Daily Papers

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.

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.

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.

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

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.

Classifier guidance is a recently introduced method to trade off mode coverage and sample fidelity in conditional diffusion models post training, in the same spirit as low temperature sampling or truncation in other types of generative models. Classifier guidance combines the score estimate of a diffusion model with the gradient of an image classifier and thereby requires training an image classifier separate from the diffusion model. It also raises the question of whether guidance can be performed without a classifier. We show that guidance can be indeed performed by a pure generative model without such a classifier: in what we call classifier-free guidance, we jointly train a conditional and an unconditional diffusion model, and we combine the resulting conditional and unconditional score estimates to attain a trade-off between sample quality and diversity similar to that obtained using classifier guidance.

Test-time scaling improves large language model performance by adding extra compute during decoding. Best-of-N (BoN) sampling serves as a common scaling technique, broadening the search space for finding better solutions from the model distribution. However, traditional BoN requires N full generations, leading to high GPU memory overhead and time latency. Moreover, some methods depend on reward models, adding computational cost and limiting domain generalization. In this paper, we propose Self-Truncation Best-of-N (ST-BoN), a novel decoding method that avoids fully generating all samplings and eliminates the need for reward models. ST-BoN introduces early sampling consistency to estimate the most promising sample, truncating suboptimal ones to free memory and accelerate inference. This pushes the sampling-efficient test-time scaling. Compared to traditional BoN, ST-BoN can reduce dynamic GPU memory overhead by over 90% and time latency by 50%, while achieving comparable or even better performance across reasoning and open-ended domains.

In the stochastic multi-armed bandit problem, a randomized probability matching policy called Thompson sampling (TS) has shown excellent performance in various reward models. In addition to the empirical performance, TS has been shown to achieve asymptotic problem-dependent lower bounds in several models. However, its optimality has been mainly addressed under light-tailed or one-parameter models that belong to exponential families. In this paper, we consider the optimality of TS for the Pareto model that has a heavy tail and is parameterized by two unknown parameters. Specifically, we discuss the optimality of TS with probability matching priors that include the Jeffreys prior and the reference priors. We first prove that TS with certain probability matching priors can achieve the optimal regret bound. Then, we show the suboptimality of TS with other priors, including the Jeffreys and the reference priors. Nevertheless, we find that TS with the Jeffreys and reference priors can achieve the asymptotic lower bound if one uses a truncation procedure. These results suggest carefully choosing noninformative priors to avoid suboptimality and show the effectiveness of truncation procedures in TS-based policies.

Recent years have witnessed the rapid progress and broad application of diffusion probabilistic models (DPMs). Sampling from DPMs can be viewed as solving an ordinary differential equation (ODE). Despite the promising performance, the generation of DPMs usually consumes much time due to the large number of function evaluations (NFE). Though recent works have accelerated the sampling to around 20 steps with high-order solvers, the sample quality with less than 10 NFE can still be improved. In this paper, we propose a unified sampling framework (USF) to study the optional strategies for solver. Under this framework, we further reveal that taking different solving strategies at different timesteps may help further decrease the truncation error, and a carefully designed solver schedule has the potential to improve the sample quality by a large margin. Therefore, we propose a new sampling framework based on the exponential integral formulation that allows free choices of solver strategy at each step and design specific decisions for the framework. Moreover, we propose S^3, a predictor-based search method that automatically optimizes the solver schedule to get a better time-quality trade-off of sampling. We demonstrate that S^3 can find outstanding solver schedules which outperform the state-of-the-art sampling methods on CIFAR-10, CelebA, ImageNet, and LSUN-Bedroom datasets. Specifically, we achieve 2.69 FID with 10 NFE and 6.86 FID with 5 NFE on CIFAR-10 dataset, outperforming the SOTA method significantly. We further apply S^3 to Stable-Diffusion model and get an acceleration ratio of 2times, showing the feasibility of sampling in very few steps without retraining the neural network.

Despite the extensive studies on Generative Adversarial Networks (GANs), how to reliably sample high-quality images from their latent spaces remains an under-explored topic. In this paper, we propose a novel GAN latent sampling method by exploring and exploiting the hubness priors of GAN latent distributions. Our key insight is that the high dimensionality of the GAN latent space will inevitably lead to the emergence of hub latents that usually have much larger sampling densities than other latents in the latent space. As a result, these hub latents are better trained and thus contribute more to the synthesis of high-quality images. Unlike the a posterior "cherry-picking", our method is highly efficient as it is an a priori method that identifies high-quality latents before the synthesis of images. Furthermore, we show that the well-known but purely empirical truncation trick is a naive approximation to the central clustering effect of hub latents, which not only uncovers the rationale of the truncation trick, but also indicates the superiority and fundamentality of our method. Extensive experimental results demonstrate the effectiveness of the proposed method.

Straightening the probability flow of the continuous-time generative models, such as diffusion models or flow-based models, is the key to fast sampling through the numerical solvers, existing methods learn a linear path by directly generating the probability path the joint distribution between the noise and data distribution. One key reason for the slow sampling speed of the ODE-based solvers that simulate these generative models is the global truncation error of the ODE solver, caused by the high curvature of the ODE trajectory, which explodes the truncation error of the numerical solvers in the low-NFE regime. To address this challenge, We propose a novel method called SeqRF, a learning technique that straightens the probability flow to reduce the global truncation error and hence enable acceleration of sampling and improve the synthesis quality. In both theoretical and empirical studies, we first observe the straightening property of our SeqRF. Through empirical evaluations via SeqRF over flow-based generative models, We achieve surpassing results on CIFAR-10, CelebA-64 times 64, and LSUN-Church datasets.

In Reinforcement Learning (RL), an agent acts in an unknown environment to maximize the expected cumulative discounted sum of an external reward signal, i.e., the expected return. In practice, in many tasks of interest, such as policy optimization, the agent usually spends its interaction budget by collecting episodes of fixed length within a simulator (i.e., Monte Carlo simulation). However, given the discounted nature of the RL objective, this data collection strategy might not be the best option. Indeed, the rewards taken in early simulation steps weigh exponentially more than future rewards. Taking a cue from this intuition, in this paper, we design an a-priori budget allocation strategy that leads to the collection of trajectories of different lengths, i.e., truncated. The proposed approach provably minimizes the width of the confidence intervals around the empirical estimates of the expected return of a policy. After discussing the theoretical properties of our method, we make use of our trajectory truncation mechanism to extend Policy Optimization via Importance Sampling (POIS, Metelli et al., 2018) algorithm. Finally, we conduct a numerical comparison between our algorithm and POIS: the results are consistent with our theory and show that an appropriate truncation of the trajectories can succeed in improving performance.

Reasoning language models such as OpenAI-o1, DeepSeek-R1, and Qwen achieve strong performance via extended chains of thought but often generate unnecessarily long outputs. Maximizing intelligence per token--accuracy relative to response length--remains an open problem. We revisit reinforcement learning (RL) with the simplest length penalty--truncation--and show that accuracy degradation arises not from the lack of sophisticated penalties but from inadequate RL optimization. We identify three key challenges: (i) large bias in advantage estimation, (ii) entropy collapse, and (iii) sparse reward signal. We address them with Doing Length pEnalty Right (DLER), a training recipe combining batch-wise reward normalization, higher clipping, dynamic sampling, and a simple truncation length penalty. DLER achieves state-of-the-art accuracy--efficiency trade-offs, cutting output length by over 70 percent while surpassing all previous baseline accuracy. It also improves test-time scaling: compared to DeepSeek-R1-7B, DLER-7B generates multiple concise responses in parallel with 28 percent higher accuracy and lower latency. We further introduce Difficulty-Aware DLER, which adaptively tightens truncation on easier questions for additional efficiency gains. We also propose an update-selective merging method that preserves baseline accuracy while retaining the concise reasoning ability of the DLER model, which is useful for scenarios where RL training data is scarce.

Zero-shot transfer learning for dialogue state tracking (DST) enables us to handle a variety of task-oriented dialogue domains without the expense of collecting in-domain data. In this work, we propose to transfer the cross-task knowledge from general question answering (QA) corpora for the zero-shot DST task. Specifically, we propose TransferQA, a transferable generative QA model that seamlessly combines extractive QA and multi-choice QA via a text-to-text transformer framework, and tracks both categorical slots and non-categorical slots in DST. In addition, we introduce two effective ways to construct unanswerable questions, namely, negative question sampling and context truncation, which enable our model to handle "none" value slots in the zero-shot DST setting. The extensive experiments show that our approaches substantially improve the existing zero-shot and few-shot results on MultiWoz. Moreover, compared to the fully trained baseline on the Schema-Guided Dialogue dataset, our approach shows better generalization ability in unseen domains.

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.

This paper investigates the problem of generalized linear bandits with heavy-tailed rewards, whose (1+epsilon)-th moment is bounded for some epsilonin (0,1]. Although there exist methods for generalized linear bandits, most of them focus on bounded or sub-Gaussian rewards and are not well-suited for many real-world scenarios, such as financial markets and web-advertising. To address this issue, we propose two novel algorithms based on truncation and mean of medians. These algorithms achieve an almost optimal regret bound of O(dT^{1{1+epsilon}}), where d is the dimension of contextual information and T is the time horizon. Our truncation-based algorithm supports online learning, distinguishing it from existing truncation-based approaches. Additionally, our mean-of-medians-based algorithm requires only O(log T) rewards and one estimator per epoch, making it more practical. Moreover, our algorithms improve the regret bounds by a logarithmic factor compared to existing algorithms when epsilon=1. Numerical experimental results confirm the merits of our algorithms.

Estimating truncated density models is difficult, as these models have intractable normalising constants and hard to satisfy boundary conditions. Score matching can be adapted to solve the truncated density estimation problem, but requires a continuous weighting function which takes zero at the boundary and is positive elsewhere. Evaluation of such a weighting function (and its gradient) often requires a closed-form expression of the truncation boundary and finding a solution to a complicated optimisation problem. In this paper, we propose approximate Stein classes, which in turn leads to a relaxed Stein identity for truncated density estimation. We develop a novel discrepancy measure, truncated kernelised Stein discrepancy (TKSD), which does not require fixing a weighting function in advance, and can be evaluated using only samples on the boundary. We estimate a truncated density model by minimising the Lagrangian dual of TKSD. Finally, experiments show the accuracy of our method to be an improvement over previous works even without the explicit functional form of the boundary.

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

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

Flow-matching-based text-to-speech (TTS) models, such as Voicebox, E2 TTS, and F5-TTS, have attracted significant attention in recent years. These models require multiple sampling steps to reconstruct speech from noise, making inference speed a key challenge. Reducing the number of sampling steps can greatly improve inference efficiency. To this end, we introduce Fast F5-TTS, a training-free approach to accelerate the inference of flow-matching-based TTS models. By inspecting the sampling trajectory of F5-TTS, we identify redundant steps and propose Empirically Pruned Step Sampling (EPSS), a non-uniform time-step sampling strategy that effectively reduces the number of sampling steps. Our approach achieves a 7-step generation with an inference RTF of 0.030 on an NVIDIA RTX 3090 GPU, making it 4 times faster than the original F5-TTS while maintaining comparable performance. Furthermore, EPSS performs well on E2 TTS models, demonstrating its strong generalization ability.

We consider the problem of approximating a function from L^2 by an element of a given m-dimensional space V_m, associated with some feature map varphi, using evaluations of the function at random points x_1,dots,x_n. After recalling some results on optimal weighted least-squares using independent and identically distributed points, we consider weighted least-squares using projection determinantal point processes (DPP) or volume sampling. These distributions introduce dependence between the points that promotes diversity in the selected features varphi(x_i). We first provide a generalized version of volume-rescaled sampling yielding quasi-optimality results in expectation with a number of samples n = O(mlog(m)), that means that the expected L^2 error is bounded by a constant times the best approximation error in L^2. Also, further assuming that the function is in some normed vector space H continuously embedded in L^2, we further prove that the approximation is almost surely bounded by the best approximation error measured in the H-norm. This includes the cases of functions from L^infty or reproducing kernel Hilbert spaces. Finally, we present an alternative strategy consisting in using independent repetitions of projection DPP (or volume sampling), yielding similar error bounds as with i.i.d. or volume sampling, but in practice with a much lower number of samples. Numerical experiments illustrate the performance of the different strategies.

We study a missing-value imputation method, termed kNNSampler, that imputes a given unit's missing response by randomly sampling from the observed responses of the k most similar units to the given unit in terms of the observed covariates. This method can sample unknown missing values from their distributions, quantify the uncertainties of missing values, and be readily used for multiple imputation. Unlike popular kNNImputer, which estimates the conditional mean of a missing response given an observed covariate, kNNSampler is theoretically shown to estimate the conditional distribution of a missing response given an observed covariate. Experiments demonstrate its effectiveness in recovering the distribution of missing values. The code for kNNSampler is made publicly available (https://github.com/SAP/knn-sampler).

In large language model training, input documents are typically concatenated together and then split into sequences of equal length to avoid padding tokens. Despite its efficiency, the concatenation approach compromises data integrity -- it inevitably breaks many documents into incomplete pieces, leading to excessive truncations that hinder the model from learning to compose logically coherent and factually consistent content that is grounded on the complete context. To address the issue, we propose Best-fit Packing, a scalable and efficient method that packs documents into training sequences through length-aware combinatorial optimization. Our method completely eliminates unnecessary truncations while retaining the same training efficiency as concatenation. Empirical results from both text and code pre-training show that our method achieves superior performance (e.g., relatively +4.7% on reading comprehension; +16.8% in context following; and +9.2% on program synthesis), and reduces closed-domain hallucination effectively by up to 58.3%.

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.

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

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.

Frontier models that generate extended reasoning traces inadvertently produce rich token sequences that can facilitate model distillation. Recognizing this vulnerability, model owners may seek sampling strategies that limit the effectiveness of distillation without compromising model performance. Antidistillation sampling provides exactly this capability. By strategically modifying a model's next-token probability distribution, antidistillation sampling poisons reasoning traces, rendering them significantly less effective for distillation while preserving the model's practical utility. For further details, see https://antidistillation.com.

Inference-time scaling techniques have significantly bolstered the reasoning capabilities of large language models (LLMs) by harnessing additional computational effort at inference without retraining. Similarly, Chain-of-Thought (CoT) prompting and its extension, Long CoT, improve accuracy by generating rich intermediate reasoning trajectories, but these approaches incur substantial token costs that impede their deployment in latency-sensitive settings. In this work, we first show that truncated CoT, which stops reasoning before completion and directly generates the final answer, often matches full CoT sampling while using dramatically fewer tokens. Building on this insight, we introduce Fractured Sampling, a unified inference-time strategy that interpolates between full CoT and solution-only sampling along three orthogonal axes: (1) the number of reasoning trajectories, (2) the number of final solutions per trajectory, and (3) the depth at which reasoning traces are truncated. Through extensive experiments on five diverse reasoning benchmarks and several model scales, we demonstrate that Fractured Sampling consistently achieves superior accuracy-cost trade-offs, yielding steep log-linear scaling gains in Pass@k versus token budget. Our analysis reveals how to allocate computation across these dimensions to maximize performance, paving the way for more efficient and scalable LLM reasoning.

Exploratory data analytics (EDA) is a sequential decision making process where analysts choose subsequent queries that might lead to some interesting insights based on the previous queries and corresponding results. Data processing systems often execute the queries on samples to produce results with low latency. Different downsampling strategy preserves different statistics of the data and have different magnitude of latency reductions. The optimum choice of sampling strategy often depends on the particular context of the analysis flow and the hidden intent of the analyst. In this paper, we are the first to consider the impact of sampling in interactive data exploration settings as they introduce approximation errors. We propose a Deep Reinforcement Learning (DRL) based framework which can optimize the sample selection in order to keep the analysis and insight generation flow intact. Evaluations with 3 real datasets show that our technique can preserve the original insight generation flow while improving the interaction latency, compared to baseline methods.

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 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.

Some classical uncertainty quantification problems require the estimation of multiple expectations. Estimating all of them accurately is crucial and can have a major impact on the analysis to perform, and standard existing Monte Carlo methods can be costly to do so. We propose here a new procedure based on importance sampling and control variates for estimating more efficiently multiple expectations with the same sample. We first show that there exists a family of optimal estimators combining both importance sampling and control variates, which however cannot be used in practice because they require the knowledge of the values of the expectations to estimate. Motivated by the form of these optimal estimators and some interesting properties, we therefore propose an adaptive algorithm. The general idea is to adaptively update the parameters of the estimators for approaching the optimal ones. We suggest then a quantitative stopping criterion that exploits the trade-off between approaching these optimal parameters and having a sufficient budget left. This left budget is then used to draw a new independent sample from the final sampling distribution, allowing to get unbiased estimators of the expectations. We show how to apply our procedure to sensitivity analysis, by estimating Sobol' indices and quantifying the impact of the input distributions. Finally, realistic test cases show the practical interest of the proposed algorithm, and its significant improvement over estimating the expectations separately.

The overestimation bias is one of the major impediments to accurate off-policy learning. This paper investigates a novel way to alleviate the overestimation bias in a continuous control setting. Our method---Truncated Quantile Critics, TQC,---blends three ideas: distributional representation of a critic, truncation of critics prediction, and ensembling of multiple critics. Distributional representation and truncation allow for arbitrary granular overestimation control, while ensembling provides additional score improvements. TQC outperforms the current state of the art on all environments from the continuous control benchmark suite, demonstrating 25% improvement on the most challenging Humanoid environment.

The past few years have witnessed the great success of Diffusion models~(DMs) in generating high-fidelity samples in generative modeling tasks. A major limitation of the DM is its notoriously slow sampling procedure which normally requires hundreds to thousands of time discretization steps of the learned diffusion process to reach the desired accuracy. Our goal is to develop a fast sampling method for DMs with a much less number of steps while retaining high sample quality. To this end, we systematically analyze the sampling procedure in DMs and identify key factors that affect the sample quality, among which the method of discretization is most crucial. By carefully examining the learned diffusion process, we propose Diffusion Exponential Integrator Sampler~(DEIS). It is based on the Exponential Integrator designed for discretizing ordinary differential equations (ODEs) and leverages a semilinear structure of the learned diffusion process to reduce the discretization error. The proposed method can be applied to any DMs and can generate high-fidelity samples in as few as 10 steps. In our experiments, it takes about 3 minutes on one A6000 GPU to generate 50k images from CIFAR10. Moreover, by directly using pre-trained DMs, we achieve the state-of-art sampling performance when the number of score function evaluation~(NFE) is limited, e.g., 4.17 FID with 10 NFEs, 3.37 FID, and 9.74 IS with only 15 NFEs on CIFAR10. Code is available at https://github.com/qsh-zh/deis

Group-based reinforcement learning algorithms such as Group Reward Policy Optimization (GRPO) have proven effective for fine-tuning large language models (LLMs) with human feedback. However, generating and storing multiple responses per prompt incurs substantial memory overhead, especially as the sample group size increases, limiting scalability under constrained hardware. We propose Infinite Sampling, a framework that enables efficient and stable GRPO training by decoupling group size from GPU memory usage. It consists of: (1) micro sampling groups that decompose large groups into memory-feasible rounds; (2) continuous sampling that interleaves generation across groups to improve utilization; and (3) a length-aware scheduler combining token-conditioned sequence length prediction with a two-stage plan: global grouping via FPTAS and runtime refill via SJF. Experiments show that our Micro Sampling Groups reduce peak memory usage by over 50% compared to full-group decoding (e.g., from 21.55 GB to 10.64 GB on Qwen3-1.7B). Building on this, Infinite Sampling improves throughput by over 25% compared to the naive micro sampling group method, reducing decoding steps while maintaining full-length completions and memory usage. Our hybrid scheduling ensures efficient and stable GRPO training with larger groups under realistic GPU memory constraints.

We present speculative sampling, an algorithm for accelerating transformer decoding by enabling the generation of multiple tokens from each transformer call. Our algorithm relies on the observation that the latency of parallel scoring of short continuations, generated by a faster but less powerful draft model, is comparable to that of sampling a single token from the larger target model. This is combined with a novel modified rejection sampling scheme which preserves the distribution of the target model within hardware numerics. We benchmark speculative sampling with Chinchilla, a 70 billion parameter language model, achieving a 2-2.5x decoding speedup in a distributed setup, without compromising the sample quality or making modifications to the model itself.

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

We discuss the numerical solution of initial value problems for varepsilon^2,varphi''+a(x),varphi=0 in the highly oscillatory regime, i.e., with a(x)>0 and 0<varepsilonll 1. We analyze and implement an approximate solution based on the well-known WKB-ansatz. The resulting approximation error is of magnitude O(varepsilon^{N}) where N refers to the truncation order of the underlying asymptotic series. When the optimal truncation order N_{opt} is chosen, the error behaves like O(varepsilon^{-2}exp(-cvarepsilon^{-1})) with some c>0.

Overparametrization often helps improve the generalization performance. This paper proposes a dual view of overparametrization suggesting that downsampling may also help generalize. Motivated by this dual view, we characterize two out-of-sample prediction risks of the sketched ridgeless least square estimator in the proportional regime masymp n asymp p, where m is the sketching size, n the sample size, and p the feature dimensionality. Our results reveal the statistical role of downsampling. Specifically, downsampling does not always hurt the generalization performance, and may actually help improve it in some cases. We identify the optimal sketching sizes that minimize the out-of-sample prediction risks, and find that the optimally sketched estimator has stabler risk curves that eliminates the peaks of those for the full-sample estimator. We then propose a practical procedure to empirically identify the optimal sketching size. Finally, we extend our results to cover central limit theorems and misspecified models. Numerical studies strongly support our theory.

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

We introduce infty-Diff, a generative diffusion model which directly operates on infinite resolution data. By randomly sampling subsets of coordinates during training and learning to denoise the content at those coordinates, a continuous function is learned that allows sampling at arbitrary resolutions. In contrast to other recent infinite resolution generative models, our approach operates directly on the raw data, not requiring latent vector compression for context, using hypernetworks, nor relying on discrete components. As such, our approach achieves significantly higher sample quality, as evidenced by lower FID scores, as well as being able to effectively scale to higher resolutions than the training data while retaining detail.

RANSAC-based algorithms are the standard techniques for robust estimation in computer vision. These algorithms are iterative and computationally expensive; they alternate between random sampling of data, computing hypotheses, and running inlier counting. Many authors tried different approaches to improve efficiency. One of the major improvements is having a guided sampling, letting the RANSAC cycle stop sooner. This paper presents a new adaptive sampling process for RANSAC. Previous methods either assume no prior information about the inlier/outlier classification of data points or use some previously computed scores in the sampling. In this paper, we derive a dynamic Bayesian network that updates individual data points' inlier scores while iterating RANSAC. At each iteration, we apply weighted sampling using the updated scores. Our method works with or without prior data point scorings. In addition, we use the updated inlier/outlier scoring for deriving a new stopping criterion for the RANSAC loop. We test our method in multiple real-world datasets for several applications and obtain state-of-the-art results. Our method outperforms the baselines in accuracy while needing less computational time.

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

While score-based generative models are the model of choice across diverse domains, there are limited tools available for controlling inference-time behavior in a principled manner, e.g. for composing multiple pretrained models. Existing classifier-free guidance methods use a simple heuristic to mix conditional and unconditional scores to approximately sample from conditional distributions. However, such methods do not approximate the intermediate distributions, necessitating additional 'corrector' steps. In this work, we provide an efficient and principled method for sampling from a sequence of annealed, geometric-averaged, or product distributions derived from pretrained score-based models. We derive a weighted simulation scheme which we call Feynman-Kac Correctors (FKCs) based on the celebrated Feynman-Kac formula by carefully accounting for terms in the appropriate partial differential equations (PDEs). To simulate these PDEs, we propose Sequential Monte Carlo (SMC) resampling algorithms that leverage inference-time scaling to improve sampling quality. We empirically demonstrate the utility of our methods by proposing amortized sampling via inference-time temperature annealing, improving multi-objective molecule generation using pretrained models, and improving classifier-free guidance for text-to-image generation. Our code is available at https://github.com/martaskrt/fkc-diffusion.

We introduce a theoretical framework for sampling from unnormalized densities based on a smoothing scheme that uses an isotropic Gaussian kernel with a single fixed noise scale. We prove one can decompose sampling from a density (minimal assumptions made on the density) into a sequence of sampling from log-concave conditional densities via accumulation of noisy measurements with equal noise levels. Our construction is unique in that it keeps track of a history of samples, making it non-Markovian as a whole, but it is lightweight algorithmically as the history only shows up in the form of a running empirical mean of samples. Our sampling algorithm generalizes walk-jump sampling (Saremi & Hyv\"arinen, 2019). The "walk" phase becomes a (non-Markovian) chain of (log-concave) Markov chains. The "jump" from the accumulated measurements is obtained by empirical Bayes. We study our sampling algorithm quantitatively using the 2-Wasserstein metric and compare it with various Langevin MCMC algorithms. We also report a remarkable capacity of our algorithm to "tunnel" between modes of a distribution.

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

Diffusion probabilistic models (DPMs) have achieved impressive success in visual generation. While, they suffer from slow inference speed due to iterative sampling. Employing fewer sampling steps is an intuitive solution, but this will also introduces discretization error. Existing fast samplers make inspiring efforts to reduce discretization error through the adoption of high-order solvers, potentially reaching a plateau in terms of optimization. This raises the question: can the sampling process be accelerated further? In this paper, we re-examine the nature of sampling errors, discerning that they comprise two distinct elements: the widely recognized discretization error and the less explored approximation error. Our research elucidates the dynamics between these errors and the step by implementing a dual-error disentanglement strategy. Building on these foundations, we introduce an unified and training-free acceleration framework, DualFast, designed to enhance the speed of DPM sampling by concurrently accounting for both error types, thereby minimizing the total sampling error. DualFast is seamlessly compatible with existing samplers and significantly boost their sampling quality and speed, particularly in extremely few sampling steps. We substantiate the effectiveness of our framework through comprehensive experiments, spanning both unconditional and conditional sampling domains, across both pixel-space and latent-space DPMs.

Diffusion probabilistic models (DPMs) have achieved impressive success in high-resolution image synthesis, especially in recent large-scale text-to-image generation applications. An essential technique for improving the sample quality of DPMs is guided sampling, which usually needs a large guidance scale to obtain the best sample quality. The commonly-used fast sampler for guided sampling is DDIM, a first-order diffusion ODE solver that generally needs 100 to 250 steps for high-quality samples. Although recent works propose dedicated high-order solvers and achieve a further speedup for sampling without guidance, their effectiveness for guided sampling has not been well-tested before. In this work, we demonstrate that previous high-order fast samplers suffer from instability issues, and they even become slower than DDIM when the guidance scale grows large. To further speed up guided sampling, we propose DPM-Solver++, a high-order solver for the guided sampling of DPMs. DPM-Solver++ solves the diffusion ODE with the data prediction model and adopts thresholding methods to keep the solution matches training data distribution. We further propose a multistep variant of DPM-Solver++ to address the instability issue by reducing the effective step size. Experiments show that DPM-Solver++ can generate high-quality samples within only 15 to 20 steps for guided sampling by pixel-space and latent-space DPMs.

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

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.

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

In the realm of recommender systems (RS), Top-K ranking metrics such as NDCG@K are the gold standard for evaluating recommendation performance. However, during the training of recommendation models, optimizing NDCG@K poses significant challenges due to its inherent discontinuous nature and the intricate Top-K truncation. Recent efforts to optimize NDCG@K have either overlooked the Top-K truncation or suffered from high computational costs and training instability. To overcome these limitations, we propose SoftmaxLoss@K (SL@K), a novel recommendation loss tailored for NDCG@K optimization. Specifically, we integrate the quantile technique to handle Top-K truncation and derive a smooth upper bound for optimizing NDCG@K to address discontinuity. The resulting SL@K loss has several desirable properties, including theoretical guarantees, ease of implementation, computational efficiency, gradient stability, and noise robustness. Extensive experiments on four real-world datasets and three recommendation backbones demonstrate that SL@K outperforms existing losses with a notable average improvement of 6.03%. The code is available at https://github.com/Tiny-Snow/IR-Benchmark.

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 .

In this study, we propose Shortcut Fine-Tuning (SFT), a new approach for addressing the challenge of fast sampling of pretrained Denoising Diffusion Probabilistic Models (DDPMs). SFT advocates for the fine-tuning of DDPM samplers through the direct minimization of Integral Probability Metrics (IPM), instead of learning the backward diffusion process. This enables samplers to discover an alternative and more efficient sampling shortcut, deviating from the backward diffusion process. Inspired by a control perspective, we propose a new algorithm SFT-PG: Shortcut Fine-Tuning with Policy Gradient, and prove that under certain assumptions, gradient descent of diffusion models with respect to IPM is equivalent to performing policy gradient. To our best knowledge, this is the first attempt to utilize reinforcement learning (RL) methods to train diffusion models. Through empirical evaluation, we demonstrate that our fine-tuning method can further enhance existing fast DDPM samplers, resulting in sample quality comparable to or even surpassing that of the full-step model across various datasets.

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.

Autoregressive language models accumulate errors due to their fixed, irrevocable left-to-right token generation. To address this, we propose a new sampling method called Resample-Previous-Tokens (RPT). RPT mitigates error accumulation by iteratively revisiting and potentially replacing tokens in a window of previously generated text. This method can be integrated into existing autoregressive models, preserving their next-token-prediction quality and speed. Fine-tuning a pretrained 8B parameter model with RPT for only 100B resulted in ~10% relative improvements on reasoning and coding benchmarks compared to the standard sampling.

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.

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

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

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

The performance of Deep Neural Networks (DNNs) keeps elevating in recent years with increasing network depth and width. To enable DNNs on edge devices like mobile phones, researchers proposed several network compression methods including pruning, quantization and factorization. Among the factorization-based approaches, low-rank approximation has been widely adopted because of its solid theoretical rationale and efficient implementations. Several previous works attempted to directly approximate a pre-trained model by low-rank decomposition; however, small approximation errors in parameters can ripple a large prediction loss. As a result, performance usually drops significantly and a sophisticated fine-tuning is required to recover accuracy. We argue that it is not optimal to separate low-rank approximation from training. Unlike previous works, this paper integrates low rank approximation and regularization into the training. We propose Trained Rank Pruning (TRP), which iterates low rank approximation and training. TRP maintains the capacity of original network while imposes low-rank constraints during training. A stochastic sub-gradient descent optimized nuclear regularization is utilized to further encourage low rank in TRP. The TRP trained network has low-rank structure in nature, and can be approximated with negligible performance loss, eliminating fine-tuning after low rank approximation. The methods are comprehensively evaluated on CIFAR-10 and ImageNet, outperforming previous compression methods using low rank approximation. Code is available: https://github.com/yuhuixu1993/Trained-Rank-Pruning

Posterior sampling, i.e., exponential mechanism to sample from the posterior distribution, provides varepsilon-pure differential privacy (DP) guarantees and does not suffer from potentially unbounded privacy breach introduced by (varepsilon,delta)-approximate DP. In practice, however, one needs to apply approximate sampling methods such as Markov chain Monte Carlo (MCMC), thus re-introducing the unappealing delta-approximation error into the privacy guarantees. To bridge this gap, we propose the Approximate SAample Perturbation (abbr. ASAP) algorithm which perturbs an MCMC sample with noise proportional to its Wasserstein-infinity (W_infty) distance from a reference distribution that satisfies pure DP or pure Gaussian DP (i.e., delta=0). We then leverage a Metropolis-Hastings algorithm to generate the sample and prove that the algorithm converges in W_infty distance. We show that by combining our new techniques with a careful localization step, we obtain the first nearly linear-time algorithm that achieves the optimal rates in the DP-ERM problem with strongly convex and smooth losses.

Diffusion models and flow-matching models have enabled generating diverse and realistic images by learning to transfer noise to data. However, sampling from these models involves iterative denoising over many neural network passes, making generation slow and expensive. Previous approaches for speeding up sampling require complex training regimes, such as multiple training phases, multiple networks, or fragile scheduling. We introduce shortcut models, a family of generative models that use a single network and training phase to produce high-quality samples in a single or multiple sampling steps. Shortcut models condition the network not only on the current noise level but also on the desired step size, allowing the model to skip ahead in the generation process. Across a wide range of sampling step budgets, shortcut models consistently produce higher quality samples than previous approaches, such as consistency models and reflow. Compared to distillation, shortcut models reduce complexity to a single network and training phase and additionally allow varying step budgets at inference time.

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

Diffusion-based text-to-speech (TTS) systems have made remarkable progress in zero-shot speech synthesis, yet optimizing all components for perceptual metrics remains challenging. Prior work with DMOSpeech demonstrated direct metric optimization for speech generation components, but duration prediction remained unoptimized. This paper presents DMOSpeech 2, which extends metric optimization to the duration predictor through a reinforcement learning approach. The proposed system implements a novel duration policy framework using group relative preference optimization (GRPO) with speaker similarity and word error rate as reward signals. By optimizing this previously unoptimized component, DMOSpeech 2 creates a more complete metric-optimized synthesis pipeline. Additionally, this paper introduces teacher-guided sampling, a hybrid approach leveraging a teacher model for initial denoising steps before transitioning to the student model, significantly improving output diversity while maintaining efficiency. Comprehensive evaluations demonstrate superior performance across all metrics compared to previous systems, while reducing sampling steps by half without quality degradation. These advances represent a significant step toward speech synthesis systems with metric optimization across multiple components. The audio samples, code and pre-trained models are available at https://dmospeech2.github.io/.

Sequential models achieve state-of-the-art results in audio, visual and textual domains with respect to both estimating the data distribution and generating high-quality samples. Efficient sampling for this class of models has however remained an elusive problem. With a focus on text-to-speech synthesis, we describe a set of general techniques for reducing sampling time while maintaining high output quality. We first describe a single-layer recurrent neural network, the WaveRNN, with a dual softmax layer that matches the quality of the state-of-the-art WaveNet model. The compact form of the network makes it possible to generate 24kHz 16-bit audio 4x faster than real time on a GPU. Second, we apply a weight pruning technique to reduce the number of weights in the WaveRNN. We find that, for a constant number of parameters, large sparse networks perform better than small dense networks and this relationship holds for sparsity levels beyond 96%. The small number of weights in a Sparse WaveRNN makes it possible to sample high-fidelity audio on a mobile CPU in real time. Finally, we propose a new generation scheme based on subscaling that folds a long sequence into a batch of shorter sequences and allows one to generate multiple samples at once. The Subscale WaveRNN produces 16 samples per step without loss of quality and offers an orthogonal method for increasing sampling efficiency.

Temperature scaling is a popular technique for tuning the sharpness of a model distribution. It is used extensively for sampling likely generations and calibrating model uncertainty, and even features as a controllable parameter to many large language models in deployment. However, autoregressive models rely on myopic temperature scaling that greedily optimizes the next token. To address this, we propose Long Horizon Temperature Scaling (LHTS), a novel approach for sampling from temperature-scaled joint distributions. LHTS is compatible with all likelihood-based models, and optimizes for the long-horizon likelihood of samples. We derive a temperature-dependent LHTS objective, and show that fine-tuning a model on a range of temperatures produces a single model capable of generation with a controllable long-horizon temperature parameter. We experiment with LHTS on image diffusion models and character/language autoregressive models, demonstrating advantages over myopic temperature scaling in likelihood and sample quality, and showing improvements in accuracy on a multiple choice analogy task by 10%.

Denoising Diffusion Probabilistic Models have shown an impressive generation quality, although their long sampling chain leads to high computational costs. In this paper, we observe that a long sampling chain also leads to an error accumulation phenomenon, which is similar to the exposure bias problem in autoregressive text generation. Specifically, we note that there is a discrepancy between training and testing, since the former is conditioned on the ground truth samples, while the latter is conditioned on the previously generated results. To alleviate this problem, we propose a very simple but effective training regularization, consisting in perturbing the ground truth samples to simulate the inference time prediction errors. We empirically show that, without affecting the recall and precision, the proposed input perturbation leads to a significant improvement in the sample quality while reducing both the training and the inference times. For instance, on CelebA 64times64, we achieve a new state-of-the-art FID score of 1.27, while saving 37.5% of the training time. The code is publicly available at https://github.com/forever208/DDPM-IP

We propose a Monte Carlo sampler from the reverse diffusion process. Unlike the practice of diffusion models, where the intermediary updates -- the score functions -- are learned with a neural network, we transform the score matching problem into a mean estimation one. By estimating the means of the regularized posterior distributions, we derive a novel Monte Carlo sampling algorithm called reverse diffusion Monte Carlo (rdMC), which is distinct from the Markov chain Monte Carlo (MCMC) methods. We determine the sample size from the error tolerance and the properties of the posterior distribution to yield an algorithm that can approximately sample the target distribution with any desired accuracy. Additionally, we demonstrate and prove under suitable conditions that sampling with rdMC can be significantly faster than that with MCMC. For multi-modal target distributions such as those in Gaussian mixture models, rdMC greatly improves over the Langevin-style MCMC sampling methods both theoretically and in practice. The proposed rdMC method offers a new perspective and solution beyond classical MCMC algorithms for the challenging complex distributions.

We initiate the study of proper losses for evaluating generative models in the discrete setting. Unlike traditional proper losses, we treat both the generative model and the target distribution as black-boxes, only assuming ability to draw i.i.d. samples. We define a loss to be black-box proper if the generative distribution that minimizes expected loss is equal to the target distribution. Using techniques from statistical estimation theory, we give a general construction and characterization of black-box proper losses: they must take a polynomial form, and the number of draws from the model and target distribution must exceed the degree of the polynomial. The characterization rules out a loss whose expectation is the cross-entropy between the target distribution and the model. By extending the construction to arbitrary sampling schemes such as Poisson sampling, however, we show that one can construct such a loss.

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.

We introduce Reprompting, an iterative sampling algorithm that searches for the Chain-of-Thought (CoT) recipes for a given task without human intervention. Through Gibbs sampling, we infer CoT recipes that work consistently well for a set of training samples. Our method iteratively samples new recipes using previously sampled solutions as parent prompts to solve other training problems. On five Big-Bench Hard tasks that require multi-step reasoning, Reprompting achieves consistently better performance than the zero-shot, few-shot, and human-written CoT baselines. Reprompting can also facilitate transfer of knowledge from a stronger model to a weaker model leading to substantially improved performance of the weaker model. Overall, Reprompting brings up to +17 point improvements over the previous state-of-the-art method that uses human-written CoT prompts.

Hamiltonian Monte Carlo (HMC) is a powerful algorithm to sample latent variables from Bayesian models. The advent of probabilistic programming languages (PPLs) frees users from writing inference algorithms and lets users focus on modeling. However, many models are difficult for HMC to solve directly, and often require tricks like model reparameterization. We are motivated by the fact that many of those models could be simplified by marginalization. We propose to use automatic marginalization as part of the sampling process using HMC in a graphical model extracted from a PPL, which substantially improves sampling from real-world hierarchical models.

We introduce a novel framework for efficient sampling from complex, unnormalised target distributions by exploiting multiscale dynamics. Traditional score-based sampling methods either rely on learned approximations of the score function or involve computationally expensive nested Markov chain Monte Carlo (MCMC) loops. In contrast, the proposed approach leverages stochastic averaging within a slow-fast system of stochastic differential equations (SDEs) to estimate intermediate scores along a diffusion path without training or inner-loop MCMC. Two algorithms are developed under this framework: MultALMC, which uses multiscale annealed Langevin dynamics, and MultCDiff, based on multiscale controlled diffusions for the reverse-time Ornstein-Uhlenbeck process. Both overdamped and underdamped variants are considered, with theoretical guarantees of convergence to the desired diffusion path. The framework is extended to handle heavy-tailed target distributions using Student's t-based noise models and tailored fast-process dynamics. Empirical results across synthetic and real-world benchmarks, including multimodal and high-dimensional distributions, demonstrate that the proposed methods are competitive with existing samplers in terms of accuracy and efficiency, without the need for learned models.

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

Masked diffusion models (MDMs) have emerged as a popular research topic for generative modeling of discrete data, thanks to their superior performance over other discrete diffusion models, and are rivaling the auto-regressive models (ARMs) for language modeling tasks. The recent effort in simplifying the masked diffusion framework further leads to alignment with continuous-space diffusion models and more principled training and sampling recipes. In this paper, however, we reveal that both training and sampling of MDMs are theoretically free from the time variable, arguably the key signature of diffusion models, and are instead equivalent to masked models. The connection on the sampling aspect is drawn by our proposed first-hitting sampler (FHS). Specifically, we show that the FHS is theoretically equivalent to MDMs' original generation process while significantly alleviating the time-consuming categorical sampling and achieving a 20times speedup. In addition, our investigation raises doubts about whether MDMs can truly beat ARMs. We identify, for the first time, an underlying numerical issue, even with the commonly used 32-bit floating-point precision, which results in inaccurate categorical sampling. We show that the numerical issue lowers the effective temperature both theoretically and empirically, and the resulting decrease in token diversity makes previous evaluations, which assess the generation quality solely through the incomplete generative perplexity metric, somewhat unfair.

Recent advances in large reasoning language models (LRLMs) rely on test-time scaling, which extends long chain-of-thought (CoT) generation to solve complex tasks. However, overthinking in long CoT not only slows down the efficiency of problem solving, but also risks accuracy loss due to the extremely detailed or redundant reasoning steps. We propose a simple yet effective method that allows LLMs to self-truncate CoT sequences by early exit during generation. Instead of relying on fixed heuristics, the proposed method monitors model behavior at potential reasoning transition points (e.g.,"Wait" tokens) and dynamically terminates the next reasoning chain's generation when the model exhibits high confidence in a trial answer. Our method requires no additional training and can be seamlessly integrated into existing o1-like reasoning LLMs. Experiments on 10 reasoning benchmarks (e.g., GSM8K, MATH-500, AMC, GPQA, AIME and LiveCodeBench) show that the proposed method is consistently effective on 11 cutting-edge reasoning LLMs of varying series and sizes, reducing the length of CoT sequences by an average of 19.1% to 80.1% while improving accuracy by 0.3% to 5.0%.

We study the scaling properties of latent diffusion models (LDMs) with an emphasis on their sampling efficiency. While improved network architecture and inference algorithms have shown to effectively boost sampling efficiency of diffusion models, the role of model size -- a critical determinant of sampling efficiency -- has not been thoroughly examined. Through empirical analysis of established text-to-image diffusion models, we conduct an in-depth investigation into how model size influences sampling efficiency across varying sampling steps. Our findings unveil a surprising trend: when operating under a given inference budget, smaller models frequently outperform their larger equivalents in generating high-quality results. Moreover, we extend our study to demonstrate the generalizability of the these findings by applying various diffusion samplers, exploring diverse downstream tasks, evaluating post-distilled models, as well as comparing performance relative to training compute. These findings open up new pathways for the development of LDM scaling strategies which can be employed to enhance generative capabilities within limited inference budgets.

The success of the machine learning field has reliably depended on training on large datasets. While effective, this trend comes at an extraordinary cost. This is due to two deeply intertwined factors: the size of models and the size of datasets. While promising research efforts focus on reducing the size of models, the other half of the equation remains fairly mysterious. Indeed, it is surprising that the standard approach to training remains to iterate over and over, uniformly sampling the training dataset. In this paper we explore a series of alternative training paradigms that leverage insights from hard-data-mining and dropout, simple enough to implement and use that can become the new training standard. The proposed Progressive Data Dropout reduces the number of effective epochs to as little as 12.4% of the baseline. This savings actually do not come at any cost for accuracy. Surprisingly, the proposed method improves accuracy by up to 4.82%. Our approach requires no changes to model architecture or optimizer, and can be applied across standard training pipelines, thus posing an excellent opportunity for wide adoption. Code can be found here: https://github.com/bazyagami/LearningWithRevision

Major Internet advertising platforms offer budget pacing tools as a standard service for advertisers to manage their ad campaigns. Given the inherent non-stationarity in an advertiser's value and also competing advertisers' values over time, a commonly used approach is to learn a target expenditure plan that specifies a target spend as a function of time, and then run a controller that tracks this plan. This raises the question: how many historical samples are required to learn a good expenditure plan? We study this question by considering an advertiser repeatedly participating in T second-price auctions, where the tuple of her value and the highest competing bid is drawn from an unknown time-varying distribution. The advertiser seeks to maximize her total utility subject to her budget constraint. Prior work has shown the sufficiency of Tlog T samples per distribution to achieve the optimal O(T)-regret. We dramatically improve this state-of-the-art and show that just one sample per distribution is enough to achieve the near-optimal tilde O(T)-regret, while still being robust to noise in the sampling distributions.

The success of language models in code assistance has spurred the proposal of repository-level code completion as a means to enhance prediction accuracy, utilizing the context from the entire codebase. However, this amplified context can inadvertently increase inference latency, potentially undermining the developer experience and deterring tool adoption - a challenge we termed the Context-Latency Conundrum. This paper introduces REPOFUSE, a pioneering solution designed to enhance repository-level code completion without the latency trade-off. REPOFUSE uniquely fuses two types of context: the analogy context, rooted in code analogies, and the rationale context, which encompasses in-depth semantic relationships. We propose a novel rank truncated generation (RTG) technique that efficiently condenses these contexts into prompts with restricted size. This enables REPOFUSE to deliver precise code completions while maintaining inference efficiency. Through testing with the CrossCodeEval suite, REPOFUSE has demonstrated a significant leap over existing models, achieving a 40.90% to 59.75% increase in exact match (EM) accuracy for code completions and a 26.8% enhancement in inference speed. Beyond experimental validation, REPOFUSE has been integrated into the workflow of a large enterprise, where it actively supports various coding tasks.

By learning the gradient of smoothed data distributions, diffusion models can iteratively generate samples from complex distributions. The learned score function enables their generalization capabilities, but how the learned score relates to the score of the underlying data manifold remains largely unclear. Here, we aim to elucidate this relationship by comparing learned neural scores to the scores of two kinds of analytically tractable distributions: Gaussians and Gaussian mixtures. The simplicity of the Gaussian model makes it theoretically attractive, and we show that it admits a closed-form solution and predicts many qualitative aspects of sample generation dynamics. We claim that the learned neural score is dominated by its linear (Gaussian) approximation for moderate to high noise scales, and supply both theoretical and empirical arguments to support this claim. Moreover, the Gaussian approximation empirically works for a larger range of noise scales than naive theory suggests it should, and is preferentially learned early in training. At smaller noise scales, we observe that learned scores are better described by a coarse-grained (Gaussian mixture) approximation of training data than by the score of the training distribution, a finding consistent with generalization. Our findings enable us to precisely predict the initial phase of trained models' sampling trajectories through their Gaussian approximations. We show that this allows the skipping of the first 15-30% of sampling steps while maintaining high sample quality (with a near state-of-the-art FID score of 1.93 on CIFAR-10 unconditional generation). This forms the foundation of a novel hybrid sampling method, termed analytical teleportation, which can seamlessly integrate with and accelerate existing samplers, including DPM-Solver-v3 and UniPC. Our findings suggest ways to improve the design and training of diffusion models.

Diffusion probabilistic models (DPMs) have shown remarkable performance in visual synthesis but are computationally expensive due to the need for multiple evaluations during the sampling. Recent predictor-corrector diffusion samplers have significantly reduced the required number of function evaluations (NFE), but inherently suffer from a misalignment issue caused by the extra corrector step, especially with a large classifier-free guidance scale (CFG). In this paper, we introduce a new fast DPM sampler called DC-Solver, which leverages dynamic compensation (DC) to mitigate the misalignment of the predictor-corrector samplers. The dynamic compensation is controlled by compensation ratios that are adaptive to the sampling steps and can be optimized on only 10 datapoints by pushing the sampling trajectory toward a ground truth trajectory. We further propose a cascade polynomial regression (CPR) which can instantly predict the compensation ratios on unseen sampling configurations. Additionally, we find that the proposed dynamic compensation can also serve as a plug-and-play module to boost the performance of predictor-only samplers. Extensive experiments on both unconditional sampling and conditional sampling demonstrate that our DC-Solver can consistently improve the sampling quality over previous methods on different DPMs with a wide range of resolutions up to 1024times1024. Notably, we achieve 10.38 FID (NFE=5) on unconditional FFHQ and 0.394 MSE (NFE=5, CFG=7.5) on Stable-Diffusion-2.1. Code is available at https://github.com/wl-zhao/DC-Solver

Score distillation sampling (SDS) has shown great promise in text-to-3D generation by distilling pretrained large-scale text-to-image diffusion models, but suffers from over-saturation, over-smoothing, and low-diversity problems. In this work, we propose to model the 3D parameter as a random variable instead of a constant as in SDS and present variational score distillation (VSD), a principled particle-based variational framework to explain and address the aforementioned issues in text-to-3D generation. We show that SDS is a special case of VSD and leads to poor samples with both small and large CFG weights. In comparison, VSD works well with various CFG weights as ancestral sampling from diffusion models and simultaneously improves the diversity and sample quality with a common CFG weight (i.e., 7.5). We further present various improvements in the design space for text-to-3D such as distillation time schedule and density initialization, which are orthogonal to the distillation algorithm yet not well explored. Our overall approach, dubbed ProlificDreamer, can generate high rendering resolution (i.e., 512times512) and high-fidelity NeRF with rich structure and complex effects (e.g., smoke and drops). Further, initialized from NeRF, meshes fine-tuned by VSD are meticulously detailed and photo-realistic. Project page: https://ml.cs.tsinghua.edu.cn/prolificdreamer/

Data availability across domains often follows a long-tail distribution: a few domains have abundant data, while most face dat . a scarcity. This imbalance poses challenges in training language models uniformly across all domains. In our study, we focus on multilingual settings, where data sizes vary significantly between high- and low-resource languages. Common strategies to address this include upsampling low-resource languages (Temperature Sampling) or upweighting their loss (Scalarization). Although often considered equivalent, this assumption has not been proven, which motivates our study. Through both theoretical and empirical analysis, we identify the conditions under which these approaches are equivalent and when they diverge. Specifically, we demonstrate that these two methods are equivalent under full gradient descent, but this equivalence breaks down with stochastic gradient descent. Empirically, we observe that Temperature Sampling converges more quickly but is prone to overfitting. We argue that this faster convergence is likely due to the lower variance in gradient estimations, as shown theoretically. Based on these insights, we propose Cooldown, a strategy that reduces sampling temperature during training, accelerating convergence without overfitting to low-resource languages. Our method is competitive with existing data re-weighting and offers computational efficiency.

One of the most profound challenges of modern machine learning is performing well on the long-tail of rare and underrepresented features. Large general-purpose models are trained for many tasks, but work best on high-frequency use cases. After training, it is hard to adapt a model to perform well on specific use cases underrepresented in the training corpus. Relying on prompt engineering or few-shot examples to maximize the output quality on a particular test case can be frustrating, as models can be highly sensitive to small changes, react in unpredicted ways or rely on a fixed system prompt for maintaining performance. In this work, we ask: "Can we optimize our training protocols to both improve controllability and performance on underrepresented use cases at inference time?" We revisit the divide between training and inference techniques to improve long-tail performance while providing users with a set of control levers the model is trained to be responsive to. We create a detailed taxonomy of data characteristics and task provenance to explicitly control generation attributes and implicitly condition generations at inference time. We fine-tune a base model to infer these markers automatically, which makes them optional at inference time. This principled and flexible approach yields pronounced improvements in performance, especially on examples from the long tail of the training distribution. While we observe an average lift of 5.7% win rates in open-ended generation quality with our markers, we see over 9.1% gains in underrepresented domains. We also observe relative lifts of up to 14.1% on underrepresented tasks like CodeRepair and absolute improvements of 35.3% on length instruction following evaluations.

Diffusion and flow-matching models achieve remarkable generative performance but at the cost of many sampling steps, this slows inference and limits applicability to time-critical tasks. The ReFlow procedure can accelerate sampling by straightening generation trajectories. However, ReFlow is an iterative procedure, typically requiring training on simulated data, and results in reduced sample quality. To mitigate sample deterioration, we examine the design space of ReFlow and highlight potential pitfalls in prior heuristic practices. We then propose seven improvements for training dynamics, learning and inference, which are verified with thorough ablation studies on CIFAR10 32 times 32, AFHQv2 64 times 64, and FFHQ 64 times 64. Combining all our techniques, we achieve state-of-the-art FID scores (without / with guidance, resp.) for fast generation via neural ODEs: 2.23 / 1.98 on CIFAR10, 2.30 / 1.91 on AFHQv2, 2.84 / 2.67 on FFHQ, and 3.49 / 1.74 on ImageNet-64, all with merely 9 neural function evaluations.

Diffusion distillation models effectively accelerate reverse sampling by compressing the process into fewer steps. However, these models still exhibit a performance gap compared to their pre-trained diffusion model counterparts, exacerbated by distribution shifts and accumulated errors during multi-step sampling. To address this, we introduce Distillation++, a novel inference-time distillation framework that reduces this gap by incorporating teacher-guided refinement during sampling. Inspired by recent advances in conditional sampling, our approach recasts student model sampling as a proximal optimization problem with a score distillation sampling loss (SDS). To this end, we integrate distillation optimization during reverse sampling, which can be viewed as teacher guidance that drives student sampling trajectory towards the clean manifold using pre-trained diffusion models. Thus, Distillation++ improves the denoising process in real-time without additional source data or fine-tuning. Distillation++ demonstrates substantial improvements over state-of-the-art distillation baselines, particularly in early sampling stages, positioning itself as a robust guided sampling process crafted for diffusion distillation models. Code: https://github.com/geonyeong-park/inference_distillation.

Scaling test-time compute is crucial for enhancing the reasoning capabilities of large language models (LLMs). Existing approaches typically employ reinforcement learning (RL) to maximize a verifiable reward obtained at the end of reasoning traces. However, such methods optimize only the final performance under a large and fixed token budget, which hinders efficiency in both training and deployment. In this work, we present a novel framework, AnytimeReasoner, to optimize anytime reasoning performance, which aims to improve token efficiency and the flexibility of reasoning under varying token budget constraints. To achieve this, we truncate the complete thinking process to fit within sampled token budgets from a prior distribution, compelling the model to summarize the optimal answer for each truncated thinking for verification. This introduces verifiable dense rewards into the reasoning process, facilitating more effective credit assignment in RL optimization. We then optimize the thinking and summary policies in a decoupled manner to maximize the cumulative reward. Additionally, we introduce a novel variance reduction technique, Budget Relative Policy Optimization (BRPO), to enhance the robustness and efficiency of the learning process when reinforcing the thinking policy. Empirical results in mathematical reasoning tasks demonstrate that our method consistently outperforms GRPO across all thinking budgets under various prior distributions, enhancing both training and token efficiency.

While data are the primary fuel for machine learning models, they often suffer from missing values, especially when collected in real-world scenarios. However, many off-the-shelf machine learning models, including artificial neural network models, are unable to handle these missing values directly. Therefore, extra data preprocessing and curation steps, such as data imputation, are inevitable before learning and prediction processes. In this study, we propose a simple and intuitive yet effective method for pruning missing values (PROMISSING) during learning and inference steps in neural networks. In this method, there is no need to remove or impute the missing values; instead, the missing values are treated as a new source of information (representing what we do not know). Our experiments on simulated data, several classification and regression benchmarks, and a multi-modal clinical dataset show that PROMISSING results in similar prediction performance compared to various imputation techniques. In addition, our experiments show models trained using PROMISSING techniques are becoming less decisive in their predictions when facing incomplete samples with many unknowns. This finding hopefully advances machine learning models from being pure predicting machines to more realistic thinkers that can also say "I do not know" when facing incomplete sources of information.

Diffusion models have been widely adopted in image and video generation. However, their complex network architecture leads to high inference overhead for its generation process. Existing diffusion quantization methods primarily focus on the quantization of the model structure while ignoring the impact of time-steps variation during sampling. At the same time, most current approaches fail to account for significant activations that cannot be eliminated, resulting in substantial performance degradation after quantization. To address these issues, we propose Time-Rotation Diffusion Quantization (TR-DQ), a novel quantization method incorporating time-step and rotation-based optimization. TR-DQ first divides the sampling process based on time-steps and applies a rotation matrix to smooth activations and weights dynamically. For different time-steps, a dedicated hyperparameter is introduced for adaptive timing modeling, which enables dynamic quantization across different time steps. Additionally, we also explore the compression potential of Classifier-Free Guidance (CFG-wise) to establish a foundation for subsequent work. TR-DQ achieves state-of-the-art (SOTA) performance on image generation and video generation tasks and a 1.38-1.89x speedup and 1.97-2.58x memory reduction in inference compared to existing quantization methods.

We develop a framework for non-asymptotic analysis of deterministic samplers used for diffusion generative modeling. Several recent works have analyzed stochastic samplers using tools like Girsanov's theorem and a chain rule variant of the interpolation argument. Unfortunately, these techniques give vacuous bounds when applied to deterministic samplers. We give a new operational interpretation for deterministic sampling by showing that one step along the probability flow ODE can be expressed as two steps: 1) a restoration step that runs gradient ascent on the conditional log-likelihood at some infinitesimally previous time, and 2) a degradation step that runs the forward process using noise pointing back towards the current iterate. This perspective allows us to extend denoising diffusion implicit models to general, non-linear forward processes. We then develop the first polynomial convergence bounds for these samplers under mild conditions on the data distribution.

We propose Delta L Normalization, a simple yet effective loss aggregation method tailored to the characteristic of dynamic generation lengths in Reinforcement Learning with Verifiable Rewards (RLVR). Recently, RLVR has demonstrated strong potential in improving the reasoning capabilities of large language models (LLMs), but a major challenge lies in the large variability of response lengths during training, which leads to high gradient variance and unstable optimization. Although previous methods such as GRPO, DAPO, and Dr. GRPO introduce different loss normalization terms to address this issue, they either produce biased estimates or still suffer from high gradient variance. By analyzing the effect of varying lengths on policy loss both theoretically and empirically, we reformulate the problem as finding a minimum-variance unbiased estimator. Our proposed Delta L Normalization not only provides an unbiased estimate of the true policy loss but also minimizes gradient variance in theory. Extensive experiments show that it consistently achieves superior results across different model sizes, maximum lengths, and tasks. Our code will be made public at https://github.com/zerolllin/Delta-L-Normalization.

Sampling from diffusion probabilistic models (DPMs) is often expensive for high-quality image generation and typically requires many steps with a large model. In this paper, we introduce sampling Trajectory Stitching T-Stitch, a simple yet efficient technique to improve the sampling efficiency with little or no generation degradation. Instead of solely using a large DPM for the entire sampling trajectory, T-Stitch first leverages a smaller DPM in the initial steps as a cheap drop-in replacement of the larger DPM and switches to the larger DPM at a later stage. Our key insight is that different diffusion models learn similar encodings under the same training data distribution and smaller models are capable of generating good global structures in the early steps. Extensive experiments demonstrate that T-Stitch is training-free, generally applicable for different architectures, and complements most existing fast sampling techniques with flexible speed and quality trade-offs. On DiT-XL, for example, 40% of the early timesteps can be safely replaced with a 10x faster DiT-S without performance drop on class-conditional ImageNet generation. We further show that our method can also be used as a drop-in technique to not only accelerate the popular pretrained stable diffusion (SD) models but also improve the prompt alignment of stylized SD models from the public model zoo. Code is released at https://github.com/NVlabs/T-Stitch

The goal of data attribution is to trace model predictions back to training data. Despite a long line of work towards this goal, existing approaches to data attribution tend to force users to choose between computational tractability and efficacy. That is, computationally tractable methods can struggle with accurately attributing model predictions in non-convex settings (e.g., in the context of deep neural networks), while methods that are effective in such regimes require training thousands of models, which makes them impractical for large models or datasets. In this work, we introduce TRAK (Tracing with the Randomly-projected After Kernel), a data attribution method that is both effective and computationally tractable for large-scale, differentiable models. In particular, by leveraging only a handful of trained models, TRAK can match the performance of attribution methods that require training thousands of models. We demonstrate the utility of TRAK across various modalities and scales: image classifiers trained on ImageNet, vision-language models (CLIP), and language models (BERT and mT5). We provide code for using TRAK (and reproducing our work) at https://github.com/MadryLab/trak .

Diffusion Probabilistic Models (DPM) have shown remarkable efficacy in the synthesis of high-quality images. However, their inference process characteristically requires numerous, potentially hundreds, of iterative steps, which could exaggerate the problem of exposure bias due to the training and inference discrepancy. Previous work has attempted to mitigate this issue by perturbing inputs during training, which consequently mandates the retraining of the DPM. In this work, we conduct a systematic study of exposure bias in DPM and, intriguingly, we find that the exposure bias could be alleviated with a novel sampling method that we propose, without retraining the model. We empirically and theoretically show that, during inference, for each backward time step t and corresponding state x_t, there might exist another time step t_s which exhibits superior coupling with x_t. Based on this finding, we introduce a sampling method named Time-Shift Sampler. Our framework can be seamlessly integrated to existing sampling algorithms, such as DDPM, DDIM and other high-order solvers, inducing merely minimal additional computations. Experimental results show our method brings significant and consistent improvements in FID scores on different datasets and sampling methods. For example, integrating Time-Shift Sampler to F-PNDM yields a FID=3.88, achieving 44.49\% improvements as compared to F-PNDM, on CIFAR-10 with 10 sampling steps, which is more performant than the vanilla DDIM with 100 sampling steps. Our code is available at https://github.com/Mingxiao-Li/TS-DPM.

We present a novel quasi-Monte Carlo mechanism to improve graph-based sampling, coined repelling random walks. By inducing correlations between the trajectories of an interacting ensemble such that their marginal transition probabilities are unmodified, we are able to explore the graph more efficiently, improving the concentration of statistical estimators whilst leaving them unbiased. The mechanism has a trivial drop-in implementation. We showcase the effectiveness of repelling random walks in a range of settings including estimation of graph kernels, the PageRank vector and graphlet concentrations. We provide detailed experimental evaluation and robust theoretical guarantees. To our knowledge, repelling random walks constitute the first rigorously studied quasi-Monte Carlo scheme correlating the directions of walkers on a graph, inviting new research in this exciting nascent domain.

The rapid development of large-scale text-to-speech (TTS) models has led to significant advancements in modeling diverse speaker prosody and voices. However, these models often face issues such as slow inference speeds, reliance on complex pre-trained neural codec representations, and difficulties in achieving naturalness and high similarity to reference speakers. To address these challenges, this work introduces StyleTTS-ZS, an efficient zero-shot TTS model that leverages distilled time-varying style diffusion to capture diverse speaker identities and prosodies. We propose a novel approach that represents human speech using input text and fixed-length time-varying discrete style codes to capture diverse prosodic variations, trained adversarially with multi-modal discriminators. A diffusion model is then built to sample this time-varying style code for efficient latent diffusion. Using classifier-free guidance, StyleTTS-ZS achieves high similarity to the reference speaker in the style diffusion process. Furthermore, to expedite sampling, the style diffusion model is distilled with perceptual loss using only 10k samples, maintaining speech quality and similarity while reducing inference speed by 90%. Our model surpasses previous state-of-the-art large-scale zero-shot TTS models in both naturalness and similarity, offering a 10-20 faster sampling speed, making it an attractive alternative for efficient large-scale zero-shot TTS systems. The audio demo, code and models are available at https://styletts-zs.github.io/.

We introduce ensembles within score-based sampling methods to develop gradient-free approximate sampling techniques that leverage the collective dynamics of particle ensembles to compute approximate reverse diffusion drifts. We introduce the underlying methodology, emphasizing its relationship with generative diffusion models and the previously introduced F\"ollmer sampler. We demonstrate the efficacy of ensemble strategies through various examples, ranging from low- to medium-dimensionality sampling problems, including multi-modal and highly non-Gaussian probability distributions, and provide comparisons to traditional methods like NUTS. Our findings highlight the potential of ensemble strategies for modeling complex probability distributions in situations where gradients are unavailable. Finally, we showcase its application in the context of Bayesian inversion problems within the geophysical sciences.

Long-form generation is crucial for academic writing papers and repo-level code generation. Despite this, current models, including GPT-4o, still exhibit unsatisfactory performance. Existing methods that utilize preference learning with outcome supervision often fail to provide detailed feedback for extended contexts. This shortcoming can lead to content that does not fully satisfy query requirements, resulting in issues like length deviations, and diminished quality. In this paper, we propose enhancing long-form generation by incorporating process supervision. We employ Monte Carlo Tree Search to gather stepwise preference pairs, utilizing a global memory pool to maintain consistency. To address the issue of suboptimal candidate selection, we integrate external critiques to refine and improve the quality of the preference pairs. Finally, we apply step-level DPO using the collected stepwise preference pairs. Experimental results show that our method improves length and quality on long-form generation benchmarks, with almost lossless performance on general benchmarks across various model backbones.

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

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

Guided sampling is a vital approach for applying diffusion models in real-world tasks that embeds human-defined guidance during the sampling procedure. This paper considers a general setting where the guidance is defined by an (unnormalized) energy function. The main challenge for this setting is that the intermediate guidance during the diffusion sampling procedure, which is jointly defined by the sampling distribution and the energy function, is unknown and is hard to estimate. To address this challenge, we propose an exact formulation of the intermediate guidance as well as a novel training objective named contrastive energy prediction (CEP) to learn the exact guidance. Our method is guaranteed to converge to the exact guidance under unlimited model capacity and data samples, while previous methods can not. We demonstrate the effectiveness of our method by applying it to offline reinforcement learning (RL). Extensive experiments on D4RL benchmarks demonstrate that our method outperforms existing state-of-the-art algorithms. We also provide some examples of applying CEP for image synthesis to demonstrate the scalability of CEP on high-dimensional data.

In recent years, there have been remarkable advancements in the performance of Transformer-based Large Language Models (LLMs) across various domains. As these LLMs are deployed for increasingly complex tasks, they often face the needs to conduct longer reasoning processes or understanding larger contexts. In these situations, the length generalization failure of LLMs on long sequences become more prominent. Most pre-training schemes truncate training sequences to a fixed length (such as 2048 for LLaMa). LLMs often struggle to generate fluent texts, let alone carry out downstream tasks, after longer contexts, even with relative positional encoding which is designed to cope with this problem. Common solutions such as finetuning on longer corpora often involves daunting hardware and time costs and requires careful training process design. To more efficiently leverage the generation capacity of existing LLMs, we theoretically and empirically investigate the main out-of-distribution (OOD) factors contributing to this problem. Inspired by this diagnosis, we propose a simple yet effective solution for on-the-fly length generalization, LM-Infinite, which involves only a Lambda-shaped attention mask and a distance limit while requiring no parameter updates or learning. We find it applicable to a variety of LLMs using relative-position encoding methods. LM-Infinite is computational efficient with O(n) time and space, and demonstrates consistent fluency and generation quality to as long as 32k tokens on ArXiv and OpenWebText2 datasets, with 2.72x decoding speedup. On downstream task such as passkey retrieval, it continues to work on inputs much longer than training lengths where vanilla models fail immediately.

Inspired by the principle of deliberate practice in human learning, we propose Deliberate Practice for Synthetic Data Generation (DP), a novel framework that improves sample efficiency through dynamic synthetic data generation. Prior work has shown that scaling synthetic data is inherently challenging, as naively adding new data leads to diminishing returns. To address this, pruning has been identified as a key mechanism for improving scaling, enabling models to focus on the most informative synthetic samples. Rather than generating a large dataset and pruning it afterward, DP efficiently approximates the direct generation of informative samples. We theoretically show how training on challenging, informative examples improves scaling laws and empirically validate that DP achieves better scaling performance with significantly fewer training samples and iterations. On ImageNet-100, DP generates 3.4x fewer samples and requires six times fewer iterations, while on ImageNet-1k, it generates 8x fewer samples with a 30 percent reduction in iterations, all while achieving superior performance compared to prior work.

Despite the remarkable success of diffusion models in image generation, slow sampling remains a persistent issue. To accelerate the sampling process, prior studies have reformulated diffusion sampling as an ODE/SDE and introduced higher-order numerical methods. However, these methods often produce divergence artifacts, especially with a low number of sampling steps, which limits the achievable acceleration. In this paper, we investigate the potential causes of these artifacts and suggest that the small stability regions of these methods could be the principal cause. To address this issue, we propose two novel techniques. The first technique involves the incorporation of Heavy Ball (HB) momentum, a well-known technique for improving optimization, into existing diffusion numerical methods to expand their stability regions. We also prove that the resulting methods have first-order convergence. The second technique, called Generalized Heavy Ball (GHVB), constructs a new high-order method that offers a variable trade-off between accuracy and artifact suppression. Experimental results show that our techniques are highly effective in reducing artifacts and improving image quality, surpassing state-of-the-art diffusion solvers on both pixel-based and latent-based diffusion models for low-step sampling. Our research provides novel insights into the design of numerical methods for future diffusion work.

The Multi-armed bandit offer the advantage to learn and exploit the already learnt knowledge at the same time. This capability allows this approach to be applied in different domains, going from clinical trials where the goal is investigating the effects of different experimental treatments while minimizing patient losses, to adaptive routing where the goal is to minimize the delays in a network. This article provides a review of the recent results on applying bandit to real-life scenario and summarize the state of the art for each of these fields. Different techniques has been proposed to solve this problem setting, like epsilon-greedy, Upper confident bound (UCB) and Thompson Sampling (TS). We are showing here how this algorithms were adapted to solve the different problems of exploration exploitation.

We propose TR0N, a highly general framework to turn pre-trained unconditional generative models, such as GANs and VAEs, into conditional models. The conditioning can be highly arbitrary, and requires only a pre-trained auxiliary model. For example, we show how to turn unconditional models into class-conditional ones with the help of a classifier, and also into text-to-image models by leveraging CLIP. TR0N learns a lightweight stochastic mapping which "translates" between the space of conditions and the latent space of the generative model, in such a way that the generated latent corresponds to a data sample satisfying the desired condition. The translated latent samples are then further improved upon through Langevin dynamics, enabling us to obtain higher-quality data samples. TR0N requires no training data nor fine-tuning, yet can achieve a zero-shot FID of 10.9 on MS-COCO, outperforming competing alternatives not only on this metric, but also in sampling speed -- all while retaining a much higher level of generality. Our code is available at https://github.com/layer6ai-labs/tr0n.

Diffusion models have achieved remarkable success in text-to-image generation. However, their practical applications are hindered by the misalignment between generated images and corresponding text prompts. To tackle this issue, reinforcement learning (RL) has been considered for diffusion model fine-tuning. Yet, RL's effectiveness is limited by the challenge of sparse reward, where feedback is only available at the end of the generation process. This makes it difficult to identify which actions during the denoising process contribute positively to the final generated image, potentially leading to ineffective or unnecessary denoising policies. To this end, this paper presents a novel RL-based framework that addresses the sparse reward problem when training diffusion models. Our framework, named B^2-DiffuRL, employs two strategies: Backward progressive training and Branch-based sampling. For one thing, backward progressive training focuses initially on the final timesteps of denoising process and gradually extends the training interval to earlier timesteps, easing the learning difficulty from sparse rewards. For another, we perform branch-based sampling for each training interval. By comparing the samples within the same branch, we can identify how much the policies of the current training interval contribute to the final image, which helps to learn effective policies instead of unnecessary ones. B^2-DiffuRL is compatible with existing optimization algorithms. Extensive experiments demonstrate the effectiveness of B^2-DiffuRL in improving prompt-image alignment and maintaining diversity in generated images. The code for this work is available.

For learning with noisy labels, the transition matrix, which explicitly models the relation between noisy label distribution and clean label distribution, has been utilized to achieve the statistical consistency of either the classifier or the risk. Previous researches have focused more on how to estimate this transition matrix well, rather than how to utilize it. We propose good utilization of the transition matrix is crucial and suggest a new utilization method based on resampling, coined RENT. Specifically, we first demonstrate current utilizations can have potential limitations for implementation. As an extension to Reweighting, we suggest the Dirichlet distribution-based per-sample Weight Sampling (DWS) framework, and compare reweighting and resampling under DWS framework. With the analyses from DWS, we propose RENT, a REsampling method with Noise Transition matrix. Empirically, RENT consistently outperforms existing transition matrix utilization methods, which includes reweighting, on various benchmark datasets. Our code is available at https://github.com/BaeHeeSun/RENT.

We present a faster algorithm to generate a warm start for sampling an arbitrary logconcave density specified by an evaluation oracle, leading to the first sub-cubic sampling algorithms for inputs in (near-)isotropic position. A long line of prior work incurred a warm-start penalty of at least linear in the dimension, hitting a cubic barrier, even for the special case of uniform sampling from convex bodies. Our improvement relies on two key ingredients of independent interest. (1) We show how to sample given a warm start in weaker notions of distance, in particular q-R\'enyi divergence for q=mathcal{O}(1), whereas previous analyses required stringent infty-R\'enyi divergence (with the exception of Hit-and-Run, whose known mixing time is higher). This marks the first improvement in the required warmness since Lov\'asz and Simonovits (1991). (2) We refine and generalize the log-Sobolev inequality of Lee and Vempala (2018), originally established for isotropic logconcave distributions in terms of the diameter of the support, to logconcave distributions in terms of a geometric average of the support diameter and the largest eigenvalue of the covariance matrix.

Model pruning seeks to induce sparsity in a deep neural network's various connection matrices, thereby reducing the number of nonzero-valued parameters in the model. Recent reports (Han et al., 2015; Narang et al., 2017) prune deep networks at the cost of only a marginal loss in accuracy and achieve a sizable reduction in model size. This hints at the possibility that the baseline models in these experiments are perhaps severely over-parameterized at the outset and a viable alternative for model compression might be to simply reduce the number of hidden units while maintaining the model's dense connection structure, exposing a similar trade-off in model size and accuracy. We investigate these two distinct paths for model compression within the context of energy-efficient inference in resource-constrained environments and propose a new gradual pruning technique that is simple and straightforward to apply across a variety of models/datasets with minimal tuning and can be seamlessly incorporated within the training process. We compare the accuracy of large, but pruned models (large-sparse) and their smaller, but dense (small-dense) counterparts with identical memory footprint. Across a broad range of neural network architectures (deep CNNs, stacked LSTM, and seq2seq LSTM models), we find large-sparse models to consistently outperform small-dense models and achieve up to 10x reduction in number of non-zero parameters with minimal loss in accuracy.

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.

Diffusion models have achieved remarkable success across various domains. However, their slow generation speed remains a critical challenge. Existing acceleration methods, while aiming to reduce steps, often compromise sample quality, controllability, or introduce training complexities. Therefore, we propose RayFlow, a novel diffusion framework that addresses these limitations. Unlike previous methods, RayFlow guides each sample along a unique path towards an instance-specific target distribution. This method minimizes sampling steps while preserving generation diversity and stability. Furthermore, we introduce Time Sampler, an importance sampling technique to enhance training efficiency by focusing on crucial timesteps. Extensive experiments demonstrate RayFlow's superiority in generating high-quality images with improved speed, control, and training efficiency compared to existing acceleration techniques.

Image generation models have achieved widespread applications. As an instance, the TarFlow model combines the transformer architecture with Normalizing Flow models, achieving state-of-the-art results on multiple benchmarks. However, due to the causal form of attention requiring sequential computation, TarFlow's sampling process is extremely slow. In this paper, we demonstrate that through a series of optimization strategies, TarFlow sampling can be greatly accelerated by using the Gauss-Seidel-Jacobi (abbreviated as GS-Jacobi) iteration method. Specifically, we find that blocks in the TarFlow model have varying importance: a small number of blocks play a major role in image generation tasks, while other blocks contribute relatively little; some blocks are sensitive to initial values and prone to numerical overflow, while others are relatively robust. Based on these two characteristics, we propose the Convergence Ranking Metric (CRM) and the Initial Guessing Metric (IGM): CRM is used to identify whether a TarFlow block is "simple" (converges in few iterations) or "tough" (requires more iterations); IGM is used to evaluate whether the initial value of the iteration is good. Experiments on four TarFlow models demonstrate that GS-Jacobi sampling can significantly enhance sampling efficiency while maintaining the quality of generated images (measured by FID), achieving speed-ups of 4.53x in Img128cond, 5.32x in AFHQ, 2.96x in Img64uncond, and 2.51x in Img64cond without degrading FID scores or sample quality. Code and checkpoints are accessible on https://github.com/encoreus/GS-Jacobi_for_TarFlow

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.

BACKGROUND: Radiology reports are typically written in a free-text format, making clinical information difficult to extract and use. Recently the adoption of structured reporting (SR) has been recommended by various medical societies thanks to the advantages it offers, e.g. standardization, completeness and information retrieval. We propose a pipeline to extract information from free-text radiology reports, that fits with the items of the reference SR registry proposed by a national society of interventional and medical radiology, focusing on CT staging of patients with lymphoma. METHODS: Our work aims to leverage the potential of Natural Language Processing (NLP) and Transformer-based models to deal with automatic SR registry filling. With the availability of 174 radiology reports, we investigate a rule-free generative Question Answering approach based on a domain-specific version of T5 (IT5). Two strategies (batch-truncation and ex-post combination) are implemented to comply with the model's context length limitations. Performance is evaluated in terms of strict accuracy, F1, and format accuracy, and compared with the widely used GPT-3.5 Large Language Model. A 5-point Likert scale questionnaire is used to collect human-expert feedback on the similarity between medical annotations and generated answers. RESULTS: The combination of fine-tuning and batch splitting allows IT5 to achieve notable results; it performs on par with GPT-3.5 albeit its size being a thousand times smaller in terms of parameters. Human-based assessment scores show a high correlation (Spearman's correlation coefficients>0.88, p-values<0.001) with AI performance metrics (F1) and confirm the superior ability of LLMs (i.e., GPT-3.5, 175B of parameters) in generating plausible human-like statements.

LLM inference often generates a batch of candidates for a prompt and selects one via strategies like majority voting or Best-of- N (BoN). For difficult tasks, this single-shot selection often underperforms. Consequently, evaluations commonly report Pass@k: the agent may submit up to k responses, and only the best of them is used when computing regret. Motivated by this, we study inference scaling in the more general Pass@k inference setting, and prove that neither majority voting nor BoN exhibits the desirable scaling with k and the sampling budget N. Combining the advantages of majority voting and BoN, we propose a new inference strategy called Best-of-Majority (BoM), with a pivotal step that restricts the candidates to the responses with high frequency in the N samples before selecting the top-k rewards. We prove that when the sampling budget is N=tildeOmega(C^*), the regret of BoM is O(epsilon_{opt}+epsilon_{mathrm{RM}^2C^*/k}), where C^* is the coverage coefficient, epsilon_{RM} is the estimation error of the reward model, and epsilon_{opt} is the estimation error of reward at the optimal response. We further establish a matching lower bound, certifying that our algorithm is minimax optimal. Beyond optimality, BoM has a key advantage: unlike majority voting and BoN, its performance does not degrade when increasing N. Experimental results of inference on math problems show BoM outperforming both majority voting and BoN.

With the proliferation of domain-specific models, model merging has emerged as a set of techniques that combine the capabilities of multiple models into one that can multitask without the cost of additional training. In this paper, we propose a new model merging technique, Drop and rEscaLe via sampLing with mAgnitude (DELLA-Merging), that employs a novel pruning technique, MAGPRUNE, which shows significant advantages over DARE and TIES. MAGPRUNE first ranks the parameters in order of their magnitude and assigns higher dropout probabilities (p) to parameters with lower ranks corresponding to lower magnitudes. To approximate the original embeddings, MAGPRUNE employs a rescaling operation on the parameters that survive the random dropping by 1/(1 - p). On three different expert models considered for merging (LM, Math, Code) and corresponding benchmark datasets (AlpacaEval, GSM8K, MBPP), DELLA shows an average improvement of 2.4 points over baseline methods employing delta parameter pruning (an improvement of 3.6 points over TIES, 1.2 points over DARE), and 11.1 points over the no-pruning baseline (TA). We release the source code at: https://github.com/declare-lab/della.

Flow-based generative models have been employed for sampling the Boltzmann distribution, but their application to high-dimensional systems is hindered by the significant computational cost of obtaining the Jacobian of the flow. To overcome this challenge, we introduce the flow perturbation method, which incorporates optimized stochastic perturbations into the flow. By reweighting trajectories generated by the perturbed flow, our method achieves unbiased sampling of the Boltzmann distribution with orders of magnitude speedup compared to both brute force Jacobian calculations and the Hutchinson estimator. Notably, it accurately sampled the Chignolin protein with all atomic Cartesian coordinates explicitly represented, which, to our best knowledge, is the largest molecule ever Boltzmann sampled in such detail using generative models.

We present a trainable framework for efficiently generating gauge configurations, and discuss ongoing work in this direction. In particular, we consider the problem of sampling configurations from a 4D SU(3) lattice gauge theory, and consider a generalized leapfrog integrator in the molecular dynamics update that can be trained to improve sampling efficiency. Code is available online at https://github.com/saforem2/l2hmc-qcd.

While diffusion models can learn complex distributions, sampling requires a computationally expensive iterative process. Existing distillation methods enable efficient sampling, but have notable limitations, such as performance degradation with very few sampling steps, reliance on training data access, or mode-seeking optimization that may fail to capture the full distribution. We propose EM Distillation (EMD), a maximum likelihood-based approach that distills a diffusion model to a one-step generator model with minimal loss of perceptual quality. Our approach is derived through the lens of Expectation-Maximization (EM), where the generator parameters are updated using samples from the joint distribution of the diffusion teacher prior and inferred generator latents. We develop a reparametrized sampling scheme and a noise cancellation technique that together stabilizes the distillation process. We further reveal an interesting connection of our method with existing methods that minimize mode-seeking KL. EMD outperforms existing one-step generative methods in terms of FID scores on ImageNet-64 and ImageNet-128, and compares favorably with prior work on distilling text-to-image diffusion models.

Score distillation sampling (SDS) and its variants have greatly boosted the development of text-to-3D generation, but are vulnerable to geometry collapse and poor textures yet. To solve this issue, we first deeply analyze the SDS and find that its distillation sampling process indeed corresponds to the trajectory sampling of a stochastic differential equation (SDE): SDS samples along an SDE trajectory to yield a less noisy sample which then serves as a guidance to optimize a 3D model. However, the randomness in SDE sampling often leads to a diverse and unpredictable sample which is not always less noisy, and thus is not a consistently correct guidance, explaining the vulnerability of SDS. Since for any SDE, there always exists an ordinary differential equation (ODE) whose trajectory sampling can deterministically and consistently converge to the desired target point as the SDE, we propose a novel and effective "Consistent3D" method that explores the ODE deterministic sampling prior for text-to-3D generation. Specifically, at each training iteration, given a rendered image by a 3D model, we first estimate its desired 3D score function by a pre-trained 2D diffusion model, and build an ODE for trajectory sampling. Next, we design a consistency distillation sampling loss which samples along the ODE trajectory to generate two adjacent samples and uses the less noisy sample to guide another more noisy one for distilling the deterministic prior into the 3D model. Experimental results show the efficacy of our Consistent3D in generating high-fidelity and diverse 3D objects and large-scale scenes, as shown in Fig. 1. The codes are available at https://github.com/sail-sg/Consistent3D.

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

We develop a method to generate predictive regions that cover a multivariate response variable with a user-specified probability. Our work is composed of two components. First, we use a deep generative model to learn a representation of the response that has a unimodal distribution. Existing multiple-output quantile regression approaches are effective in such cases, so we apply them on the learned representation, and then transform the solution to the original space of the response. This process results in a flexible and informative region that can have an arbitrary shape, a property that existing methods lack. Second, we propose an extension of conformal prediction to the multivariate response setting that modifies any method to return sets with a pre-specified coverage level. The desired coverage is theoretically guaranteed in the finite-sample case for any distribution. Experiments conducted on both real and synthetic data show that our method constructs regions that are significantly smaller compared to existing techniques.

As the vocabulary size of modern word-based language models becomes ever larger, many sampling-based training criteria are proposed and investigated. The essence of these sampling methods is that the softmax-related traversal over the entire vocabulary can be simplified, giving speedups compared to the baseline. A problem we notice about the current landscape of such sampling methods is the lack of a systematic comparison and some myths about preferring one over another. In this work, we consider Monte Carlo sampling, importance sampling, a novel method we call compensated partial summation, and noise contrastive estimation. Linking back to the three traditional criteria, namely mean squared error, binary cross-entropy, and cross-entropy, we derive the theoretical solutions to the training problems. Contrary to some common belief, we show that all these sampling methods can perform equally well, as long as we correct for the intended class posterior probabilities. Experimental results in language modeling and automatic speech recognition on Switchboard and LibriSpeech support our claim, with all sampling-based methods showing similar perplexities and word error rates while giving the expected speedups.

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.

Diffusion or flow-based models are powerful generative paradigms that are notoriously hard to sample as samples are defined as solutions to high-dimensional Ordinary or Stochastic Differential Equations (ODEs/SDEs) which require a large Number of Function Evaluations (NFE) to approximate well. Existing methods to alleviate the costly sampling process include model distillation and designing dedicated ODE solvers. However, distillation is costly to train and sometimes can deteriorate quality, while dedicated solvers still require relatively large NFE to produce high quality samples. In this paper we introduce "Bespoke solvers", a novel framework for constructing custom ODE solvers tailored to the ODE of a given pre-trained flow model. Our approach optimizes an order consistent and parameter-efficient solver (e.g., with 80 learnable parameters), is trained for roughly 1% of the GPU time required for training the pre-trained model, and significantly improves approximation and generation quality compared to dedicated solvers. For example, a Bespoke solver for a CIFAR10 model produces samples with Fr\'echet Inception Distance (FID) of 2.73 with 10 NFE, and gets to 1% of the Ground Truth (GT) FID (2.59) for this model with only 20 NFE. On the more challenging ImageNet-64times64, Bespoke samples at 2.2 FID with 10 NFE, and gets within 2% of GT FID (1.71) with 20 NFE.

This article considers the popular MCMC method of unadjusted Langevin Monte Carlo (LMC) and provides a non-asymptotic analysis of its sampling error in 2-Wasserstein distance. The proof is based on a refinement of mean-square analysis in Li et al. (2019), and this refined framework automates the analysis of a large class of sampling algorithms based on discretizations of contractive SDEs. Using this framework, we establish an O(d/epsilon) mixing time bound for LMC, without warm start, under the common log-smooth and log-strongly-convex conditions, plus a growth condition on the 3rd-order derivative of the potential of target measures. This bound improves the best previously known O(d/epsilon) result and is optimal (in terms of order) in both dimension d and accuracy tolerance epsilon for target measures satisfying the aforementioned assumptions. Our theoretical analysis is further validated by numerical experiments.

Variational inference using the reparameterization trick has enabled large-scale approximate Bayesian inference in complex probabilistic models, leveraging stochastic optimization to sidestep intractable expectations. The reparameterization trick is applicable when we can simulate a random variable by applying a differentiable deterministic function on an auxiliary random variable whose distribution is fixed. For many distributions of interest (such as the gamma or Dirichlet), simulation of random variables relies on acceptance-rejection sampling. The discontinuity introduced by the accept-reject step means that standard reparameterization tricks are not applicable. We propose a new method that lets us leverage reparameterization gradients even when variables are outputs of a acceptance-rejection sampling algorithm. Our approach enables reparameterization on a larger class of variational distributions. In several studies of real and synthetic data, we show that the variance of the estimator of the gradient is significantly lower than other state-of-the-art methods. This leads to faster convergence of stochastic gradient variational inference.

We advance the study of incentivized bandit exploration, in which arm choices are viewed as recommendations and are required to be Bayesian incentive compatible. Recent work has shown under certain independence assumptions that after collecting enough initial samples, the popular Thompson sampling algorithm becomes incentive compatible. We give an analog of this result for linear bandits, where the independence of the prior is replaced by a natural convexity condition. This opens up the possibility of efficient and regret-optimal incentivized exploration in high-dimensional action spaces. In the semibandit model, we also improve the sample complexity for the pre-Thompson sampling phase of initial data collection.

Recent advances in text-to-image synthesis largely benefit from sophisticated sampling strategies and classifier-free guidance (CFG) to ensure high-quality generation. However, CFG's reliance on two forward passes, especially when combined with intricate sampling algorithms, results in prohibitively high inference costs. To address this, we introduce TeEFusion (Text Embeddings Fusion), a novel and efficient distillation method that directly incorporates the guidance magnitude into the text embeddings and distills the teacher model's complex sampling strategy. By simply fusing conditional and unconditional text embeddings using linear operations, TeEFusion reconstructs the desired guidance without adding extra parameters, simultaneously enabling the student model to learn from the teacher's output produced via its sophisticated sampling approach. Extensive experiments on state-of-the-art models such as SD3 demonstrate that our method allows the student to closely mimic the teacher's performance with a far simpler and more efficient sampling strategy. Consequently, the student model achieves inference speeds up to 6times faster than the teacher model, while maintaining image quality at levels comparable to those obtained through the teacher's complex sampling approach. The code is publicly available at https://github.com/AIDC-AI/TeEFusion{github.com/AIDC-AI/TeEFusion}.

Sample selection is a prevalent method in learning with noisy labels, where small-loss data are typically considered as correctly labeled data. However, this method may not effectively identify clean hard examples with large losses, which are critical for achieving the model's close-to-optimal generalization performance. In this paper, we propose a new framework, Late Stopping, which leverages the intrinsic robust learning ability of DNNs through a prolonged training process. Specifically, Late Stopping gradually shrinks the noisy dataset by removing high-probability mislabeled examples while retaining the majority of clean hard examples in the training set throughout the learning process. We empirically observe that mislabeled and clean examples exhibit differences in the number of epochs required for them to be consistently and correctly classified, and thus high-probability mislabeled examples can be removed. Experimental results on benchmark-simulated and real-world noisy datasets demonstrate that the proposed method outperforms state-of-the-art counterparts.

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/.

Recent ODE/SDE-based generative models, such as diffusion models, rectified flows, and flow matching, define a generative process as a time reversal of a fixed forward process. Even though these models show impressive performance on large-scale datasets, numerical simulation requires multiple evaluations of a neural network, leading to a slow sampling speed. We attribute the reason to the high curvature of the learned generative trajectories, as it is directly related to the truncation error of a numerical solver. Based on the relationship between the forward process and the curvature, here we present an efficient method of training the forward process to minimize the curvature of generative trajectories without any ODE/SDE simulation. Experiments show that our method achieves a lower curvature than previous models and, therefore, decreased sampling costs while maintaining competitive performance. Code is available at https://github.com/sangyun884/fast-ode.

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make predictions and provide uncertainty quantification for chaotic dynamical systems. In these applications, diffusion models can implicitly represent knowledge about outliers and extreme events; however, querying that knowledge through conditional sampling or measuring probabilities is surprisingly difficult. Existing methods for conditional sampling at inference time seek mainly to enforce the constraints, which is insufficient to match the statistics of the distribution or compute the probability of the chosen events. To achieve these ends, optimally one would use the conditional score function, but its computation is typically intractable. In this work, we develop a probabilistic approximation scheme for the conditional score function which provably converges to the true distribution as the noise level decreases. With this scheme we are able to sample conditionally on nonlinear userdefined events at inference time, and matches data statistics even when sampling from the tails of the distribution.

Reinforcement Learning (RL) has recently emerged as a powerful technique for improving image and video generation in Diffusion and Flow Matching models, specifically for enhancing output quality and alignment with prompts. A critical step for applying online RL methods on Flow Matching is the introduction of stochasticity into the deterministic framework, commonly realized by Stochastic Differential Equation (SDE). Our investigation reveals a significant drawback to this approach: SDE-based sampling introduces pronounced noise artifacts in the generated images, which we found to be detrimental to the reward learning process. A rigorous theoretical analysis traces the origin of this noise to an excess of stochasticity injected during inference. To address this, we draw inspiration from Denoising Diffusion Implicit Models (DDIM) to reformulate the sampling process. Our proposed method, Coefficients-Preserving Sampling (CPS), eliminates these noise artifacts. This leads to more accurate reward modeling, ultimately enabling faster and more stable convergence for reinforcement learning-based optimizers like Flow-GRPO and Dance-GRPO. Code will be released at https://github.com/IamCreateAI/FlowCPS

We present a scalable and effective exploration strategy based on Thompson sampling for reinforcement learning (RL). One of the key shortcomings of existing Thompson sampling algorithms is the need to perform a Gaussian approximation of the posterior distribution, which is not a good surrogate in most practical settings. We instead directly sample the Q function from its posterior distribution, by using Langevin Monte Carlo, an efficient type of Markov Chain Monte Carlo (MCMC) method. Our method only needs to perform noisy gradient descent updates to learn the exact posterior distribution of the Q function, which makes our approach easy to deploy in deep RL. We provide a rigorous theoretical analysis for the proposed method and demonstrate that, in the linear Markov decision process (linear MDP) setting, it has a regret bound of O(d^{3/2}H^{3/2}T), where d is the dimension of the feature mapping, H is the planning horizon, and T is the total number of steps. We apply this approach to deep RL, by using Adam optimizer to perform gradient updates. Our approach achieves better or similar results compared with state-of-the-art deep RL algorithms on several challenging exploration tasks from the Atari57 suite.

In traditional RAG framework, the basic retrieval units are normally short. The common retrievers like DPR normally work with 100-word Wikipedia paragraphs. Such a design forces the retriever to search over a large corpus to find the `needle' unit. In contrast, the readers only need to extract answers from the short retrieved units. Such an imbalanced `heavy' retriever and `light' reader design can lead to sub-optimal performance. In order to alleviate the imbalance, we propose a new framework LongRAG, consisting of a `long retriever' and a `long reader'. LongRAG processes the entire Wikipedia into 4K-token units, which is 30x longer than before. By increasing the unit size, we significantly reduce the total units from 22M to 700K. This significantly lowers the burden of retriever, which leads to a remarkable retrieval score: answer recall@1=71% on NQ (previously 52%) and answer recall@2=72% (previously 47%) on HotpotQA (full-wiki). Then we feed the top-k retrieved units (approx 30K tokens) to an existing long-context LLM to perform zero-shot answer extraction. Without requiring any training, LongRAG achieves an EM of 62.7% on NQ, which is the best known result. LongRAG also achieves 64.3% on HotpotQA (full-wiki), which is on par of the SoTA model. Our study offers insights into the future roadmap for combining RAG with long-context LLMs.

Large language models (LLMs) struggle with multi-step reasoning, where inference-time scaling has emerged as a promising strategy for performance improvement. Verifier-guided search outperforms repeated sampling when sample size is limited by selecting and prioritizing valid reasoning paths. However, we identify a critical limitation: scaling flaws, prevalent across different models (Mistral 7B and DeepSeekMath 7B), benchmarks (GSM8K and MATH), and verifiers (outcome value models and process reward models). As sample size increases, verifier-guided search exhibits diminishing advantages and eventually underperforms repeated sampling. Our analysis attributes this to verifier failures, where imperfect verifiers misrank candidates and erroneously prune all valid paths. These issues are further exacerbated in challenging and out-of-distribution problems, restricting search effectiveness. To mitigate verifier failures, we explore reducing reliance on verifiers and conduct preliminary investigations using two simple methods. Our findings reveal fundamental limitations in verifier-guided search and suggest future directions.

During 2023, two interesting results were proven about the limit behavior of game dynamics: First, it was shown that there is a game for which no dynamics converges to the Nash equilibria. Second, it was shown that the sink equilibria of a game adequately capture the limit behavior of natural game dynamics. These two results have created a need and opportunity to articulate a principled computational theory of the meaning of the game that is based on game dynamics. Given any game in normal form, and any prior distribution of play, we study the problem of computing the asymptotic behavior of a class of natural dynamics called the noisy replicator dynamics as a limit distribution over the sink equilibria of the game. When the prior distribution has pure strategy support, we prove this distribution can be computed efficiently, in near-linear time to the size of the best-response graph. When the distribution can be sampled -- for example, if it is the uniform distribution over all mixed strategy profiles -- we show through experiments that the limit distribution of reasonably large games can be estimated quite accurately through sampling and simulation.

A great deal of effort has been devoted to reducing the risk of spurious scientific discoveries, from the use of sophisticated validation techniques, to deep statistical methods for controlling the false discovery rate in multiple hypothesis testing. However, there is a fundamental disconnect between the theoretical results and the practice of data analysis: the theory of statistical inference assumes a fixed collection of hypotheses to be tested, or learning algorithms to be applied, selected non-adaptively before the data are gathered, whereas in practice data is shared and reused with hypotheses and new analyses being generated on the basis of data exploration and the outcomes of previous analyses. In this work we initiate a principled study of how to guarantee the validity of statistical inference in adaptive data analysis. As an instance of this problem, we propose and investigate the question of estimating the expectations of m adaptively chosen functions on an unknown distribution given n random samples. We show that, surprisingly, there is a way to estimate an exponential in n number of expectations accurately even if the functions are chosen adaptively. This gives an exponential improvement over standard empirical estimators that are limited to a linear number of estimates. Our result follows from a general technique that counter-intuitively involves actively perturbing and coordinating the estimates, using techniques developed for privacy preservation. We give additional applications of this technique to our question.

Existing private synthetic data generation algorithms are agnostic to downstream tasks. However, end users may have specific requirements that the synthetic data must satisfy. Failure to meet these requirements could significantly reduce the utility of the data for downstream use. We introduce a post-processing technique that improves the utility of the synthetic data with respect to measures selected by the end user, while preserving strong privacy guarantees and dataset quality. Our technique involves resampling from the synthetic data to filter out samples that do not meet the selected utility measures, using an efficient stochastic first-order algorithm to find optimal resampling weights. Through comprehensive numerical experiments, we demonstrate that our approach consistently improves the utility of synthetic data across multiple benchmark datasets and state-of-the-art synthetic data generation algorithms.

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

Autoregressive large language models (LLMs) compress knowledge from their training data through next-token conditional distributions. This limits tractable querying of this knowledge to start-to-end autoregressive sampling. However, many tasks of interest -- including sequence continuation, infilling, and other forms of constrained generation -- involve sampling from intractable posterior distributions. We address this limitation by using amortized Bayesian inference to sample from these intractable posteriors. Such amortization is algorithmically achieved by fine-tuning LLMs via diversity-seeking reinforcement learning algorithms: generative flow networks (GFlowNets). We empirically demonstrate that this distribution-matching paradigm of LLM fine-tuning can serve as an effective alternative to maximum-likelihood training and reward-maximizing policy optimization. As an important application, we interpret chain-of-thought reasoning as a latent variable modeling problem and demonstrate that our approach enables data-efficient adaptation of LLMs to tasks that require multi-step rationalization and tool use.

Self-consistency (SC) has been a widely used decoding strategy for chain-of-thought reasoning. Despite bringing significant performance improvements across a variety of multi-step reasoning tasks, it is a high-cost method that requires multiple sampling with the preset size. In this paper, we propose a simple and scalable sampling process, Early-Stopping Self-Consistency (ESC), to greatly reduce the cost of SC without sacrificing performance. On this basis, one control scheme for ESC is further derivated to dynamically choose the performance-cost balance for different tasks and models. To demonstrate ESC's effectiveness, we conducted extensive experiments on three popular categories of reasoning tasks: arithmetic, commonsense and symbolic reasoning over language models with varying scales. The empirical results show that ESC reduces the average number of sampling of chain-of-thought reasoning by a significant margin on six benchmarks, including MATH (-33.8%), GSM8K (-80.1%), StrategyQA (-76.8%), CommonsenseQA (-78.5%), Coin Flip (-84.2%) and Last Letters (-67.4%), while attaining comparable performances.

In molecular dynamics (MD) simulations, rare events, such as protein folding, are typically studied by means of enhanced sampling techniques, most of which rely on the definition of a collective variable (CV) along which the acceleration occurs. Obtaining an expressive CV is crucial, but often hindered by the lack of information about the particular event, e.g., the transition from unfolded to folded conformation. We propose a simulation-free data augmentation strategy using physics-inspired metrics to generate geodesic interpolations resembling protein folding transitions, thereby improving sampling efficiency without true transition state samples. Leveraging interpolation progress parameters, we introduce a regression-based learning scheme for CV models, which outperforms classifier-based methods when transition state data is limited and noisy

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.

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

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.

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.

We introduce GUIDE, a novel continual learning approach that directs diffusion models to rehearse samples at risk of being forgotten. Existing generative strategies combat catastrophic forgetting by randomly sampling rehearsal examples from a generative model. Such an approach contradicts buffer-based approaches where sampling strategy plays an important role. We propose to bridge this gap by incorporating classifier guidance into the diffusion process to produce rehearsal examples specifically targeting information forgotten by a continuously trained model. This approach enables the generation of samples from preceding task distributions, which are more likely to be misclassified in the context of recently encountered classes. Our experimental results show that GUIDE significantly reduces catastrophic forgetting, outperforming conventional random sampling approaches and surpassing recent state-of-the-art methods in continual learning with generative replay.

The rapid growth of dataset scales has been a key driver in advancing deep learning research. However, as dataset scale increases, the training process becomes increasingly inefficient due to the presence of low-value samples, including excessive redundant samples, overly challenging samples, and inefficient easy samples that contribute little to model improvement.To address this challenge, we propose Scale Efficient Training (SeTa) for large datasets, a dynamic sample pruning approach that losslessly reduces training time. To remove low-value samples, SeTa first performs random pruning to eliminate redundant samples, then clusters the remaining samples according to their learning difficulty measured by loss. Building upon this clustering, a sliding window strategy is employed to progressively remove both overly challenging and inefficient easy clusters following an easy-to-hard curriculum.We conduct extensive experiments on large-scale synthetic datasets, including ToCa, SS1M, and ST+MJ, each containing over 3 million samples.SeTa reduces training costs by up to 50\% while maintaining or improving performance, with minimal degradation even at 70\% cost reduction. Furthermore, experiments on various scale real datasets across various backbones (CNNs, Transformers, and Mambas) and diverse tasks (instruction tuning, multi-view stereo, geo-localization, composed image retrieval, referring image segmentation) demonstrate the powerful effectiveness and universality of our approach. Code is available at https://github.com/mrazhou/SeTa.

Efficient equilibrium sampling of molecular conformations remains a core challenge in computational chemistry and statistical inference. Classical approaches such as molecular dynamics or Markov chain Monte Carlo inherently lack amortization; the computational cost of sampling must be paid in-full for each system of interest. The widespread success of generative models has inspired interest into overcoming this limitation through learning sampling algorithms. Despite performing on par with conventional methods when trained on a single system, learned samplers have so far demonstrated limited ability to transfer across systems. We prove that deep learning enables the design of scalable and transferable samplers by introducing Prose, a 280 million parameter all-atom transferable normalizing flow trained on a corpus of peptide molecular dynamics trajectories up to 8 residues in length. Prose draws zero-shot uncorrelated proposal samples for arbitrary peptide systems, achieving the previously intractable transferability across sequence length, whilst retaining the efficient likelihood evaluation of normalizing flows. Through extensive empirical evaluation we demonstrate the efficacy of Prose as a proposal for a variety of sampling algorithms, finding a simple importance sampling-based finetuning procedure to achieve superior performance to established methods such as sequential Monte Carlo on unseen tetrapeptides. We open-source the Prose codebase, model weights, and training dataset, to further stimulate research into amortized sampling methods and finetuning objectives.

Quantization methods reduce the number of bits required to represent each parameter in a model, trading accuracy for smaller memory footprints and inference latencies. However, the final model size depends on both the number of parameters of the original model and the rate of compression. For example, a 30B 8-bit model and a 60B 4-bit model have the same number of bits but may have very different zero-shot accuracies. In this work, we study this trade-off by developing inference scaling laws of zero-shot performance in Large Language Models (LLMs) to determine the bit-precision and model size that maximizes zero-shot performance. We run more than 35,000 experiments with 16-bit inputs and k-bit parameters to examine which zero-shot quantization methods improve scaling for 3 to 8-bit precision at scales of 19M to 176B parameters across the LLM families BLOOM, OPT, NeoX/Pythia, and GPT-2. We find that it is challenging to improve the bit-level scaling trade-off, with the only improvements being the use of a small block size -- splitting the parameters into small independently quantized blocks -- and the quantization data type being used (e.g., Int vs Float). Overall, our findings show that {4-bit} precision is almost universally optimal for total model bits and zero-shot accuracy.

Diffusion models suffer from slow sample generation at inference time. Therefore, developing a principled framework for fast deterministic/stochastic sampling for a broader class of diffusion models is a promising direction. We propose two complementary frameworks for accelerating sample generation in pre-trained models: Conjugate Integrators and Splitting Integrators. Conjugate integrators generalize DDIM, mapping the reverse diffusion dynamics to a more amenable space for sampling. In contrast, splitting-based integrators, commonly used in molecular dynamics, reduce the numerical simulation error by cleverly alternating between numerical updates involving the data and auxiliary variables. After extensively studying these methods empirically and theoretically, we present a hybrid method that leads to the best-reported performance for diffusion models in augmented spaces. Applied to Phase Space Langevin Diffusion [Pandey & Mandt, 2023] on CIFAR-10, our deterministic and stochastic samplers achieve FID scores of 2.11 and 2.36 in only 100 network function evaluations (NFE) as compared to 2.57 and 2.63 for the best-performing baselines, respectively. Our code and model checkpoints will be made publicly available at https://github.com/mandt-lab/PSLD.

We introduce Trove, an easy-to-use open-source retrieval toolkit that simplifies research experiments without sacrificing flexibility or speed. For the first time, we introduce efficient data management features that load and process (filter, select, transform, and combine) retrieval datasets on the fly, with just a few lines of code. This gives users the flexibility to easily experiment with different dataset configurations without the need to compute and store multiple copies of large datasets. Trove is highly customizable: in addition to many built-in options, it allows users to freely modify existing components or replace them entirely with user-defined objects. It also provides a low-code and unified pipeline for evaluation and hard negative mining, which supports multi-node execution without any code changes. Trove's data management features reduce memory consumption by a factor of 2.6. Moreover, Trove's easy-to-use inference pipeline incurs no overhead, and inference times decrease linearly with the number of available nodes. Most importantly, we demonstrate how Trove simplifies retrieval experiments and allows for arbitrary customizations, thus facilitating exploratory research.

We study regret minimization for reinforcement learning (RL) in Latent Markov Decision Processes (LMDPs) with context in hindsight. We design a novel model-based algorithmic framework which can be instantiated with both a model-optimistic and a value-optimistic solver. We prove an O(mathsf{Var^star M Gamma S A K}) regret bound where O hides logarithm factors, M is the number of contexts, S is the number of states, A is the number of actions, K is the number of episodes, Gamma le S is the maximum transition degree of any state-action pair, and Var^star is a variance quantity describing the determinism of the LMDP. The regret bound only scales logarithmically with the planning horizon, thus yielding the first (nearly) horizon-free regret bound for LMDP. This is also the first problem-dependent regret bound for LMDP. Key in our proof is an analysis of the total variance of alpha vectors (a generalization of value functions), which is handled with a truncation method. We complement our positive result with a novel Omega(mathsf{Var^star M S A K}) regret lower bound with Gamma = 2, which shows our upper bound minimax optimal when Gamma is a constant for the class of variance-bounded LMDPs. Our lower bound relies on new constructions of hard instances and an argument inspired by the symmetrization technique from theoretical computer science, both of which are technically different from existing lower bound proof for MDPs, and thus can be of independent interest.

Numerical simulation of non-linear partial differential equations plays a crucial role in modeling physical science and engineering phenomena, such as weather, climate, and aerodynamics. Recent Machine Learning (ML) models trained on low-resolution spatio-temporal signals have shown new promises in capturing important dynamics in high-resolution signals, under the condition that the models can effectively recover the missing details. However, this study shows that significant information is often lost in the low-resolution down-sampled features. To address such issues, we propose a new approach, namely Temporal Stencil Modeling (TSM), which combines the strengths of advanced time-series sequence modeling (with the HiPPO features) and state-of-the-art neural PDE solvers (with learnable stencil modeling). TSM aims to recover the lost information from the PDE trajectories and can be regarded as a temporal generalization of classic finite volume methods such as WENO. Our experimental results show that TSM achieves the new state-of-the-art simulation accuracy for 2-D incompressible Navier-Stokes turbulent flows: it significantly outperforms the previously reported best results by 19.9% in terms of the highly-correlated duration time and reduces the inference latency into 80%. We also show a strong generalization ability of the proposed method to various out-of-distribution turbulent flow settings. Our code is available at "https://github.com/Edward-Sun/TSM-PDE".

Diffusion models have shown great promise for image and video generation, but sampling from state-of-the-art models requires expensive numerical integration of a generative ODE. One approach for tackling this problem is rectified flows, which iteratively learn smooth ODE paths that are less susceptible to truncation error. However, rectified flows still require a relatively large number of function evaluations (NFEs). In this work, we propose improved techniques for training rectified flows, allowing them to compete with knowledge distillation methods even in the low NFE setting. Our main insight is that under realistic settings, a single iteration of the Reflow algorithm for training rectified flows is sufficient to learn nearly straight trajectories; hence, the current practice of using multiple Reflow iterations is unnecessary. We thus propose techniques to improve one-round training of rectified flows, including a U-shaped timestep distribution and LPIPS-Huber premetric. With these techniques, we improve the FID of the previous 2-rectified flow by up to 72% in the 1 NFE setting on CIFAR-10. On ImageNet 64times64, our improved rectified flow outperforms the state-of-the-art distillation methods such as consistency distillation and progressive distillation in both one-step and two-step settings and rivals the performance of improved consistency training (iCT) in FID. Code is available at https://github.com/sangyun884/rfpp.

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.

Neural networks performance has been significantly improved in the last few years, at the cost of an increasing number of floating point operations per second (FLOPs). However, more FLOPs can be an issue when computational resources are limited. As an attempt to solve this problem, pruning filters is a common solution, but most existing pruning methods do not preserve the model accuracy efficiently and therefore require a large number of finetuning epochs. In this paper, we propose an automatic pruning method that learns which neurons to preserve in order to maintain the model accuracy while reducing the FLOPs to a predefined target. To accomplish this task, we introduce a trainable bottleneck that only requires one single epoch with 25.6% (CIFAR-10) or 7.49% (ILSVRC2012) of the dataset to learn which filters to prune. Experiments on various architectures and datasets show that the proposed method can not only preserve the accuracy after pruning but also outperform existing methods after finetuning. We achieve a 52.00% FLOPs reduction on ResNet-50, with a Top-1 accuracy of 47.51% after pruning and a state-of-the-art (SOTA) accuracy of 76.63% after finetuning on ILSVRC2012. Code available at https://github.com/nota-github/autobot_AAAI23.

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.

Extensive compute and memory requirements limit the deployment of large language models (LLMs) on any hardware. Compression methods, such as pruning, can reduce model size, which in turn reduces resource requirements. State-of-the-art pruning is based on coarse-grained methods. They are time-consuming and inherently remove critical model parameters, adversely impacting the quality of the pruned model. This paper introduces projection pruning, a novel fine-grained method for pruning LLMs. In addition, LLM projection pruning is enhanced by a new approach we refer to as composite projection pruning - the synergistic combination of unstructured pruning that retains accuracy and structured pruning that reduces model size. We develop Mosaic, a novel system to create and deploy pruned LLMs using composite projection pruning. Mosaic is evaluated using a range of performance and quality metrics on multiple hardware platforms, LLMs, and datasets. Mosaic is 7.19x faster in producing models than existing approaches. Mosaic models achieve up to 84.2% lower perplexity and 31.4% higher accuracy than models obtained from coarse-grained pruning. Up to 67% faster inference and 68% lower GPU memory use is noted for Mosaic models.

We revisit the well-studied problem of approximating a matrix product, A^TB, based on small space sketches S(A) and S(B) of A in R^{n times d} and Bin R^{n times m}. We are interested in the setting where the sketches must be computed independently of each other, except for the use of a shared random seed. We prove that, when A and B are sparse, methods based on coordinated random sampling can outperform classical linear sketching approaches, like Johnson-Lindenstrauss Projection or CountSketch. For example, to obtain Frobenius norm error epsilon|A|_F|B|_F, coordinated sampling requires sketches of size O(s/epsilon^2) when A and B have at most s leq d,m non-zeros per row. In contrast, linear sketching leads to sketches of size O(d/epsilon^2) and O(m/epsilon^2) for A and B. We empirically evaluate our approach on two applications: 1) distributed linear regression in databases, a problem motivated by tasks like dataset discovery and augmentation, and 2) approximating attention matrices in transformer-based language models. In both cases, our sampling algorithms yield an order of magnitude improvement over linear sketching.

We introduce Adjoint Sampling, a highly scalable and efficient algorithm for learning diffusion processes that sample from unnormalized densities, or energy functions. It is the first on-policy approach that allows significantly more gradient updates than the number of energy evaluations and model samples, allowing us to scale to much larger problem settings than previously explored by similar methods. Our framework is theoretically grounded in stochastic optimal control and shares the same theoretical guarantees as Adjoint Matching, being able to train without the need for corrective measures that push samples towards the target distribution. We show how to incorporate key symmetries, as well as periodic boundary conditions, for modeling molecules in both cartesian and torsional coordinates. We demonstrate the effectiveness of our approach through extensive experiments on classical energy functions, and further scale up to neural network-based energy models where we perform amortized conformer generation across many molecular systems. To encourage further research in developing highly scalable sampling methods, we plan to open source these challenging benchmarks, where successful methods can directly impact progress in computational chemistry.

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.

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

Discrete diffusion models (DDMs) have shown powerful generation ability for discrete data modalities like text and molecules. However, their practical application is hindered by inefficient sampling, requiring a large number of sampling steps. Accelerating DDMs by using larger step sizes typically introduces significant problems in generation quality, as it amplifies the impact of both the compounding decoding error due to factorized predictions and discretization error from numerical approximations, leading to a significant decrease in sampling quality. To address these challenges, we propose learnable sampler distillation (LSD), a novel approach to train fast and high-fidelity samplers for DDMs. LSD employs a distillation approach where a student sampler with a few steps learns to align its intermediate score trajectory with that of a high-quality teacher sampler with numerous steps. This alignment is achieved by optimizing learnable sampler coefficients that adaptively adjust sampling dynamics. Additionally, we further propose LSD+, which also learns time schedules that allocate steps non-uniformly. Experiments across text generation, image generation, and synthetic tasks demonstrate that our proposed approaches outperform existing samplers for DDMs, achieving substantially higher sampling quality with significantly fewer sampling steps. Our code is available at https://github.com/feiyangfu/LSD{https://github.com/feiyangfu/LSD}.

Can scaling transform reasoning? In this work, we explore the untapped potential of scaling Long Chain-of-Thought (Long-CoT) data to 1000k samples, pioneering the development of a slow-thinking model, RedStar. Through extensive experiments with various LLMs and different sizes, we uncover the ingredients for specialization and scale for Long-CoT training. Surprisingly, even smaller models show significant performance gains with limited data, revealing the sample efficiency of Long-CoT and the critical role of sample difficulty in the learning process. Our findings demonstrate that Long-CoT reasoning can be effectively triggered with just a few thousand examples, while larger models achieve unparalleled improvements. We also introduce reinforcement learning (RL)-scale training as a promising direction for advancing slow-thinking systems. RedStar shines across domains: on the MATH-Hard benchmark, RedStar-code-math boosts performance from 66.2\% to 81.6\%, and on the USA Math Olympiad (AIME), it solves 46.7\% of problems using only 21k mixed-code-math datasets. In multimodal tasks like GeoQA and MathVista-GEO, RedStar-Geo achieves competitive results with minimal Long-CoT data, outperforming other slow-thinking systems like QvQ-Preview. Compared to QwQ, RedStar strikes the perfect balance between reasoning and generalizability. Our work highlights that, with careful tuning, scaling Long-CoT can unlock extraordinary reasoning capabilities-even with limited dataset and set a new standard for slow-thinking models across diverse challenges. Our data and models are released at https://huggingface.co/RedStar-Reasoning.

We introduce and make publicly available the NIFTY Financial News Headlines dataset, designed to facilitate and advance research in financial market forecasting using large language models (LLMs). This dataset comprises two distinct versions tailored for different modeling approaches: (i) NIFTY-LM, which targets supervised fine-tuning (SFT) of LLMs with an auto-regressive, causal language-modeling objective, and (ii) NIFTY-RL, formatted specifically for alignment methods (like reinforcement learning from human feedback (RLHF)) to align LLMs via rejection sampling and reward modeling. Each dataset version provides curated, high-quality data incorporating comprehensive metadata, market indices, and deduplicated financial news headlines systematically filtered and ranked to suit modern LLM frameworks. We also include experiments demonstrating some applications of the dataset in tasks like stock price movement and the role of LLM embeddings in information acquisition/richness. The NIFTY dataset along with utilities (like truncating prompt's context length systematically) are available on Hugging Face at https://huggingface.co/datasets/raeidsaqur/NIFTY.

Diffusion-based generative models have demonstrated their powerful performance across various tasks, but this comes at a cost of the slow sampling speed. To achieve both efficient and high-quality synthesis, various distillation-based accelerated sampling methods have been developed recently. However, they generally require time-consuming fine tuning with elaborate designs to achieve satisfactory performance in a specific number of function evaluation (NFE), making them difficult to employ in practice. To address this issue, we propose Simple and Fast Distillation (SFD) of diffusion models, which simplifies the paradigm used in existing methods and largely shortens their fine-tuning time up to 1000times. We begin with a vanilla distillation-based sampling method and boost its performance to state of the art by identifying and addressing several small yet vital factors affecting the synthesis efficiency and quality. Our method can also achieve sampling with variable NFEs using a single distilled model. Extensive experiments demonstrate that SFD strikes a good balance between the sample quality and fine-tuning costs in few-step image generation task. For example, SFD achieves 4.53 FID (NFE=2) on CIFAR-10 with only 0.64 hours of fine-tuning on a single NVIDIA A100 GPU. Our code is available at https://github.com/zju-pi/diff-sampler.

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.

Learning to denoise has emerged as a prominent paradigm to design state-of-the-art deep generative models for natural images. How to use it to model the distributions of both continuous real-valued data and categorical data has been well studied in recently proposed diffusion models. However, it is found in this paper to have limited ability in modeling some other types of data, such as count and non-negative continuous data, that are often highly sparse, skewed, heavy-tailed, and/or overdispersed. To this end, we propose learning to jump as a general recipe for generative modeling of various types of data. Using a forward count thinning process to construct learning objectives to train a deep neural network, it employs a reverse count thickening process to iteratively refine its generation through that network. We demonstrate when learning to jump is expected to perform comparably to learning to denoise, and when it is expected to perform better. For example, learning to jump is recommended when the training data is non-negative and exhibits strong sparsity, skewness, heavy-tailedness, and/or heterogeneity.

The curvature of ODE trajectories in diffusion models hinders their ability to generate high-quality images in a few number of function evaluations (NFE). In this paper, we propose a novel and effective approach to reduce trajectory curvature by utilizing adaptive conditions. By employing a extremely light-weight quantized encoder, our method incurs only an additional 1% of training parameters, eliminates the need for extra regularization terms, yet achieves significantly better sample quality. Our approach accelerates ODE sampling while preserving the downstream task image editing capabilities of SDE techniques. Extensive experiments verify that our method can generate high quality results under extremely limited sampling costs. With only 6 NFE, we achieve 5.14 FID on CIFAR-10, 6.91 FID on FFHQ 64x64 and 3.10 FID on AFHQv2.

Recent years have witnessed significant progress in developing efficient training and fast sampling approaches for diffusion models. A recent remarkable advancement is the use of stochastic differential equations (SDEs) to describe data perturbation and generative modeling in a unified mathematical framework. In this paper, we reveal several intriguing geometric structures of diffusion models and contribute a simple yet powerful interpretation to their sampling dynamics. Through carefully inspecting a popular variance-exploding SDE and its marginal-preserving ordinary differential equation (ODE) for sampling, we discover that the data distribution and the noise distribution are smoothly connected with an explicit, quasi-linear sampling trajectory, and another implicit denoising trajectory, which even converges faster in terms of visual quality. We also establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm, with which we can characterize the asymptotic behavior of diffusion models and identify the score deviation. These new geometric observations enable us to improve previous sampling algorithms, re-examine latent interpolation, as well as re-explain the working principles of distillation-based fast sampling techniques.

In applications of diffusion models, controllable generation is of practical significance, but is also challenging. Current methods for controllable generation primarily focus on modifying the score function of diffusion models, while Mean Reverting (MR) Diffusion directly modifies the structure of the stochastic differential equation (SDE), making the incorporation of image conditions simpler and more natural. However, current training-free fast samplers are not directly applicable to MR Diffusion. And thus MR Diffusion requires hundreds of NFEs (number of function evaluations) to obtain high-quality samples. In this paper, we propose a new algorithm named MRS (MR Sampler) to reduce the sampling NFEs of MR Diffusion. We solve the reverse-time SDE and the probability flow ordinary differential equation (PF-ODE) associated with MR Diffusion, and derive semi-analytical solutions. The solutions consist of an analytical function and an integral parameterized by a neural network. Based on this solution, we can generate high-quality samples in fewer steps. Our approach does not require training and supports all mainstream parameterizations, including noise prediction, data prediction and velocity prediction. Extensive experiments demonstrate that MR Sampler maintains high sampling quality with a speedup of 10 to 20 times across ten different image restoration tasks. Our algorithm accelerates the sampling procedure of MR Diffusion, making it more practical in controllable generation.

Algorithms such as Differentially Private SGD enable training machine learning models with formal privacy guarantees. However, there is a discrepancy between the protection that such algorithms guarantee in theory and the protection they afford in practice. An emerging strand of work empirically estimates the protection afforded by differentially private training as a confidence interval for the privacy budget varepsilon spent on training a model. Existing approaches derive confidence intervals for varepsilon from confidence intervals for the false positive and false negative rates of membership inference attacks. Unfortunately, obtaining narrow high-confidence intervals for epsilon using this method requires an impractically large sample size and training as many models as samples. We propose a novel Bayesian method that greatly reduces sample size, and adapt and validate a heuristic to draw more than one sample per trained model. Our Bayesian method exploits the hypothesis testing interpretation of differential privacy to obtain a posterior for varepsilon (not just a confidence interval) from the joint posterior of the false positive and false negative rates of membership inference attacks. For the same sample size and confidence, we derive confidence intervals for varepsilon around 40% narrower than prior work. The heuristic, which we adapt from label-only DP, can be used to further reduce the number of trained models needed to get enough samples by up to 2 orders of magnitude.

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.

Diffusion models have demonstrated remarkable success in various domains, including molecular generation. However, conditional molecular generation remains a fundamental challenge due to an intrinsic trade-off between targeting specific chemical properties and generating meaningful samples from the data distribution. In this work, we present Time-Aware Conditional Synthesis (TACS), a novel approach to conditional generation on diffusion models. It integrates adaptively controlled plug-and-play "online" guidance into a diffusion model, driving samples toward the desired properties while maintaining validity and stability. A key component of our algorithm is our new type of diffusion sampler, Time Correction Sampler (TCS), which is used to control guidance and ensure that the generated molecules remain on the correct manifold at each reverse step of the diffusion process at the same time. Our proposed method demonstrates significant performance in conditional 3D molecular generation and offers a promising approach towards inverse molecular design, potentially facilitating advancements in drug discovery, materials science, and other related fields.

Consider a random uniform sample of n points in a compact region A of Euclidean d-space, d geq 2, with a smooth or (when d=2) polygonal boundary. Fix k bf N. Let T_{n,k} be the threshold r at which the geometric graph on these n vertices with distance parameter r becomes k-connected. We show that if d=2 then n (pi/|A|) T_{n,1}^2 - log n is asymptotically standard Gumbel. For (d,k) neq (2,1), it is n (theta_d/|A|) T_{n,k}^d - (2-2/d) log n - (4-2k-2/d) log log n that converges in distribution to a nondegenerate limit, where theta_d is the volume of the unit ball. The limit is Gumbel with scale parameter 2 except when (d,k)=(2,2) where the limit is two component extreme value distributed. The different cases reflect the fact that boundary effects are more more important in some cases than others. We also give similar results for the largest k-nearest neighbour link U_{n,k} in the sample, and show T_{n,k}=U_{n,k} with high probability. We provide estimates on rates of convergence and give similar results for Poisson samples in A. Finally, we give similar results even for non-uniform samples, with a less explicit sequence of centring constants.

As deep neural networks include a high number of parameters and operations, it can be a challenge to implement these models on devices with limited computational resources. Despite the development of novel pruning methods toward resource-efficient models, it has become evident that these models are not capable of handling "imbalanced" and "limited number of data points". We proposed a novel filter pruning method by considering the input and output of filters along with the values of the filters that deal with imbalanced datasets better than others. Our pruning method considers the fact that all information about the importance of a filter may not be reflected in the value of the filter. Instead, it is reflected in the changes made to the data after the filter is applied to it. In this work, three methods are compared with the same training conditions except for the ranking values of each method, and 14 methods are compared from other papers. We demonstrated that our model performed significantly better than other methods for imbalanced medical datasets. For example, when we removed up to 58% of FLOPs for the IDRID dataset and up to 45% for the ISIC dataset, our model was able to yield an equivalent (or even superior) result to the baseline model. To evaluate FLOP and parameter reduction using our model in real-world settings, we built a smartphone app, where we demonstrated a reduction of up to 79% in memory usage and 72% in prediction time. All codes and parameters for training different models are available at https://github.com/mohofar/Beta-Rank

We present a new algorithm to optimize distributions defined implicitly by parameterized stochastic diffusions. Doing so allows us to modify the outcome distribution of sampling processes by optimizing over their parameters. We introduce a general framework for first-order optimization of these processes, that performs jointly, in a single loop, optimization and sampling steps. This approach is inspired by recent advances in bilevel optimization and automatic implicit differentiation, leveraging the point of view of sampling as optimization over the space of probability distributions. We provide theoretical guarantees on the performance of our method, as well as experimental results demonstrating its effectiveness in real-world settings.

Recent advances demonstrate that increasing inference-time computation can significantly boost the reasoning capabilities of large language models (LLMs). Although repeated sampling (i.e., generating multiple candidate outputs) is a highly effective strategy, it does not leverage external feedback signals for refinement, which are often available in tasks like coding. In this work, we propose Adaptive Branching Monte Carlo Tree Search (AB-MCTS), a novel inference-time framework that generalizes repeated sampling with principled multi-turn exploration and exploitation. At each node in the search tree, AB-MCTS dynamically decides whether to "go wider" by expanding new candidate responses or "go deeper" by revisiting existing ones based on external feedback signals. We evaluate our method on complex coding and engineering tasks using frontier models. Empirical results show that AB-MCTS consistently outperforms both repeated sampling and standard MCTS, underscoring the importance of combining the response diversity of LLMs with multi-turn solution refinement for effective inference-time scaling.

Recent studies indicate that NLU models are prone to rely on shortcut features for prediction, without achieving true language understanding. As a result, these models fail to generalize to real-world out-of-distribution data. In this work, we show that the words in the NLU training set can be modeled as a long-tailed distribution. There are two findings: 1) NLU models have strong preference for features located at the head of the long-tailed distribution, and 2) Shortcut features are picked up during very early few iterations of the model training. These two observations are further employed to formulate a measurement which can quantify the shortcut degree of each training sample. Based on this shortcut measurement, we propose a shortcut mitigation framework LTGR, to suppress the model from making overconfident predictions for samples with large shortcut degree. Experimental results on three NLU benchmarks demonstrate that our long-tailed distribution explanation accurately reflects the shortcut learning behavior of NLU models. Experimental analysis further indicates that LTGR can improve the generalization accuracy on OOD data, while preserving the accuracy on in-distribution data.

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 consider the problem of estimating the optimal transport map between two probability distributions, P and Q in mathbb R^d, on the basis of i.i.d. samples. All existing statistical analyses of this problem require the assumption that the transport map is Lipschitz, a strong requirement that, in particular, excludes any examples where the transport map is discontinuous. As a first step towards developing estimation procedures for discontinuous maps, we consider the important special case where the data distribution Q is a discrete measure supported on a finite number of points in mathbb R^d. We study a computationally efficient estimator initially proposed by Pooladian and Niles-Weed (2021), based on entropic optimal transport, and show in the semi-discrete setting that it converges at the minimax-optimal rate n^{-1/2}, independent of dimension. Other standard map estimation techniques both lack finite-sample guarantees in this setting and provably suffer from the curse of dimensionality. We confirm these results in numerical experiments, and provide experiments for other settings, not covered by our theory, which indicate that the entropic estimator is a promising methodology for other discontinuous transport map estimation problems.

While conditional diffusion models are known to have good coverage of the data distribution, they still face limitations in output diversity, particularly when sampled with a high classifier-free guidance scale for optimal image quality or when trained on small datasets. We attribute this problem to the role of the conditioning signal in inference and offer an improved sampling strategy for diffusion models that can increase generation diversity, especially at high guidance scales, with minimal loss of sample quality. Our sampling strategy anneals the conditioning signal by adding scheduled, monotonically decreasing Gaussian noise to the conditioning vector during inference to balance diversity and condition alignment. Our Condition-Annealed Diffusion Sampler (CADS) can be used with any pretrained model and sampling algorithm, and we show that it boosts the diversity of diffusion models in various conditional generation tasks. Further, using an existing pretrained diffusion model, CADS achieves a new state-of-the-art FID of 1.70 and 2.31 for class-conditional ImageNet generation at 256times256 and 512times512 respectively.

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

Although randomized smoothing has demonstrated high certified robustness and superior scalability to other certified defenses, the high computational overhead of the robustness certification bottlenecks the practical applicability, as it depends heavily on the large sample approximation for estimating the confidence interval. In existing works, the sample size for the confidence interval is universally set and agnostic to the input for prediction. This Input-Agnostic Sampling (IAS) scheme may yield a poor Average Certified Radius (ACR)-runtime trade-off which calls for improvement. In this paper, we propose Input-Specific Sampling (ISS) acceleration to achieve the cost-effectiveness for robustness certification, in an adaptive way of reducing the sampling size based on the input characteristic. Furthermore, our method universally controls the certified radius decline from the ISS sample size reduction. The empirical results on CIFAR-10 and ImageNet show that ISS can speed up the certification by more than three times at a limited cost of 0.05 certified radius. Meanwhile, ISS surpasses IAS on the average certified radius across the extensive hyperparameter settings. Specifically, ISS achieves ACR=0.958 on ImageNet (sigma=1.0) in 250 minutes, compared to ACR=0.917 by IAS under the same condition. We release our code in https://github.com/roy-ch/Input-Specific-Certification.