataset, finding that ADS performs competitively with supervised methods. Code available at https://active-diffusion-subsampling.github.io/.

Multimodal large language models (MLLMs) incur substantial inference cost due to the processing of hundreds of visual tokens per image. Although token pruning has proven effective for accelerating inference, determining when and where to prune remains largely heuristic. Existing approaches typically rely on static, empirically selected layers, which limit interpretability and transferability across models. In this work, we introduce a matrix-entropy perspective and identify an "Entropy Collapse Layer" (ECL), where the information content of visual representations exhibits a sharp and consistent drop, which provides a principled criterion for selecting the pruning stage. Building on this observation, we propose EntropyPrune, a novel matrix-entropy-guided token pruning framework that quantifies the information value of individual visual tokens and prunes redundant ones without relying on attention maps. Moreover, to enable efficient computation, we exploit the spectral equivalence of dual Gram matrices, reducing the complexity of entropy computation and yielding up to a 64x theoretical speedup. Extensive experiments on diverse multimodal benchmarks demonstrate that EntropyPrune consistently outperforms state-of-the-art pruning methods in both accuracy and efficiency. On LLaVA-1.5-7B, our method achieves a 68.2% reduction in FLOPs while preserving 96.0% of the original performance. Furthermore, EntropyPrune generalizes effectively to high-resolution and video-based models, highlighting the strong robustness and scalability in practical MLLM acceleration. The code will be publicly available at https://github.com/YahongWang1/EntropyPrune.

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.

While speculative decoding has recently appeared as a promising direction for accelerating the inference of large language models (LLMs), the speedup and scalability are strongly bounded by the token acceptance rate. Prevalent methods usually organize predicted tokens as independent chains or fixed token trees, which fails to generalize to diverse query distributions. In this paper, we propose DySpec, a faster speculative decoding algorithm with a novel dynamic token tree structure. We begin by bridging the draft distribution and acceptance rate from intuitive and empirical clues, and successfully show that the two variables are strongly correlated. Based on this, we employ a greedy strategy to dynamically expand the token tree at run time. Theoretically, we show that our method can achieve optimal results under mild assumptions. Empirically, DySpec yields a higher acceptance rate and speedup than fixed trees. DySpec can drastically improve the throughput and reduce the latency of token generation across various data distribution and model sizes, which significantly outperforms strong competitors, including Specinfer and Sequoia. Under low temperature setting, DySpec can improve the throughput up to 9.1times and reduce the latency up to 9.4times on Llama2-70B. Under high temperature setting, DySpec can also improve the throughput up to 6.21times, despite the increasing difficulty of speculating more than one token per step for draft model.

Reinforcement learning is the method of choice to train models in sampling-based setups with binary outcome feedback, such as navigation, code generation, and mathematical problem solving. In such settings, models implicitly induce a likelihood over correct rollouts. However, we observe that reinforcement learning does not maximize this likelihood, and instead optimizes only a lower-order approximation. Inspired by this observation, we introduce Maximum Likelihood Reinforcement Learning (MaxRL), a sampling-based framework to approximate maximum likelihood using reinforcement learning techniques. MaxRL addresses the challenges of non-differentiable sampling by defining a compute-indexed family of sample-based objectives that interpolate between standard reinforcement learning and exact maximum likelihood as additional sampling compute is allocated. The resulting objectives admit a simple, unbiased policy-gradient estimator and converge to maximum likelihood optimization in the infinite-compute limit. Empirically, we show that MaxRL Pareto-dominates existing methods in all models and tasks we tested, achieving up to 20x test-time scaling efficiency gains compared to its GRPO-trained counterpart. We also observe MaxRL to scale better with additional data and compute. Our results suggest MaxRL is a promising framework for scaling RL training in correctness based settings.

Bayesian optimisation is a popular, surrogate model-based approach for optimising expensive black-box functions. Given a surrogate model, the next location to expensively evaluate is chosen via maximisation of a cheap-to-query acquisition function. We present an epsilon-greedy procedure for Bayesian optimisation in batch settings in which the black-box function can be evaluated multiple times in parallel. Our epsilon-shotgun algorithm leverages the model's prediction, uncertainty, and the approximated rate of change of the landscape to determine the spread of batch solutions to be distributed around a putative location. The initial target location is selected either in an exploitative fashion on the mean prediction, or -- with probability epsilon -- from elsewhere in the design space. This results in locations that are more densely sampled in regions where the function is changing rapidly and in locations predicted to be good (i.e close to predicted optima), with more scattered samples in regions where the function is flatter and/or of poorer quality. We empirically evaluate the epsilon-shotgun methods on a range of synthetic functions and two real-world problems, finding that they perform at least as well as state-of-the-art batch methods and in many cases exceed their performance.

We study linear contextual bandits in the misspecified setting, where the expected reward function can be approximated by a linear function class up to a bounded misspecification level zeta>0. We propose an algorithm based on a novel data selection scheme, which only selects the contextual vectors with large uncertainty for online regression. We show that, when the misspecification level zeta is dominated by tilde O (Delta / d) with Delta being the minimal sub-optimality gap and d being the dimension of the contextual vectors, our algorithm enjoys the same gap-dependent regret bound tilde O (d^2/Delta) as in the well-specified setting up to logarithmic factors. In addition, we show that an existing algorithm SupLinUCB (Chu et al., 2011) can also achieve a gap-dependent constant regret bound without the knowledge of sub-optimality gap Delta. Together with a lower bound adapted from Lattimore et al. (2020), our result suggests an interplay between misspecification level and the sub-optimality gap: (1) the linear contextual bandit model is efficiently learnable when zeta leq tilde O(Delta / d); and (2) it is not efficiently learnable when zeta geq tilde Omega({Delta} / {d}). Experiments on both synthetic and real-world datasets corroborate our theoretical results.

Large language models (LLMs) must balance diversity and creativity against logical coherence in open-ended generation. Existing truncation-based samplers are effective but largely heuristic, relying mainly on probability mass and entropy while ignoring semantic geometry of the token space. We present Top-W, a geometry-aware truncation rule that uses Wasserstein distance-defined over token-embedding geometry-to keep the cropped distribution close to the original, while explicitly balancing retained probability mass against the entropy of the kept set. Our theory yields a simple closed-form structure for the fixed-potential subset update: depending on the mass-entropy trade-off, the optimal crop either collapses to a single token or takes the form of a one-dimensional prefix that can be found efficiently with a linear scan. We implement Top-W using efficient geometry-based potentials (nearest-set or k-NN) and pair it with an alternating decoding routine that keeps the standard truncation-and-sampling interface unchanged. Extensive experiments on four benchmarks (GSM8K, GPQA, AlpacaEval, and MT-Bench) across three instruction-tuned models show that Top-W consistently outperforms prior state-of-the-art decoding approaches achieving up to 33.7% improvement. Moreover, we find that Top-W not only improves accuracy-focused performance, but also boosts creativity under judge-based open-ended evaluation.

Using language models to scalably approximate human preferences on text quality (LLM-as-a-judge) has become a standard practice applicable to many tasks. A judgment is often extracted from the judge's textual output alone, typically with greedy decoding. However, LLM judges naturally provide distributions over judgment tokens, inviting a breadth of inference methods for extracting fine-grained preferences. We find that taking the mean of the judgment distribution consistently outperforms taking the mode (i.e. greedy decoding) in all evaluation settings (i.e. pointwise, pairwise, and listwise). We further explore novel methods of deriving preferences from judgment distributions, and find that methods incorporating risk aversion often improve performance. Lastly, we analyze LLM-as-a-judge paired with chain-of-thought (CoT) prompting, showing that CoT can collapse the spread of the judgment distribution, often harming performance. Our findings show that leveraging distributional output improves LLM-as-a-judge, as opposed to using the text interface alone.

Sampling-based decoding strategies have been widely adopted for Large Language Models (LLMs) in numerous applications, targeting a balance between diversity and quality via temperature tuning and tail truncation. Considering the strong dependency of the candidate next tokens on different prefixes, recent studies propose to adaptively truncate the tail of LLMs' predicted distribution. Although improved results have been reported with these methods on open-ended text generation tasks, the results are highly dependent on the curated parameters and the limited exemplar text. In this paper, we propose a systematic way to estimate the capacity of a truncation sampling method by considering the trade-off between diversity and risk at each decoding step, based on our collected prefix tree which preserves the context of a full sentence. Our work offers a comprehensive comparison of existing truncation sampling methods and serves as a practical user guideline for their parameter selection.

A range of recent works addresses the problem of compression of sequence of tokens into a shorter sequence of real-valued vectors to be used as inputs instead of token embeddings or key-value cache. These approaches allow to reduce the amount of compute in existing language models. Despite relying on powerful models as encoders, the maximum attainable lossless compression ratio is typically not higher than x10. This fact is highly intriguing because, in theory, the maximum information capacity of large real-valued vectors is far beyond the presented rates even for 16-bit precision and a modest vector size. In this work, we explore the limits of compression by replacing the encoder with a per-sample optimization procedure. We show that vectors with compression ratios up to x1500 exist, which highlights two orders of magnitude gap between existing and practically attainable solutions. Furthermore, we empirically show that the compression limits are determined not by the length of the input but by the amount of uncertainty to be reduced, namely, the cross-entropy loss on this sequence without any conditioning. The obtained limits highlight the substantial gap between the theoretical capacity of input embeddings and their practical utilization, suggesting significant room for optimization in model design.

Empirical Risk Minimization (ERM) is fragile in scenarios with insufficient labeled samples. A vanilla extension of ERM to unlabeled samples is Entropy Minimization (EntMin), which employs the soft-labels of unlabeled samples to guide their learning. However, EntMin emphasizes prediction discriminability while neglecting prediction diversity. To alleviate this issue, in this paper, we rethink the guidance information to utilize unlabeled samples. By analyzing the learning objective of ERM, we find that the guidance information for labeled samples in a specific category is the corresponding label encoding. Inspired by this finding, we propose a Label-Encoding Risk Minimization (LERM). It first estimates the label encodings through prediction means of unlabeled samples and then aligns them with their corresponding ground-truth label encodings. As a result, the LERM ensures both prediction discriminability and diversity, and it can be integrated into existing methods as a plugin. Theoretically, we analyze the relationships between LERM and ERM as well as EntMin. Empirically, we verify the superiority of the LERM under several label insufficient scenarios. The codes are available at https://github.com/zhangyl660/LERM.

Tabular data generation has become increasingly essential for enabling robust machine learning applications, which require large-scale, high-quality data. Existing solutions leverage generative models to learn original data distributions. However, real-world data are naturally heterogeneous with diverse distributions, making it challenging to obtain a universally good model for diverse data generation. To address this limitation, we introduce Diversity-Aware Tabular data gEnerator (DATE), a framework that (i) prepares high-quality and distributionally distinct examples for in-context learning by effectively partitioning the original heterogeneous data into multiple diverse subsets; (ii) harnesses Large Language Models (LLMs) to explore the diversity of the partitioned distribution with decision tree reasoning as feedback, generating high-quality labeled data for each subset. However, the massive generated data inherently involves a trade-off between diversity and quality. To integrate this issue, existing solutions greedily select the validation-best data. However, we prove that the selection in heterogeneous settings does not possess the greedy-choice property, and design a Multi-Arm Bandit-based sampling algorithm that balances the diversity and quality of generated data. Extensive experiments on tabular classification and regression benchmarks demonstrate that DATE consistently outperforms state-of-the-art GAN-based and LLM-based methods. On average, DATE achieves a 23.75% reduction in error rate with just 100 generated data. Empirically, we demonstrate that data generated by DATE can improve the accuracy of Direct Preference Optimization (DPO) and enhance the reasoning capability of LLMs on the target data. Code is available at https://github.com/windblow32/DATE.

Recent masked diffusion models (MDMs) have shown competitive performance compared to autoregressive models (ARMs) for language modeling. While most literature has focused on performance enhancing sampling procedures, efficient sampling from MDMs has been scarcely explored. We make the observation that often a given sequence of partially masked tokens determines the values of multiple unknown tokens deterministically, meaning that a single prediction of a masked model holds additional information unused by standard sampling procedures. Based on this observation, we introduce EB-Sampler, a simple drop-in replacement for existing samplers, utilizing an Entropy Bounded unmasking procedure that dynamically unmasks multiple tokens in one function evaluation with predefined approximate error tolerance. We formulate the EB-Sampler as part of a broad family of adaptive samplers for which we provide an error analysis that motivates our algorithmic choices. EB-Sampler accelerates sampling from current state of the art MDMs by roughly 2-3x on standard coding and math reasoning benchmarks without loss in performance. We also validate the same procedure works well on smaller reasoning tasks including maze navigation and Sudoku, tasks ARMs often struggle with.

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.

We characterize the statistical efficiency of knowledge transfer through n samples from a teacher to a probabilistic student classifier with input space mathcal S over labels mathcal A. We show that privileged information at three progressive levels accelerates the transfer. At the first level, only samples with hard labels are known, via which the maximum likelihood estimator attains the minimax rate {|{mathcal S||{mathcal A}|}/{n}}. The second level has the teacher probabilities of sampled labels available in addition, which turns out to boost the convergence rate lower bound to {{|{mathcal S}||{mathcal A}|}/{n}}. However, under this second data acquisition protocol, minimizing a naive adaptation of the cross-entropy loss results in an asymptotically biased student. We overcome this limitation and achieve the fundamental limit by using a novel empirical variant of the squared error logit loss. The third level further equips the student with the soft labels (complete logits) on {mathcal A} given every sampled input, thereby provably enables the student to enjoy a rate {|{mathcal S}|}/{n} free of |{mathcal A}|. We find any Kullback-Leibler divergence minimizer to be optimal in the last case. Numerical simulations distinguish the four learners and corroborate our theory.

Prevailing Multimodal Large Language Models (MLLMs) encode the input image(s) as vision tokens and feed them into the language backbone, similar to how Large Language Models (LLMs) process the text tokens. However, the number of vision tokens increases quadratically as the image resolutions, leading to huge computational costs. In this paper, we consider improving MLLM's efficiency from two scenarios, (I) Reducing computational cost without degrading the performance. (II) Improving the performance with given budgets. We start with our main finding that the ranking of each vision token sorted by attention scores is similar in each layer except the first layer. Based on it, we assume that the number of essential top vision tokens does not increase along layers. Accordingly, for Scenario I, we propose a greedy search algorithm (G-Search) to find the least number of vision tokens to keep at each layer from the shallow to the deep. Interestingly, G-Search is able to reach the optimal reduction strategy based on our assumption. For Scenario II, based on the reduction strategy from G-Search, we design a parametric sigmoid function (P-Sigmoid) to guide the reduction at each layer of the MLLM, whose parameters are optimized by Bayesian Optimization. Extensive experiments demonstrate that our approach can significantly accelerate those popular MLLMs, e.g. LLaVA, and InternVL2 models, by more than 2 times without performance drops. Our approach also far outperforms other token reduction methods when budgets are limited, achieving a better trade-off between efficiency and effectiveness.

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.

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.

Modern knowledge-intensive systems, such as retrieval-augmented generation (RAG), rely on effective retrievers to establish the performance ceiling for downstream modules. However, retriever training has been bottlenecked by sparse, single-positive annotations, which lead to false-negative noise and suboptimal supervision. While the advent of large language models (LLMs) makes it feasible to collect comprehensive multi-positive relevance labels at scale, the optimal strategy for incorporating these dense signals into training remains poorly understood. In this paper, we present a systematic study of multi-positive optimization objectives for retriever training. We unify representative objectives, including Joint Likelihood (JointLH), Summed Marginal Likelihood (SumMargLH), and Log-Sum-Exp Pairwise (LSEPair) loss, under a shared contrastive learning framework. Our theoretical analysis characterizes their distinct gradient behaviors, revealing how each allocates probability mass across positive document sets. Empirically, we conduct extensive evaluations on Natural Questions, MS MARCO, and the BEIR benchmark across two realistic regimes: homogeneous LLM-annotated data and heterogeneous mixtures of human and LLM labels. Our results show that LSEPair consistently achieves superior robustness and performance across settings, while JointLH and SumMargLH exhibit high sensitivity to the quality of positives. Furthermore, we find that the simple strategy of random sampling (Rand1LH) serves as a reliable baseline. By aligning theoretical insights with empirical findings, we provide practical design principles for leveraging dense, LLM-augmented supervision to enhance retriever effectiveness.

Reinforcement Learning algorithms that learn from human feedback (RLHF) need to be efficient in terms of statistical complexity, computational complexity, and query complexity. In this work, we consider the RLHF setting where the feedback is given in the format of preferences over pairs of trajectories. In the linear MDP model, using randomization in algorithm design, we present an algorithm that is sample efficient (i.e., has near-optimal worst-case regret bounds) and has polynomial running time (i.e., computational complexity is polynomial with respect to relevant parameters). Our algorithm further minimizes the query complexity through a novel randomized active learning procedure. In particular, our algorithm demonstrates a near-optimal tradeoff between the regret bound and the query complexity. To extend the results to more general nonlinear function approximation, we design a model-based randomized algorithm inspired by the idea of Thompson sampling. Our algorithm minimizes Bayesian regret bound and query complexity, again achieving a near-optimal tradeoff between these two quantities. Computation-wise, similar to the prior Thompson sampling algorithms under the regular RL setting, the main computation primitives of our algorithm are Bayesian supervised learning oracles which have been heavily investigated on the empirical side when applying Thompson sampling algorithms to RL benchmark problems.

Finding the optimal Retrieval-Augmented Generation (RAG) configuration for a given use case can be complex and expensive. Motivated by this challenge, frameworks for RAG hyper-parameter optimization (HPO) have recently emerged, yet their effectiveness has not been rigorously benchmarked. To address this gap, we present a comprehensive study involving 5 HPO algorithms over 5 datasets from diverse domains, including a new one collected for this work on real-world product documentation. Our study explores the largest HPO search space considered to date, with two optimized evaluation metrics. Analysis of the results shows that RAG HPO can be done efficiently, either greedily or with iterative random search, and that it significantly boosts RAG performance for all datasets. For greedy HPO approaches, we show that optimizing models first is preferable to the prevalent practice of optimizing sequentially according to the RAG pipeline order.

We argue that the estimation of mutual information between high dimensional continuous random variables can be achieved by gradient descent over neural networks. We present a Mutual Information Neural Estimator (MINE) that is linearly scalable in dimensionality as well as in sample size, trainable through back-prop, and strongly consistent. We present a handful of applications on which MINE can be used to minimize or maximize mutual information. We apply MINE to improve adversarially trained generative models. We also use MINE to implement Information Bottleneck, applying it to supervised classification; our results demonstrate substantial improvement in flexibility and performance in these settings.

To develop a trustworthy AI system, which aim to identify the input regions that most influence the models decisions. The primary task of existing attribution methods lies in efficiently and accurately identifying the relationships among input-prediction interactions. Particularly when the input data is discrete, such as images, analyzing the relationship between inputs and outputs poses a significant challenge due to the combinatorial explosion. In this paper, we propose a novel and efficient black-box attribution mechanism, LiMA (Less input is More faithful for Attribution), which reformulates the attribution of important regions as an optimization problem for submodular subset selection. First, to accurately assess interactions, we design a submodular function that quantifies subset importance and effectively captures their impact on decision outcomes. Then, efficiently ranking input sub-regions by their importance for attribution, we improve optimization efficiency through a novel bidirectional greedy search algorithm. LiMA identifies both the most and least important samples while ensuring an optimal attribution boundary that minimizes errors. Extensive experiments on eight foundation models demonstrate that our method provides faithful interpretations with fewer regions and exhibits strong generalization, shows an average improvement of 36.3% in Insertion and 39.6% in Deletion. Our method also outperforms the naive greedy search in attribution efficiency, being 1.6 times faster. Furthermore, when explaining the reasons behind model prediction errors, the average highest confidence achieved by our method is, on average, 86.1% higher than that of state-of-the-art attribution algorithms. The code is available at https://github.com/RuoyuChen10/LIMA.

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.

Large Language Models (LLMs) generate longform text by successively sampling the next token based on the probability distribution of the token vocabulary at each decoding step. Current popular truncation sampling methods such as top-p sampling, also known as nucleus sampling, often struggle to balance coherence and creativity in generating text, particularly when using higher temperatures. To address this issue, we propose min-p, a dynamic truncation sampling method, that establishes a minimum base percentage threshold for tokens, which the scales according to the probability of the top candidate token. Through experiments on several benchmarks, such as GPQA, GSM8K and AlpacaEval Creative Writing, we demonstrate that min-p improves the coherence and quality of generated text even at high temperatures, while also facilitating more creative and diverse outputs compared to top-p and other sampling methods. As of writing, min-p has been adopted by multiple open-source LLM implementations, and have been independently assessed by members of the open-source LLM community, further validating its practical utility and potential.

Speculative decoding is widely used in accelerating large language model (LLM) inference. In this work, we focus on the online draft model selection problem in speculative decoding. We design an algorithm that provably competes with the best draft model in hindsight for each query in terms of either the token acceptance probability or expected acceptance length. In particular, we show that we can accurately evaluate all draft models, instead of only the chosen model without incurring additional queries to the target model, which allows us to improve exponentially over the existing bandit-based approach as the number of draft models increases. Our approach is generically applicable with any speculative decoding methods (single draft, multi-drafts and draft-trees). Moreover, we design system-efficient versions of online learners and demonstrate that the overhead in computation and latency can be substantially reduced. We conduct extensive experiments on open-source LLMs and diverse datasets, demonstrating that our methods substantially outperform the state-of-the-art EAGLE3 and the BanditSpec baseline in a variety of domains where specialized domain-expert drafters are available, especially when long reasoning chains are required.

Decoding methods for large language models (LLMs) usually struggle with the tradeoff between ensuring factuality and maintaining diversity. For example, a higher p threshold in the nucleus (top-p) sampling increases the diversity but decreases the factuality, and vice versa. In this paper, we propose REAL (Residual Entropy from Asymptotic Line) sampling, a decoding method that achieves improved factuality and diversity over nucleus sampling by predicting an adaptive threshold of p. Specifically, REAL sampling predicts the step-wise likelihood of an LLM to hallucinate, and lowers the p threshold when an LLM is likely to hallucinate. Otherwise, REAL sampling increases the p threshold to boost the diversity. To predict the step-wise hallucination likelihood without supervision, we construct a Token-level Hallucination Forecasting (THF) model to predict the asymptotic entropy (i.e., inherent uncertainty) of the next token by extrapolating the next-token entropies from a series of LLMs with different sizes. If a LLM's entropy is higher than the asymptotic entropy (i.e., the LLM is more uncertain than it should be), the THF model predicts a high hallucination hazard, which leads to a lower p threshold in REAL sampling. In the FactualityPrompts benchmark, we demonstrate that REAL sampling based on a 70M THF model can substantially improve the factuality and diversity of 7B LLMs simultaneously, judged by both retrieval-based metrics and human evaluation. After combined with contrastive decoding, REAL sampling outperforms 9 sampling methods, and generates texts that are more factual than the greedy sampling and more diverse than the nucleus sampling with p=0.5. Furthermore, the predicted asymptotic entropy is also a useful unsupervised signal for hallucination detection tasks.

Given a sample of size N, it is often useful to select a subsample of smaller size n<N to be used for statistical estimation or learning. Such a data selection step is useful to reduce the requirements of data labeling and the computational complexity of learning. We assume to be given N unlabeled samples {{boldsymbol x}_i}_{ile N}, and to be given access to a `surrogate model' that can predict labels y_i better than random guessing. Our goal is to select a subset of the samples, to be denoted by {{boldsymbol x}_i}_{iin G}, of size |G|=n<N. We then acquire labels for this set and we use them to train a model via regularized empirical risk minimization. By using a mixture of numerical experiments on real and synthetic data, and mathematical derivations under low- and high- dimensional asymptotics, we show that: (i)~Data selection can be very effective, in particular beating training on the full sample in some cases; (ii)~Certain popular choices in data selection methods (e.g. unbiased reweighted subsampling, or influence function-based subsampling) can be substantially suboptimal.

Reinforcement learning (RL) has enabled complex reasoning abilities in large language models (LLMs). However, most RL algorithms suffer from performance saturation, preventing continued gains as RL training scales. This problem can be characterized by the collapse of entropy, a key diagnostic for exploration in RL. Existing attempts focus on preventing entropy collapse through regularization or clipping. However, their resulting entropy curves often exhibit instability in the long term, which hinders performance gains. In this paper, we introduce Entrocraft, a simple rejection-sampling approach that realizes user-customized entropy schedule by biasing the advantage distributions. Entrocraft requires no objective regularization and is advantage-estimator-agnostic. Theoretically, we relate per-step entropy change to the advantage distribution under minimal assumptions. This explains the behavior of existing RL and entropy-preserving methods. Entrocraft also enables a systematic study of entropy schedules, which reveals that linear annealing, which starts high and decays to a slightly lower target, performs best. Empirically, Entrocraft addresses performance saturation, significantly improving generalization, output diversity, and long-term training. It enables a 4B model to outperform an 8B baseline, sustains improvement for up to 4x longer before plateauing, and raises pass@K by 50% over the baseline.

Mutual information maximization has emerged as a powerful learning objective for unsupervised representation learning obtaining state-of-the-art performance in applications such as object recognition, speech recognition, and reinforcement learning. However, such approaches are fundamentally limited since a tight lower bound of mutual information requires sample size exponential in the mutual information. This limits the applicability of these approaches for prediction tasks with high mutual information, such as in video understanding or reinforcement learning. In these settings, such techniques are prone to overfit, both in theory and in practice, and capture only a few of the relevant factors of variation. This leads to incomplete representations that are not optimal for downstream tasks. In this work, we empirically demonstrate that mutual information-based representation learning approaches do fail to learn complete representations on a number of designed and real-world tasks. To mitigate these problems we introduce the Wasserstein dependency measure, which learns more complete representations by using the Wasserstein distance instead of the KL divergence in the mutual information estimator. We show that a practical approximation to this theoretically motivated solution, constructed using Lipschitz constraint techniques from the GAN literature, achieves substantially improved results on tasks where incomplete representations are a major challenge.

This paper addresses the difficult problem of finding an optimal neural architecture design for a given image classification task. We propose a method that aggregates two main results of the previous state-of-the-art in neural architecture search. These are, appealing to the strong sampling efficiency of a search scheme based on sequential model-based optimization (SMBO), and increasing training efficiency by sharing weights among sampled architectures. Sequential search has previously demonstrated its capabilities to find state-of-the-art neural architectures for image classification. However, its computational cost remains high, even unreachable under modest computational settings. Affording SMBO with weight-sharing alleviates this problem. On the other hand, progressive search with SMBO is inherently greedy, as it leverages a learned surrogate function to predict the validation error of neural architectures. This prediction is directly used to rank the sampled neural architectures. We propose to attenuate the greediness of the original SMBO method by relaxing the role of the surrogate function so it predicts architecture sampling probability instead. We demonstrate with experiments on the CIFAR-10 dataset that our method, denominated Efficient progressive neural architecture search (EPNAS), leads to increased search efficiency, while retaining competitiveness of found architectures.

Cropping high-resolution document images into multiple sub-images is the most widely used approach for current Multimodal Large Language Models (MLLMs) to do document understanding. Most of current document understanding methods preserve all tokens within sub-images and treat them equally. This neglects their different informativeness and leads to a significant increase in the number of image tokens. To perform a more adaptive and efficient document understanding, we propose Token-level Correlation-guided Compression, a parameter-free and plug-and-play methodology to optimize token processing. Firstly, we propose an innovative approach for assessing the pattern repetitiveness based on the correlation between each patch tokens. This method identifies redundant tokens, allowing for the determination of the sub-image's information density. Secondly, we present a token-level sampling method that efficiently captures the most informative tokens by delving into the correlation between the [CLS] token and patch tokens. By integrating these strategies, we develop a plug-and-play adaptive compressor module that can be seamlessly incorporated into MLLMs utilizing cropping techniques. This module not only enhances the processing speed during training and inference but also maintains comparable performance. We conduct experiments with the SOTA document understanding model mPLUG-DocOwl1.5 and the effectiveness is demonstrated through extensive comparisons with other compression methods.

Data pruning algorithms are commonly used to reduce the memory and computational cost of the optimization process. Recent empirical results reveal that random data pruning remains a strong baseline and outperforms most existing data pruning methods in the high compression regime, i.e., where a fraction of 30% or less of the data is kept. This regime has recently attracted a lot of interest as a result of the role of data pruning in improving the so-called neural scaling laws; in [Sorscher et al.], the authors showed the need for high-quality data pruning algorithms in order to beat the sample power law. In this work, we focus on score-based data pruning algorithms and show theoretically and empirically why such algorithms fail in the high compression regime. We demonstrate ``No Free Lunch" theorems for data pruning and present calibration protocols that enhance the performance of existing pruning algorithms in this high compression regime using randomization.

Learning to optimize has emerged as a powerful framework for various optimization and machine learning tasks. Current such "meta-optimizers" often learn in the space of continuous optimization algorithms that are point-based and uncertainty-unaware. To overcome the limitations, we propose a meta-optimizer that learns in the algorithmic space of both point-based and population-based optimization algorithms. The meta-optimizer targets at a meta-loss function consisting of both cumulative regret and entropy. Specifically, we learn and interpret the update formula through a population of LSTMs embedded with sample- and feature-level attentions. Meanwhile, we estimate the posterior directly over the global optimum and use an uncertainty measure to help guide the learning process. Empirical results over non-convex test functions and the protein-docking application demonstrate that this new meta-optimizer outperforms existing competitors.

Providers of LLM-as-a-service have predominantly adopted a simple pricing model: users pay a fixed price per token. Consequently, one may think that the price two different users would pay for the same output string under the same input prompt is the same. In our work, we show that, surprisingly, this is not (always) true. We find empirical evidence that, particularly for non-english outputs, both proprietary and open-weights LLMs often generate the same (output) string with multiple different tokenizations, even under the same input prompt, and this in turn leads to arbitrary price variation. To address the problem of tokenization multiplicity, we introduce canonical generation, a type of constrained generation that restricts LLMs to only generate canonical tokenizations -- the unique tokenization in which each string is tokenized during the training process of an LLM. Further, we introduce an efficient sampling algorithm for canonical generation based on the Gumbel-Max trick. Experiments on a variety of natural language tasks demonstrate that our sampling algorithm for canonical generation is comparable to standard sampling in terms of performance and runtime, and it solves the problem of tokenization multiplicity.

Generating samples from limited information is a fundamental problem across scientific domains. Classical maximum entropy methods provide principled uncertainty quantification from moment constraints but require sampling via MCMC or Langevin dynamics, which typically exhibit exponential slowdown in high dimensions. In contrast, generative models based on diffusion and flow matching efficiently transport noise to data but offer limited theoretical guarantees and can overfit when data is scarce. We introduce Moment Guided Diffusion (MGD), which combines elements of both approaches. Building on the stochastic interpolant framework, MGD samples maximum entropy distributions by solving a stochastic differential equation that guides moments toward prescribed values in finite time, thereby avoiding slow mixing in equilibrium-based methods. We formally obtain, in the large-volatility limit, convergence of MGD to the maximum entropy distribution and derive a tractable estimator of the resulting entropy computed directly from the dynamics. Applications to financial time series, turbulent flows, and cosmological fields using wavelet scattering moments yield estimates of negentropy for high-dimensional multiscale processes.

When trying to solve a computational problem, we are often faced with a choice between algorithms that are guaranteed to return the right answer but differ in their runtime distributions (e.g., SAT solvers, sorting algorithms). This paper aims to lay theoretical foundations for such choices by formalizing preferences over runtime distributions. It might seem that we should simply prefer the algorithm that minimizes expected runtime. However, such preferences would be driven by exactly how slow our algorithm is on bad inputs, whereas in practice we are typically willing to cut off occasional, sufficiently long runs before they finish. We propose a principled alternative, taking a utility-theoretic approach to characterize the scoring functions that describe preferences over algorithms. These functions depend on the way our value for solving our problem decreases with time and on the distribution from which captimes are drawn. We describe examples of realistic utility functions and show how to leverage a maximum-entropy approach for modeling underspecified captime distributions. Finally, we show how to efficiently estimate an algorithm's expected utility from runtime samples.

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.

Speculative sampling has emerged as an important technique for accelerating the auto-regressive generation process of large language models (LLMs) by utilizing a draft-then-verify mechanism to produce multiple tokens per forward pass. While state-of-the-art speculative sampling methods use only a single layer and a language modeling (LM) head as the draft model to achieve impressive layer compression, their efficiency gains are substantially reduced for large-vocabulary LLMs, such as Llama-3-8B with a vocabulary of 128k tokens. To address this, we present FR-Spec, a frequency-ranked speculative sampling framework that optimizes draft candidate selection through vocabulary space compression. By constraining the draft search to a frequency-prioritized token subset, our method reduces LM Head computation overhead by 75% while ensuring the equivalence of the final output distribution. Experiments across multiple datasets demonstrate an average of 1.12times speedup over the state-of-the-art speculative sampling method EAGLE-2.

Inference-time optimization scales computation to derive deliberate reasoning steps for effective performance. While previous search-based strategies address the short-sightedness of auto-regressive generation, the vast search space leads to excessive exploration and insufficient exploitation. To strike an efficient balance to derive the optimal step, we frame the decoding strategy as foresight sampling, leveraging simulated future steps to obtain globally optimal step estimation. Built on it, we propose a novel decoding strategy, named phi-Decoding. To provide a precise and expressive estimation of step value, phi-Decoding approximates two distributions via foresight and clustering. Sampling from the joint distribution, the optimal steps can be selected for exploitation. To support adaptive computation allocation, we propose in-width and in-depth pruning strategies, featuring a light-weight solution to achieve inference efficiency. Extensive experiments across seven benchmarks show phi-Decoding outperforms strong baselines in both performance and efficiency. Additional analysis demonstrates its generalization across various LLMs and scalability across a wide range of computing budgets. The code will be released at https://github.com/xufangzhi/phi-Decoding, and the open-source PyPI package is coming soon.

Sampling proper negatives from a large document pool is vital to effectively train a dense retrieval model. However, existing negative sampling strategies suffer from the uninformative or false negative problem. In this work, we empirically show that according to the measured relevance scores, the negatives ranked around the positives are generally more informative and less likely to be false negatives. Intuitively, these negatives are not too hard (may be false negatives) or too easy (uninformative). They are the ambiguous negatives and need more attention during training. Thus, we propose a simple ambiguous negatives sampling method, SimANS, which incorporates a new sampling probability distribution to sample more ambiguous negatives. Extensive experiments on four public and one industry datasets show the effectiveness of our approach. We made the code and models publicly available in https://github.com/microsoft/SimXNS.

Autoregressive sampling from large language models has led to state-of-the-art results in several natural language tasks. However, autoregressive sampling generates tokens one at a time making it slow, and even prohibitive in certain tasks. One way to speed up sampling is speculative decoding: use a small model to sample a draft (block or sequence of tokens), and then score all tokens in the draft by the large language model in parallel. A subset of the tokens in the draft are accepted (and the rest rejected) based on a statistical method to guarantee that the final output follows the distribution of the large model. In this work, we provide a principled understanding of speculative decoding through the lens of optimal transport (OT) with membership cost. This framework can be viewed as an extension of the well-known maximal-coupling problem. This new formulation enables us to generalize the speculative decoding method to allow for a set of k candidates at the token-level, which leads to an improved optimal membership cost. We show that the optimal draft selection algorithm (transport plan) can be computed via linear programming, whose best-known runtime is exponential in k. We then propose a valid draft selection algorithm whose acceptance probability is (1-1/e)-optimal multiplicatively. Moreover, it can be computed in time almost linear with size of domain of a single token. Using this new draft selection algorithm, we develop a new autoregressive sampling algorithm called SpecTr, which provides speedup in decoding while ensuring that there is no quality degradation in the decoded output. We experimentally demonstrate that for state-of-the-art large language models, the proposed approach achieves a wall clock speedup of 2.13X, a further 1.37X speedup over speculative decoding on standard benchmarks.

Neural text decoding is important for generating high-quality texts using language models. To generate high-quality text, popular decoding algorithms like top-k, top-p (nucleus), and temperature-based sampling truncate or distort the unreliable low probability tail of the language model. Though these methods generate high-quality text after parameter tuning, they are ad hoc. Not much is known about the control they provide over the statistics of the output, which is important since recent reports show text quality is highest for a specific range of likelihoods. Here, first we provide a theoretical analysis of perplexity in top-k, top-p, and temperature sampling, finding that cross-entropy behaves approximately linearly as a function of p in top-p sampling whereas it is a nonlinear function of k in top-k sampling, under Zipfian statistics. We use this analysis to design a feedback-based adaptive top-k text decoding algorithm called mirostat that generates text (of any length) with a predetermined value of perplexity, and thereby high-quality text without any tuning. Experiments show that for low values of k and p in top-k and top-p sampling, perplexity drops significantly with generated text length, which is also correlated with excessive repetitions in the text (the boredom trap). On the other hand, for large values of k and p, we find that perplexity increases with generated text length, which is correlated with incoherence in the text (confusion trap). Mirostat avoids both traps: experiments show that cross-entropy has a near-linear relation with repetition in generated text. This relation is almost independent of the sampling method but slightly dependent on the model used. Hence, for a given language model, control over perplexity also gives control over repetitions. Experiments with human raters for fluency, coherence, and quality further verify our findings.

Contextual dueling bandits, where a learner compares two options based on context and receives feedback indicating which was preferred, extends classic dueling bandits by incorporating contextual information for decision-making and preference learning. Several algorithms based on the upper confidence bound (UCB) have been proposed for linear contextual dueling bandits. However, no algorithm based on posterior sampling has been developed in this setting, despite the empirical success observed in traditional contextual bandits. In this paper, we propose a Thompson sampling algorithm, named FGTS.CDB, for linear contextual dueling bandits. At the core of our algorithm is a new Feel-Good exploration term specifically tailored for dueling bandits. This term leverages the independence of the two selected arms, thereby avoiding a cross term in the analysis. We show that our algorithm achieves nearly minimax-optimal regret, i.e., mathcal{O}(dsqrt T), where d is the model dimension and T is the time horizon. Finally, we evaluate our algorithm on synthetic data and observe that FGTS.CDB outperforms existing algorithms by a large margin.

We introduce a boosting algorithm to pre-process data for fairness. Starting from an initial fair but inaccurate distribution, our approach shifts towards better data fitting while still ensuring a minimal fairness guarantee. To do so, it learns the sufficient statistics of an exponential family with boosting-compliant convergence. Importantly, we are able to theoretically prove that the learned distribution will have a representation rate and statistical rate data fairness guarantee. Unlike recent optimization based pre-processing methods, our approach can be easily adapted for continuous domain features. Furthermore, when the weak learners are specified to be decision trees, the sufficient statistics of the learned distribution can be examined to provide clues on sources of (un)fairness. Empirical results are present to display the quality of result on real-world data.

The KV cache used in large language models has linearly growing time complexity, so LLMs face memory blow-up and reduced decoding efficiency when they process long contexts. Current KV Cache eviction has become an important research direction; however, existing methods based on fixed Soft Tokens (e.g., Judge Q) rely on a static parameter set as the query to evaluate the importance of KV pairs, so they cannot adapt dynamically to different input prompts, and they cannot precisely capture complex and changing task relevance. Also, evicted KV pairs are discarded permanently, so this causes irreversible information loss and context breaks. To address this problem, we propose Meta-Soft, a dynamic compression framework based on probe-driven context integration. Specifically, we build a meta-library with a learnable orthogonal basis matrix L, and we use a selector network with Gumbel-Softmax to produce differentiable sparse combination weights, so we dynamically synthesize the most targeted k Soft Tokens from the input prompt features. We append these Soft Tokens to the end of the input sequence to probe key information. We also introduce an attention-flow based integration mechanism, which redistributes the semantic information of removed tokens into retained tokens, and this keeps the dropped context information effectively. Experiments on multiple datasets show that our method outperforms existing state-of-the-art eviction methods and provides a new solution for KV Cache compression.

Entropy regularization is a standard technique in reinforcement learning (RL) to enhance exploration, yet it yields negligible effects or even degrades performance in Large Language Models (LLMs). We attribute this failure to the cumulative tail risk inherent to LLMs with massive vocabularies and long generation horizons. In such environments, standard global entropy maximization indiscriminately dilutes probability mass into the vast tail of invalid tokens rather than focusing on plausible candidates, thereby disrupting coherent reasoning. To address this, we propose Trust Region Entropy (TRE), a method that encourages exploration strictly within the model's trust region. Extensive experiments across mathematical reasoning (MATH), combinatorial search (Countdown), and preference alignment (HH) tasks demonstrate that TRE consistently outperforms vanilla PPO, standard entropy regularization, and other exploration baselines. Our code is available at https://github.com/WhyChaos/TRE-Encouraging-Exploration-in-the-Trust-Region.

Gradient-based methods for instance-based explanation for large language models (LLMs) are hindered by the immense dimensionality of model gradients. In practice, influence estimation is restricted to a subset of model parameters to make computation tractable, but this subset is often chosen ad hoc and rarely justified by systematic evaluation. This paper investigates if it is better to create low-dimensional representations by selecting a small, architecturally informed subset of model components or by projecting the full gradients into a lower-dimensional space. Using a novel benchmark, we show that a greedily selected subset of components captures the information about training data influence needed for a retrieval task more effectively than either the full gradient or random projection. We further find that this approach is more computationally efficient than random projection, demonstrating that targeted component selection is a practical strategy for making instance-based explanations of large models more computationally feasible.

Inference-time computation is a powerful paradigm to enhance the performance of large language models (LLMs), with Best-of-N sampling being a widely used technique. However, this method is computationally expensive, requiring both (1) an external reward model and (2) the generation of multiple samples. In this work, we introduce a new generative self-evaluation scheme designed to adaptively reduce the number of generated samples while maintaining or even improving performance. We use a generative reward model formulation, allowing the LLM to predict mid-generation the probability that restarting the generation will yield a better response. These predictions are obtained without an external reward model and can be used to decide whether or not to generate more samples, prune unpromising samples early on, or to pick the best sample. This capability is very inexpensive as it involves generating a single predefined token. Trained using a dataset constructed with real unfiltered LMSYS user prompts, Llama 3.1 8B's win rate against GPT-4 on AlpacaEval increases from 21% to 34% with 16 samples and math performance on GSM8K improves from 84% to 91%. By sampling only when the LLM determines that it is beneficial to do so and adaptively adjusting temperature annealing, we demonstrate that 74% of the improvement from using 16 samples can be achieved with only 1.2 samples on average. We further demonstrate that 50-75% of samples can be pruned early in generation with minimal degradation in performance. Overall, our methods enable more efficient and scalable compute utilization during inference for LLMs.

We demonstrate that from an algorithm guaranteeing an approximation factor for the ratio of submodular (RS) optimization problem, we can build another algorithm having a different kind of approximation guarantee -- weaker than the classical one -- for the difference of submodular (DS) optimization problem, and vice versa. We also illustrate the link between these two problems by analyzing a Greedy algorithm which approximately maximizes objective functions of the form Ψ(f,g), where f,g are two non-negative, monotone, submodular functions and Ψ is a {quasiconvex} 2-variables function, which is non decreasing with respect to the first variable. For the choice Ψ(f,g)triangleq f/g, we recover RS, and for the choice Ψ(f,g)triangleq f-g, we recover DS. To the best of our knowledge, this greedy approach is new for DS optimization. For RS optimization, it reduces to the standard GreedRatio algorithm that has already been analyzed previously. However, our analysis is novel for this case.

In many areas of medicine, security, and life sciences, we want to allocate limited resources to different sources in order to detect extreme values. In this paper, we study an efficient way to allocate these resources sequentially under limited feedback. While sequential design of experiments is well studied in bandit theory, the most commonly optimized property is the regret with respect to the maximum mean reward. However, in other problems such as network intrusion detection, we are interested in detecting the most extreme value output by the sources. Therefore, in our work we study extreme regret which measures the efficiency of an algorithm compared to the oracle policy selecting the source with the heaviest tail. We propose the ExtremeHunter algorithm, provide its analysis, and evaluate it empirically on synthetic and real-world experiments.

Motivated by the need to efficiently identify multiple candidates in high trial-and-error cost tasks such as drug discovery, we propose a near-optimal algorithm to identify all ε-best arms (i.e., those at most ε worse than the optimum). Specifically, we introduce LinFACT, an algorithm designed to optimize the identification of all ε-best arms in linear bandits. We establish a novel information-theoretic lower bound on the sample complexity of this problem and demonstrate that LinFACT achieves instance optimality by matching this lower bound up to a logarithmic factor. A key ingredient of our proof is to integrate the lower bound directly into the scaling process for upper bound derivation, determining the termination round and thus the sample complexity. We also extend our analysis to settings with model misspecification and generalized linear models. Numerical experiments, including synthetic and real drug discovery data, demonstrate that LinFACT identifies more promising candidates with reduced sample complexity, offering significant computational efficiency and accelerating early-stage exploratory experiments.

This work delved into the realm of automatic text generation, exploring a variety of techniques ranging from traditional deterministic approaches to more modern stochastic methods. Through analysis of greedy search, beam search, top-k sampling, top-p sampling, contrastive searching, and locally typical searching, this work has provided valuable insights into the strengths, weaknesses, and potential applications of each method. Each text-generating method is evaluated using several standard metrics and a comparative study has been made on the performance of the approaches. Finally, some future directions of research in the field of automatic text generation are also identified.

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.

Learning compact discrete representations of data is a key task on its own or for facilitating subsequent processing of data. In this paper we present a model that produces Discrete InfoMax Codes (DIMCO); we learn a probabilistic encoder that yields k-way d-dimensional codes associated with input data. Our model's learning objective is to maximize the mutual information between codes and labels with a regularization, which enforces entries of a codeword to be as independent as possible. We show that the infomax principle also justifies previous loss functions (e.g., cross-entropy) as its special cases. Our analysis also shows that using shorter codes, as DIMCO does, reduces overfitting in the context of few-shot classification. Through experiments in various domains, we observe this implicit meta-regularization effect of DIMCO. Furthermore, we show that the codes learned by DIMCO are efficient in terms of both memory and retrieval time compared to previous methods.

Speculative decoding (SD) accelerates large language model (LLM) reasoning by using a small draft model to generate candidate tokens, which the target LLM either accepts directly or regenerates upon rejection. However, excessive alignment between the draft and target models constrains SD to the performance of the target LLM. To address this limitation, we propose Entropy-Aware Speculative Decoding (EASD), a training-free enhancement. Building on standard SD, EASD incorporates a dynamic entropy-based penalty. At each decoding step, we employ the entropy of the sampling distribution to quantify model uncertainty. When both models exhibit high entropy with substantial overlap among their top-N predictions, the corresponding token is rejected and re-sampled by the target LLM. This penalty prevents low-confidence errors from propagating. By incorporating draft-model verification, EASD enables the possibility of surpassing the target model's inherent performance. Experiments across multiple reasoning benchmarks demonstrate that EASD consistently outperforms existing SD methods and, in most cases, surpasses the target LLM itself. We further prove that the efficiency of EASD is comparable to that of SD. The code can be found in the Supplementary Materials.

We consider a contextual combinatorial bandit problem where in each round a learning agent selects a subset of arms and receives feedback on the selected arms according to their scores. The score of an arm is an unknown function of the arm's feature. Approximating this unknown score function with deep neural networks, we propose algorithms: Combinatorial Neural UCB (CN-UCB) and Combinatorial Neural Thompson Sampling (CN-TS). We prove that CN-UCB achieves mathcal{O}(d T) or mathcal{O}(tilde{d T K}) regret, where d is the effective dimension of a neural tangent kernel matrix, K is the size of a subset of arms, and T is the time horizon. For CN-TS, we adapt an optimistic sampling technique to ensure the optimism of the sampled combinatorial action, achieving a worst-case (frequentist) regret of mathcal{O}(d TK). To the best of our knowledge, these are the first combinatorial neural bandit algorithms with regret performance guarantees. In particular, CN-TS is the first Thompson sampling algorithm with the worst-case regret guarantees for the general contextual combinatorial bandit problem. The numerical experiments demonstrate the superior performances of our proposed algorithms.

A fine-grained data recipe is crucial for pre-training large language models, as it can significantly enhance training efficiency and model performance. One important ingredient in the recipe is to select samples based on scores produced by defined rules, LLM judgment, or statistical information in embeddings, which can be roughly categorized into quality and diversity metrics. Due to the high computational cost when applied to trillion-scale token pre-training datasets such as FineWeb and DCLM, these two or more types of metrics are rarely considered jointly in a single selection process. However, in our empirical study, selecting samples based on quality metrics exhibit severe diminishing returns during long-term pre-training, while selecting on diversity metrics removes too many valuable high-quality samples, both of which limit pre-trained LLMs' capabilities. Therefore, we introduce DATAMASK, a novel and efficient joint learning framework designed for large-scale pre-training data selection that can simultaneously optimize multiple types of metrics in a unified process, with this study focusing specifically on quality and diversity metrics. DATAMASK approaches the selection process as a mask learning problem, involving iterative sampling of data masks, computation of policy gradients based on predefined objectives with sampled masks, and updating of mask sampling logits. Through policy gradient-based optimization and various acceleration enhancements, it significantly reduces selection time by 98.9% compared to greedy algorithm, enabling our study to explore joint learning within trillion-scale tokens. With DATAMASK, we select a subset of about 10% from the 15 trillion-token FineWeb dataset, termed FineWeb-Mask. Evaluated across 12 diverse tasks, we achieves significant improvements of 3.2% on a 1.5B dense model and 1.9% on a 7B MoE model.

Document understanding is a challenging task to process and comprehend large amounts of textual and visual information. Recent advances in Large Language Models (LLMs) have significantly improved the performance of this task. However, existing methods typically focus on either plain text or a limited number of document images, struggling to handle long PDF documents with interleaved text and images, especially in academic papers. In this paper, we introduce PDF-WuKong, a multimodal large language model (MLLM) which is designed to enhance multimodal question-answering (QA) for long PDF documents. PDF-WuKong incorporates a sparse sampler that operates on both text and image representations, significantly improving the efficiency and capability of the MLLM. The sparse sampler is integrated with the MLLM's image encoder and selects the paragraphs or diagrams most pertinent to user queries for processing by the language model. To effectively train and evaluate our model, we construct PaperPDF, a dataset consisting of a broad collection of academic papers sourced from arXiv, multiple strategies are proposed to generate automatically 1M QA pairs along with their corresponding evidence sources. Experimental results demonstrate the superiority and high efficiency of our approach over other models on the task of long multimodal PDF understanding, surpassing proprietary products by an average of 8.6% on F1. Our code and dataset will be released at https://github.com/yh-hust/PDF-Wukong.

Tool-Integrated Reasoning (TIR) enables large language models (LLMs) to improve their internal reasoning ability by integrating external tools. However, models employing TIR often display suboptimal behaviors, such as insufficient or excessive tool usage and overthinking after tool calls. The challenge of incentivizing LLMs to perform TIR efficiently and accurately, while stabilizing the reasoning process, remains an open question. In this paper, we start by exploring the impact of tool calls on model reasoning from the perspective of information entropy. Our findings indicate that tool call results lead to a distinct change in the information entropy of subsequent reasoning, with the overall entropy of the reasoning chain varying based on the number of tool calls. Building on these insights, we propose Tool-Light, a framework designed to encourage LLMs to perform TIR efficiently and accurately. Our framework includes dataset construction and multi-stage fine-tuning. For dataset construction, we employ continuous self-evolved sampling using the fine-tuned model, integrating both vanilla sampling and entropy-guided sampling. Besides, we establish strict criteria for selecting positive-negative pairs during sampling. The training process involves a two-stage approach, comprising Supervised Fine-Tuning (SFT) and Self-Evolved Direct Preference Optimization (DPO). Experimental results on 10 datasets demonstrate the effectiveness of Tool-Light, significantly improving the model's efficiency in executing TIR tasks.

State-of-the-art language models are autoregressive and operate on subword units known as tokens. Specifically, one must encode the conditioning string into a list of tokens before passing to the language models for next-token prediction. We show that popular encoding schemes, such as maximum prefix encoding (MPE) and byte-pair-encoding (BPE), induce a sampling bias that cannot be mitigated with more training or data. To counter this universal problem, for each encoding scheme above, we propose a novel algorithm to obtain unbiased estimates from any language model trained on tokenized data. Our methods do not require finetuning the model, and the complexity, defined as the number of model runs, scales linearly with the sequence length in the case of MPE. As a result, we show that one can simulate token-free behavior from a tokenized language model. We empirically verify the correctness of our method through a Markov-chain setup, where it accurately recovers the transition probabilities, as opposed to the conventional method of directly prompting tokens into the language model.

Diffusion large language models (dLLMs) theoretically permit token decoding in arbitrary order, a flexibility that could enable richer exploration of reasoning paths than autoregressive (AR) LLMs. In practice, however, random-order decoding often hurts generation quality. To mitigate this, low-confidence remasking improves single-sample quality (e.g., Pass@1) by prioritizing confident tokens, but it also suppresses exploration and limits multi-sample gains (e.g., Pass@k), creating a fundamental quality--exploration dilemma. In this paper, we provide a unified explanation of this dilemma. We show that low-confidence remasking improves a myopic proxy for quality while provably constraining the entropy of the induced sequence distribution. To overcome this limitation, we characterize the optimal distribution that explicitly balances quality and exploration, and develop a simple Independent Metropolis--Hastings sampler that approximately targets this distribution during decoding. Experiments across a range of reasoning benchmarks including MATH500, AIME24/25, HumanEval, and MBPP show that our approach yields better exploration-quality tradeoff than both random and low-confidence remasking.

The problem of estimating an unknown discrete distribution from its samples is a fundamental tenet of statistical learning. Over the past decade, it attracted significant research effort and has been solved for a variety of divergence measures. Surprisingly, an equally important problem, estimating an unknown Markov chain from its samples, is still far from understood. We consider two problems related to the min-max risk (expected loss) of estimating an unknown k-state Markov chain from its n sequential samples: predicting the conditional distribution of the next sample with respect to the KL-divergence, and estimating the transition matrix with respect to a natural loss induced by KL or a more general f-divergence measure. For the first measure, we determine the min-max prediction risk to within a linear factor in the alphabet size, showing it is Omega(kloglog n / n) and O(k^2loglog n / n). For the second, if the transition probabilities can be arbitrarily small, then only trivial uniform risk upper bounds can be derived. We therefore consider transition probabilities that are bounded away from zero, and resolve the problem for essentially all sufficiently smooth f-divergences, including KL-, L_2-, Chi-squared, Hellinger, and Alpha-divergences.

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.

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.

As industrial applications are increasingly automated by machine learning models, enforcing personal data ownership and intellectual property rights requires tracing training data back to their rightful owners. Membership inference algorithms approach this problem by using statistical techniques to discern whether a target sample was included in a model's training set. However, existing methods only utilize the unaltered target sample or simple augmentations of the target to compute statistics. Such a sparse sampling of the model's behavior carries little information, leading to poor inference capabilities. In this work, we use adversarial tools to directly optimize for queries that are discriminative and diverse. Our improvements achieve significantly more accurate membership inference than existing methods, especially in offline scenarios and in the low false-positive regime which is critical in legal settings. Code is available at https://github.com/YuxinWenRick/canary-in-a-coalmine.

This paper considers the problem of combinatorial multi-armed bandits with semi-bandit feedback and a cardinality constraint on the super-arm size. Existing algorithms for solving this problem typically involve two key sub-routines: (1) a parameter estimation routine that sequentially estimates a set of base-arm parameters, and (2) a super-arm selection policy for selecting a subset of base arms deemed optimal based on these parameters. State-of-the-art algorithms assume access to an exact oracle for super-arm selection with unbounded computational power. At each instance, this oracle evaluates a list of score functions, the number of which grows as low as linearly and as high as exponentially with the number of arms. This can be prohibitive in the regime of a large number of arms. This paper introduces a novel realistic alternative to the perfect oracle. This algorithm uses a combination of group-testing for selecting the super arms and quantized Thompson sampling for parameter estimation. Under a general separability assumption on the reward function, the proposed algorithm reduces the complexity of the super-arm-selection oracle to be logarithmic in the number of base arms while achieving the same regret order as the state-of-the-art algorithms that use exact oracles. This translates to at least an exponential reduction in complexity compared to the oracle-based approaches.

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.

We propose TAROT, a targeted data selection framework grounded in optimal transport theory. Previous targeted data selection methods primarily rely on influence-based greedy heuristics to enhance domain-specific performance. While effective on limited, unimodal data (i.e., data following a single pattern), these methods struggle as target data complexity increases. Specifically, in multimodal distributions, these heuristics fail to account for multiple inherent patterns, leading to suboptimal data selection. This work identifies two primary factors contributing to this limitation: (i) the disproportionate impact of dominant feature components in high-dimensional influence estimation, and (ii) the restrictive linear additive assumptions inherent in greedy selection strategies. To address these challenges, TAROT incorporates whitened feature distance to mitigate dominant feature bias, providing a more reliable measure of data influence. Building on this, TAROT uses whitened feature distance to quantify and minimize the optimal transport distance between the selected data and target domains. Notably, this minimization also facilitates the estimation of optimal selection ratios. We evaluate TAROT across multiple tasks, including semantic segmentation, motion prediction, and instruction tuning. Results consistently show that TAROT outperforms state-of-the-art methods, highlighting its versatility across various deep learning tasks. Code is available at https://github.com/vita-epfl/TAROT.

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.

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.

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.