Daily Papers

Efforts to leverage deep learning models in low-resource regimes have led to numerous augmentation studies. However, the direct application of methods such as mixup and cutout to text data, is limited due to their discrete characteristics. While methods using pretrained language models have exhibited efficiency, they require additional considerations for robustness. Inspired by recent studies on decision boundaries, this paper proposes a decision-boundary-aware data augmentation strategy to enhance robustness using pretrained language models. The proposed technique first focuses on shifting the latent features closer to the decision boundary, followed by reconstruction to generate an ambiguous version with a soft label. Additionally, mid-K sampling is suggested to enhance the diversity of the generated sentences. This paper demonstrates the performance of the proposed augmentation strategy compared to other methods through extensive experiments. Furthermore, the ablation study reveals the effect of soft labels and mid-K sampling and the extensibility of the method with curriculum data augmentation.

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

We 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.

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.

k-Clustering in R^d (e.g., k-median and k-means) is a fundamental machine learning problem. While near-linear time approximation algorithms were known in the classical setting for a dataset with cardinality n, it remains open to find sublinear-time quantum algorithms. We give quantum algorithms that find coresets for k-clustering in R^d with O(nkd^{3/2}) query complexity. Our coreset reduces the input size from n to poly(kepsilon^{-1}d), so that existing alpha-approximation algorithms for clustering can run on top of it and yield (1 + epsilon)alpha-approximation. This eventually yields a quadratic speedup for various k-clustering approximation algorithms. We complement our algorithm with a nearly matching lower bound, that any quantum algorithm must make Omega(nk) queries in order to achieve even O(1)-approximation for k-clustering.

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.

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

Kernelized Stein discrepancy (KSD) is a score-based discrepancy widely used in goodness-of-fit tests. It can be applied even when the target distribution has an unknown normalising factor, such as in Bayesian analysis. We show theoretically and empirically that the KSD test can suffer from low power when the target and the alternative distributions have the same well-separated modes but differ in mixing proportions. We propose to perturb the observed sample via Markov transition kernels, with respect to which the target distribution is invariant. This allows us to then employ the KSD test on the perturbed sample. We provide numerical evidence that with suitably chosen transition kernels the proposed approach can lead to substantially higher power than the KSD test.

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.

Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies can be achieved by reducing the input space if a minimal loss of information can be achieved. Clustering algorithms, in general, face two common problems: 1) these converge to different settings with different initial conditions and; 2) the number of clusters has to be arbitrarily decided beforehand. This problem has become critical in the realm of big data. Recently, clustering algorithms have emerged which can speedup computations using parallel processing over the grid but face the aforementioned problems. Goals: Our goals are to find methods to cluster data which: 1) guarantee convergence to the same settings irrespective of the initial conditions; 2) eliminate the need to establish the number of clusters beforehand, and 3) can be applied to cluster large datasets. Methods: We introduce a method that combines probabilistic and combinatorial clustering methods to produce repeatable and compact clusters that are not sensitive to initial conditions. This method harnesses the power of k-means (a combinatorial clustering method) to cluster/partition very large dimensional datasets and uses the Gaussian Mixture Model (a probabilistic clustering method) to validate the k-means partitions. Results: We show that this method produces very compact clusters that are not sensitive to initial conditions. This method can be used to identify the most 'separable' set in a dataset which increases the 'clusterability' of a dataset. This method also eliminates the need to specify the number of clusters in advance.

Beam search is the default decoding strategy for many sequence generation tasks in NLP. The set of approximate K-best items returned by the algorithm is a useful summary of the distribution for many applications; however, the candidates typically exhibit high overlap and may give a highly biased estimate for expectations under our model. These problems can be addressed by instead using stochastic decoding strategies. In this work, we propose a new method for turning beam search into a stochastic process: Conditional Poisson stochastic beam search. Rather than taking the maximizing set at each iteration, we sample K candidates without replacement according to the conditional Poisson sampling design. We view this as a more natural alternative to Kool et. al. 2019's stochastic beam search (SBS). Furthermore, we show how samples generated under the CPSBS design can be used to build consistent estimators and sample diverse sets from sequence models. In our experiments, we observe CPSBS produces lower variance and more efficient estimators than SBS, even showing improvements in high entropy settings.

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.

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.

Federated learning enables multiple decentralized clients to learn collaboratively without sharing the local training data. However, the expensive annotation cost to acquire data labels on local clients remains an obstacle in utilizing local data. In this paper, we propose a federated active learning paradigm to efficiently learn a global model with limited annotation budget while protecting data privacy in a decentralized learning way. The main challenge faced by federated active learning is the mismatch between the active sampling goal of the global model on the server and that of the asynchronous local clients. This becomes even more significant when data is distributed non-IID across local clients. To address the aforementioned challenge, we propose Knowledge-Aware Federated Active Learning (KAFAL), which consists of Knowledge-Specialized Active Sampling (KSAS) and Knowledge-Compensatory Federated Update (KCFU). KSAS is a novel active sampling method tailored for the federated active learning problem. It deals with the mismatch challenge by sampling actively based on the discrepancies between local and global models. KSAS intensifies specialized knowledge in local clients, ensuring the sampled data to be informative for both the local clients and the global model. KCFU, in the meantime, deals with the client heterogeneity caused by limited data and non-IID data distributions. It compensates for each client's ability in weak classes by the assistance of the global model. Extensive experiments and analyses are conducted to show the superiority of KSAS over the state-of-the-art active learning methods and the efficiency of KCFU under the federated active learning framework.

Assessing the fidelity and diversity of the generative model is a difficult but important issue for technological advancement. So, recent papers have introduced k-Nearest Neighbor (kNN) based precision-recall metrics to break down the statistical distance into fidelity and diversity. While they provide an intuitive method, we thoroughly analyze these metrics and identify oversimplified assumptions and undesirable properties of kNN that result in unreliable evaluation, such as susceptibility to outliers and insensitivity to distributional changes. Thus, we propose novel metrics, P-precision and P-recall (PP\&PR), based on a probabilistic approach that address the problems. Through extensive investigations on toy experiments and state-of-the-art generative models, we show that our PP\&PR provide more reliable estimates for comparing fidelity and diversity than the existing metrics. The codes are available at https://github.com/kdst-team/Probablistic_precision_recall.

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%.

Clustering non-Euclidean data is difficult, and one of the most used algorithms besides hierarchical clustering is the popular algorithm Partitioning Around Medoids (PAM), also simply referred to as k-medoids clustering. In Euclidean geometry the mean-as used in k-means-is a good estimator for the cluster center, but this does not exist for arbitrary dissimilarities. PAM uses the medoid instead, the object with the smallest dissimilarity to all others in the cluster. This notion of centrality can be used with any (dis-)similarity, and thus is of high relevance to many domains and applications. A key issue with PAM is its high run time cost. We propose modifications to the PAM algorithm that achieve an O(k)-fold speedup in the second ("SWAP") phase of the algorithm, but will still find the same results as the original PAM algorithm. If we relax the choice of swaps performed (while retaining comparable quality), we can further accelerate the algorithm by eagerly performing additional swaps in each iteration. With the substantially faster SWAP, we can now explore faster initialization strategies, because (i) the classic ("BUILD") initialization now becomes the bottleneck, and (ii) our swap is fast enough to compensate for worse starting conditions. We also show how the CLARA and CLARANS algorithms benefit from the proposed modifications. While we do not study the parallelization of our approach in this work, it can easily be combined with earlier approaches to use PAM and CLARA on big data (some of which use PAM as a subroutine, hence can immediately benefit from these improvements), where the performance with high k becomes increasingly important. In experiments on real data with k=100,200, we observed a 458x respectively 1191x speedup compared to the original PAM SWAP algorithm, making PAM applicable to larger data sets, and in particular to higher k.

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

Clustering non-Euclidean data is difficult, and one of the most used algorithms besides hierarchical clustering is the popular algorithm Partitioning Around Medoids (PAM), also simply referred to as k-medoids. In Euclidean geometry the mean-as used in k-means-is a good estimator for the cluster center, but this does not hold for arbitrary dissimilarities. PAM uses the medoid instead, the object with the smallest dissimilarity to all others in the cluster. This notion of centrality can be used with any (dis-)similarity, and thus is of high relevance to many domains such as biology that require the use of Jaccard, Gower, or more complex distances. A key issue with PAM is its high run time cost. We propose modifications to the PAM algorithm to achieve an O(k)-fold speedup in the second SWAP phase of the algorithm, but will still find the same results as the original PAM algorithm. If we slightly relax the choice of swaps performed (at comparable quality), we can further accelerate the algorithm by performing up to k swaps in each iteration. With the substantially faster SWAP, we can now also explore alternative strategies for choosing the initial medoids. We also show how the CLARA and CLARANS algorithms benefit from these modifications. It can easily be combined with earlier approaches to use PAM and CLARA on big data (some of which use PAM as a subroutine, hence can immediately benefit from these improvements), where the performance with high k becomes increasingly important. In experiments on real data with k=100, we observed a 200-fold speedup compared to the original PAM SWAP algorithm, making PAM applicable to larger data sets as long as we can afford to compute a distance matrix, and in particular to higher k (at k=2, the new SWAP was only 1.5 times faster, as the speedup is expected to increase with k).

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.

We consider the problem of constructing small coresets for k-Median in Euclidean spaces. Given a large set of data points Psubset R^d, a coreset is a much smaller set Ssubset R^d, so that the k-Median costs of any k centers w.r.t. P and S are close. Existing literature mainly focuses on the high-dimension case and there has been great success in obtaining dimension-independent bounds, whereas the case for small d is largely unexplored. Considering many applications of Euclidean clustering algorithms are in small dimensions and the lack of systematic studies in the current literature, this paper investigates coresets for k-Median in small dimensions. For small d, a natural question is whether existing near-optimal dimension-independent bounds can be significantly improved. We provide affirmative answers to this question for a range of parameters. Moreover, new lower bound results are also proved, which are the highest for small d. In particular, we completely settle the coreset size bound for 1-d k-Median (up to log factors). Interestingly, our results imply a strong separation between 1-d 1-Median and 1-d 2-Median. As far as we know, this is the first such separation between k=1 and k=2 in any dimension.

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.

We present a straightforward statistical test to detect certain violations of the assumption that the data are Independent and Identically Distributed (IID). The specific form of violation considered is common across real-world applications: whether the examples are ordered in the dataset such that almost adjacent examples tend to have more similar feature values (e.g. due to distributional drift, or attractive interactions between datapoints). Based on a k-Nearest Neighbors estimate, our approach can be used to audit any multivariate numeric data as well as other data types (image, text, audio, etc.) that can be numerically represented, perhaps with model embeddings. Compared with existing methods to detect drift or auto-correlation, our approach is both applicable to more types of data and also able to detect a wider variety of IID violations in practice. Code: https://github.com/cleanlab/cleanlab

We revisit the noisy binary search model of Karp and Kleinberg, in which we have n coins with unknown probabilities p_i that we can flip. The coins are sorted by increasing p_i, and we would like to find where the probability crosses (to within varepsilon) of a target value tau. This generalized the fixed-noise model of Burnashev and Zigangirov , in which p_i = 1{2} pm varepsilon, to a setting where coins near the target may be indistinguishable from it. Karp and Kleinberg showed that Theta(1{varepsilon^2} log n) samples are necessary and sufficient for this task. We produce a practical algorithm by solving two theoretical challenges: high-probability behavior and sharp constants. We give an algorithm that succeeds with probability 1-delta from \[ 1{C_{\tau, \varepsilon}} \cdot \left(\lg n + O(\log^{2/3} n \log^{1/3} 1{\delta} + \log 1{\delta})\right) \] samples, where C_{tau, varepsilon} is the optimal such constant achievable. For delta > n^{-o(1)} this is within 1 + o(1) of optimal, and for delta ll 1 it is the first bound within constant factors of optimal.

This paper studies the fair range clustering problem in which the data points are from different demographic groups and the goal is to pick k centers with the minimum clustering cost such that each group is at least minimally represented in the centers set and no group dominates the centers set. More precisely, given a set of n points in a metric space (P,d) where each point belongs to one of the ell different demographics (i.e., P = P_1 uplus P_2 uplus cdots uplus P_ell) and a set of ell intervals [alpha_1, beta_1], cdots, [alpha_ell, beta_ell] on desired number of centers from each group, the goal is to pick a set of k centers C with minimum ell_p-clustering cost (i.e., (sum_{vin P} d(v,C)^p)^{1/p}) such that for each group iin ell, |Ccap P_i| in [alpha_i, beta_i]. In particular, the fair range ell_p-clustering captures fair range k-center, k-median and k-means as its special cases. In this work, we provide efficient constant factor approximation algorithms for fair range ell_p-clustering for all values of pin [1,infty).

Compression is at the heart of intelligence. A theoretically optimal way to compress any sequence of data is to find the shortest program that outputs that sequence and then halts. However, such 'Kolmogorov compression' is uncomputable, and code generating LLMs struggle to approximate this theoretical ideal, as it requires reasoning, planning and search capabilities beyond those of current models. In this work, we introduce the KoLMogorov-Test (KT), a compression-as-intelligence test for code generating LLMs. In KT a model is presented with a sequence of data at inference time, and asked to generate the shortest program that produces the sequence. We identify several benefits of KT for both evaluation and training: an essentially infinite number of problem instances of varying difficulty is readily available, strong baselines already exist, the evaluation metric (compression) cannot be gamed, and pretraining data contamination is highly unlikely. To evaluate current models, we use audio, text, and DNA data, as well as sequences produced by random synthetic programs. Current flagship models perform poorly - both GPT4-o and Llama-3.1-405B struggle on our natural and synthetic sequences. On our synthetic distribution, we are able to train code generation models with lower compression rates than previous approaches. Moreover, we show that gains on synthetic data generalize poorly to real data, suggesting that new innovations are necessary for additional gains on KT.

Advances in hardware and language model architecture have spurred a revolution in natural language generation. However, autoregressive models compute probability distributions over next-token choices, and sampling from these distributions, known as decoding, has received significantly less attention than other design choices. Existing decoding strategies are largely based on heuristics, resulting in methods that are hard to apply or improve in a principled manner. We develop the theory of decoding strategies for language models by expressing popular decoding algorithms as equilibrium states in the language of ergodic theory and stating the functions they optimize. Using this, we analyze the effect of the local normalization step of top-k, nucleus, and temperature sampling, used to make probabilities sum to one. We argue that local normalization distortion is a fundamental defect of decoding strategies and quantify the size of this distortion and its effect on mathematical proxies for the quality and diversity of generated text. Contrary to the prevailing explanation, we argue that the major cause of the under-performance of top-k sampling relative to nucleus sampling is local normalization distortion. This yields conclusions for the future design of decoding algorithms and the detection of machine-generated text.

We propose a goodness-of-fit measure for probability densities modeling observations with varying dimensionality, such as text documents of differing lengths or variable-length sequences. The proposed measure is an instance of the kernel Stein discrepancy (KSD), which has been used to construct goodness-of-fit tests for unnormalized densities. The KSD is defined by its Stein operator: current operators used in testing apply to fixed-dimensional spaces. As our main contribution, we extend the KSD to the variable-dimension setting by identifying appropriate Stein operators, and propose a novel KSD goodness-of-fit test. As with the previous variants, the proposed KSD does not require the density to be normalized, allowing the evaluation of a large class of models. Our test is shown to perform well in practice on discrete sequential data benchmarks.

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

In statistics, independent, identically distributed random samples do not carry a natural ordering, and their statistics are typically invariant with respect to permutations of their order. Thus, an n-sample in a space M can be considered as an element of the quotient space of M^n modulo the permutation group. The present paper takes this definition of sample space and the related concept of orbit types as a starting point for developing a geometric perspective on statistics. We aim at deriving a general mathematical setting for studying the behavior of empirical and population means in spaces ranging from smooth Riemannian manifolds to general stratified spaces. We fully describe the orbifold and path-metric structure of the sample space when M is a manifold or path-metric space, respectively. These results are non-trivial even when M is Euclidean. We show that the infinite sample space exists in a Gromov-Hausdorff type sense and coincides with the Wasserstein space of probability distributions on M. We exhibit Fr\'echet means and k-means as metric projections onto 1-skeleta or k-skeleta in Wasserstein space, and we define a new and more general notion of polymeans. This geometric characterization via metric projections applies equally to sample and population means, and we use it to establish asymptotic properties of polymeans such as consistency and asymptotic normality.

We study the problem of learning mixtures of Gaussians with censored data. Statistical learning with censored data is a classical problem, with numerous practical applications, however, finite-sample guarantees for even simple latent variable models such as Gaussian mixtures are missing. Formally, we are given censored data from a mixture of univariate Gaussians $sum_{i=1}^k w_i N(mu_i,sigma^2), i.e. the sample is observed only if it lies inside a set S. The goal is to learn the weights w_i and the means \mu_i. We propose an algorithm that takes only 1{\varepsilon^{O(k)}} samples to estimate the weights w_i and the means \mu_i within \varepsilon$ error.

Large Language Models (LLMs) have been widely deployed in a variety of applications, and the context length is rapidly increasing to handle tasks such as long-document QA and complex logical reasoning. However, long context poses significant challenges for inference efficiency, including high memory costs of key-value (KV) cache and increased latency due to extensive memory accesses. Recent works have proposed compressing KV cache to approximate computation, but these methods either evict tokens permanently, never recalling them for later inference, or recall previous tokens at the granularity of pages divided by textual positions. Both approaches degrade the model accuracy and output quality. To achieve efficient and accurate recallable KV cache compression, we introduce ClusterKV, which recalls tokens at the granularity of semantic clusters. We design and implement efficient algorithms and systems for clustering, selection, indexing and caching. Experiment results show that ClusterKV attains negligible accuracy loss across various tasks with 32k context lengths, using only a 1k to 2k KV cache budget, and achieves up to a 2times speedup in latency and a 2.5times improvement in decoding throughput. Compared to SoTA recallable KV compression methods, ClusterKV demonstrates higher model accuracy and output quality, while maintaining or exceeding inference efficiency.

Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum distance estimation, generalised Bayesian inference, and within the nonparametric learning framework. The MMD is commonly estimated at a root-m rate, where m is the number of simulated samples. This can lead to significant computational challenges since a large m is required to obtain an accurate estimate, which is crucial for parameter estimation. In this paper, we propose a novel estimator for the MMD with significantly improved sample complexity. The estimator is particularly well suited for computationally expensive smooth simulators with low- to mid-dimensional inputs. This claim is supported through both theoretical results and an extensive simulation study on benchmark simulators.

The kernel thinning (KT) algorithm of Dwivedi and Mackey (2021) compresses a probability distribution more effectively than independent sampling by targeting a reproducing kernel Hilbert space (RKHS) and leveraging a less smooth square-root kernel. Here we provide four improvements. First, we show that KT applied directly to the target RKHS yields tighter, dimension-free guarantees for any kernel, any distribution, and any fixed function in the RKHS. Second, we show that, for analytic kernels like Gaussian, inverse multiquadric, and sinc, target KT admits maximum mean discrepancy (MMD) guarantees comparable to or better than those of square-root KT without making explicit use of a square-root kernel. Third, we prove that KT with a fractional power kernel yields better-than-Monte-Carlo MMD guarantees for non-smooth kernels, like Laplace and Mat\'ern, that do not have square-roots. Fourth, we establish that KT applied to a sum of the target and power kernels (a procedure we call KT+) simultaneously inherits the improved MMD guarantees of power KT and the tighter individual function guarantees of target KT. In our experiments with target KT and KT+, we witness significant improvements in integration error even in 100 dimensions and when compressing challenging differential equation posteriors.

Recent advances in large language models (LLMs) have showcased exceptional performance in long-context tasks, while facing significant inference efficiency challenges with limited GPU memory. Existing solutions first proposed the sliding-window approach to accumulate a set of historical key-value (KV) pairs for reuse, then further improvements selectively retain its subsets at each step. However, due to the sparse attention distribution across a long context, it is hard to identify and recall relevant KV pairs, as the attention is distracted by massive candidate pairs. Additionally, we found it promising to select representative tokens as probe-Query in each sliding window to effectively represent the entire context, which is an approach overlooked by existing methods. Thus, we propose ActQKV, a training-free, Activation-aware approach that dynamically determines probe-Query and leverages it to retrieve the relevant KV pairs for inference. Specifically, ActQKV monitors a token-level indicator, Activation Bias, within each context window, enabling the proper construction of probe-Query for retrieval at pre-filling stage. To accurately recall the relevant KV pairs and minimize the irrelevant ones, we design a dynamic KV cut-off mechanism guided by information density across layers at the decoding stage. Experiments on the Long-Bench and infty Benchmarks demonstrate its state-of-the-art performance with competitive inference quality and resource efficiency.

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.

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

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

We study both stream-based and pool-based active learning with neural network approximations. A recent line of works proposed bandit-based approaches that transformed active learning into a bandit problem, achieving both theoretical and empirical success. However, the performance and computational costs of these methods may be susceptible to the number of classes, denoted as K, due to this transformation. Therefore, this paper seeks to answer the question: "How can we mitigate the adverse impacts of K while retaining the advantages of principled exploration and provable performance guarantees in active learning?" To tackle this challenge, we propose two algorithms based on the newly designed exploitation and exploration neural networks for stream-based and pool-based active learning. Subsequently, we provide theoretical performance guarantees for both algorithms in a non-parametric setting, demonstrating a slower error-growth rate concerning K for the proposed approaches. We use extensive experiments to evaluate the proposed algorithms, which consistently outperform state-of-the-art baselines.

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

Pairwise re-ranking models predict which of two documents is more relevant to a query and then aggregate a final ranking from such preferences. This is often more effective than pointwise re-ranking models that directly predict a relevance value for each document. However, the high inference overhead of pairwise models limits their practical application: usually, for a set of k documents to be re-ranked, preferences for all k^2-k comparison pairs excluding self-comparisons are aggregated. We investigate whether the efficiency of pairwise re-ranking can be improved by sampling from all pairs. In an exploratory study, we evaluate three sampling methods and five preference aggregation methods. The best combination allows for an order of magnitude fewer comparisons at an acceptable loss of retrieval effectiveness, while competitive effectiveness is already achieved with about one third of the comparisons.

As large language models (LLMs) process increasing context windows, the memory usage of KV cache has become a critical bottleneck during inference. The mainstream KV compression methods, including KV pruning and KV quantization, primarily focus on either token or precision dimension and seldom explore the efficiency of their combination. In this paper, we comprehensively investigate the token-precision trade-off in KV cache compression. Experiments demonstrate that storing more tokens in the KV cache with lower precision, i.e., quantized pruning, can significantly enhance the long-context performance of LLMs. Furthermore, in-depth analysis regarding token-precision trade-off from a series of key aspects exhibit that, quantized pruning achieves substantial improvements in retrieval-related tasks and consistently performs well across varying input lengths. Moreover, quantized pruning demonstrates notable stability across different KV pruning methods, quantization strategies, and model scales. These findings provide valuable insights into the token-precision trade-off in KV cache compression. We plan to release our code in the near future.

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.

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.

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.

Machine learning especially deep neural networks have achieved great success but many of them often rely on a number of labeled samples for supervision. As sufficient labeled training data are not always ready due to e.g., continuously emerging prediction targets and costly sample annotation in real world applications, machine learning with sample shortage is now being widely investigated. Among all these studies, many prefer to utilize auxiliary information including those in the form of Knowledge Graph (KG) to reduce the reliance on labeled samples. In this survey, we have comprehensively reviewed over 90 papers about KG-aware research for two major sample shortage settings -- zero-shot learning (ZSL) where some classes to be predicted have no labeled samples, and few-shot learning (FSL) where some classes to be predicted have only a small number of labeled samples that are available. We first introduce KGs used in ZSL and FSL as well as their construction methods, and then systematically categorize and summarize KG-aware ZSL and FSL methods, dividing them into different paradigms such as the mapping-based, the data augmentation, the propagation-based and the optimization-based. We next present different applications, including not only KG augmented prediction tasks such as image classification, question answering, text classification and knowledge extraction, but also KG completion tasks, and some typical evaluation resources for each task. We eventually discuss some challenges and open problems from different perspectives.

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

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

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.

While large language models (LLMs) excel at handling long-context sequences, they require substantial key-value (KV) caches to store contextual information, which can heavily burden computational efficiency and memory usage. Previous efforts to compress these KV caches primarily focused on reducing memory demands but were limited in enhancing latency. To address this issue, we introduce FastKV, a KV cache compression method designed to enhance latency for long-context sequences. To enhance processing speeds while maintaining accuracy, FastKV adopts a novel Token-Selective Propagation (TSP) approach that retains the full context information in the initial layers of LLMs and selectively propagates only a portion of this information in deeper layers even in the prefill stage. Additionally, FastKV incorporates grouped-query attention (GQA)-aware KV cache compression to exploit the advantages of GQA in both memory and computational efficiency. Our experimental results show that FastKV achieves 2.00times and 1.40times improvements in time-to-first-token (TTFT) and throughput, respectively, compared to HeadKV, the state-of-the-art KV cache compression method. Moreover, FastKV successfully maintains accuracy on long-context benchmarks at levels comparable to the baselines. Our code is available at https://github.com/dongwonjo/FastKV.

Key-Value (KV) Caching has become an essential technique for accelerating the inference speed and throughput of generative Large Language Models~(LLMs). However, the memory footprint of the KV cache poses a critical bottleneck in LLM deployment as the cache size grows with batch size and sequence length, often surpassing even the size of the model itself. Although recent methods were proposed to select and evict unimportant KV pairs from the cache to reduce memory consumption, the potential ramifications of eviction on the generative process are yet to be thoroughly examined. In this paper, we examine the detrimental impact of cache eviction and observe that unforeseen risks arise as the information contained in the KV pairs is exhaustively discarded, resulting in safety breaches, hallucinations, and context loss. Surprisingly, we find that preserving even a small amount of information contained in the evicted KV pairs via reduced precision quantization substantially recovers the incurred degradation. On the other hand, we observe that the important KV pairs must be kept at a relatively higher precision to safeguard the generation quality. Motivated by these observations, we propose Mixed-precision KV cache~(MiKV), a reliable cache compression method that simultaneously preserves the context details by retaining the evicted KV pairs in low-precision and ensure generation quality by keeping the important KV pairs in high-precision. Experiments on diverse benchmarks and LLM backbones show that our proposed method offers a state-of-the-art trade-off between compression ratio and performance, compared to other baselines.

SGD does not produce robust results on datasets with label noise. Because the gradients calculated according to the losses of the noisy samples cause the optimization process to go in the wrong direction. In this paper, as an alternative to SGD, we recommend using samples with loss less than a threshold value determined during the optimization process, instead of using all samples in the mini-batch. Our proposed method, Adaptive-k, aims to exclude label noise samples from the optimization process and make the process robust. On noisy datasets, we found that using a threshold-based approach, such as Adaptive-k, produces better results than using all samples or a fixed number of low-loss samples in the mini-batch. Based on our theoretical analysis and experimental results, we show that the Adaptive-k method is closest to the performance of the oracle, in which noisy samples are entirely removed from the dataset. Adaptive-k is a simple but effective method. It does not require prior knowledge of the noise ratio of the dataset, does not require additional model training, and does not increase training time significantly. The code for Adaptive-k is available at https://github.com/enesdedeoglu-TR/Adaptive-k

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.

Generating diverse responses from large language models (LLMs) is crucial for applications such as planning/search and synthetic data generation, where diversity provides distinct answers across generations. Prior approaches rely on increasing temperature to increase diversity. However, contrary to popular belief, we show not only does this approach produce lower quality individual generations as temperature increases, but it depends on model's next-token probabilities being similar to the true distribution of answers. We propose , an alternative approach that uses the language model itself to partition the space into strata. At inference, a random stratum is selected and a sample drawn from within the strata. To measure diversity, we introduce CoverageQA, a dataset of underspecified questions with multiple equally plausible answers, and assess diversity by measuring KL Divergence between the output distribution and uniform distribution over valid ground truth answers. As computing probability per response/solution for proprietary models is infeasible, we measure recall on ground truth solutions. Our evaluation show using SimpleStrat achieves higher recall by 0.05 compared to GPT-4o and 0.36 average reduction in KL Divergence compared to Llama 3.

This paper presents the challenge report for the 2021 Kidney and Kidney Tumor Segmentation Challenge (KiTS21) held in conjunction with the 2021 international conference on Medical Image Computing and Computer Assisted Interventions (MICCAI). KiTS21 is a sequel to its first edition in 2019, and it features a variety of innovations in how the challenge was designed, in addition to a larger dataset. A novel annotation method was used to collect three separate annotations for each region of interest, and these annotations were performed in a fully transparent setting using a web-based annotation tool. Further, the KiTS21 test set was collected from an outside institution, challenging participants to develop methods that generalize well to new populations. Nonetheless, the top-performing teams achieved a significant improvement over the state of the art set in 2019, and this performance is shown to inch ever closer to human-level performance. An in-depth meta-analysis is presented describing which methods were used and how they faired on the leaderboard, as well as the characteristics of which cases generally saw good performance, and which did not. Overall KiTS21 facilitated a significant advancement in the state of the art in kidney tumor segmentation, and provides useful insights that are applicable to the field of semantic segmentation as a whole.

Many applications today provide users with multiple auto-complete drafts as they type, including GitHub's code completion, Gmail's smart compose, and Apple's messaging auto-suggestions. Under the hood, language models support this by running an autoregressive inference pass to provide a draft. Consequently, providing k drafts to the user requires running an expensive language model k times. To alleviate the computation cost of running k inference passes, we propose Superposed Decoding, a new decoding algorithm that generates k drafts at the computation cost of one autoregressive inference pass. We achieve this by feeding a superposition of the most recent token embeddings from the k drafts as input to the next decoding step of the language model. At every inference step we combine the k drafts with the top-k tokens to get k^2 new drafts and cache the k most likely options, using an n-gram interpolation with minimal compute overhead to filter out incoherent generations. Our experiments show that k drafts from Superposed Decoding are at least as coherent and factual as Nucleus Sampling and Greedy Decoding respectively, while being at least 2.44times faster for kge3. In a compute-normalized setting, user evaluations demonstrably favor text generated by Superposed Decoding over Nucleus Sampling. Code and more examples open-sourced at https://github.com/RAIVNLab/SuperposedDecoding.

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.

It is believed that in knowledge distillation (KD), the role of the teacher is to provide an estimate for the unknown Bayes conditional probability distribution (BCPD) to be used in the student training process. Conventionally, this estimate is obtained by training the teacher using maximum log-likelihood (MLL) method. To improve this estimate for KD, in this paper we introduce the concept of conditional mutual information (CMI) into the estimation of BCPD and propose a novel estimator called the maximum CMI (MCMI) method. Specifically, in MCMI estimation, both the log-likelihood and CMI of the teacher are simultaneously maximized when the teacher is trained. Through Eigen-CAM, it is further shown that maximizing the teacher's CMI value allows the teacher to capture more contextual information in an image cluster. Via conducting a thorough set of experiments, we show that by employing a teacher trained via MCMI estimation rather than one trained via MLL estimation in various state-of-the-art KD frameworks, the student's classification accuracy consistently increases, with the gain of up to 3.32\%. This suggests that the teacher's BCPD estimate provided by MCMI method is more accurate than that provided by MLL method. In addition, we show that such improvements in the student's accuracy are more drastic in zero-shot and few-shot settings. Notably, the student's accuracy increases with the gain of up to 5.72\% when 5\% of the training samples are available to the student (few-shot), and increases from 0\% to as high as 84\% for an omitted class (zero-shot). The code is available at https://github.com/iclr2024mcmi/ICLRMCMI.

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.

The increasing size of the Key-Value (KV) cache during the Large Language Models long-context inference is the main obstacle for its balance between the deployment cost and task accuracy. To reduce the KV cache size in such scenarios, most previous efforts leveraged on the attention weight to evict non-critical cache tokens. But there is a trade-off in those methods, they usually require major modifiation of the inference infrastructure and significant computation overhead. Base on the fact that the Large Lanuage models are autoregresssive models, we propose {\it LagKV}, a KV allocation strategy only relying on straight forward comparison among KV themself. It is a totally attention free method which offers easy integration to the main stream inference platform and comparable performance comparing to other complicated KV compression methods. Results on LongBench and PasskeyRetrieval show that, our approach achieves nearly zero loss when the ratio is 2times and approx 90% of the original model performance for 8times. Especially in the 64-digit passkey retrieval task, our mehod outperforms the attention weight based method H_2O over 60% with same compression ratios. Our code is available at https://github.com/AI-Lab-China-Merchants-Bank/LagKV.

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.

Emerging Large Language Model (LLM) applications require long input prompts to perform complex downstream tasks like document analysis and code generation. For these long context length applications, the length of the input prompt poses a significant challenge in terms of inference efficiency since the inference costs increase linearly with sequence length. However, for many of these applications, much of the context in the prompt is fixed across different user inputs, thereby providing the opportunity to perform offline optimizations to process user inputs quickly, as they are received. In this work, we propose Squeezed Attention as a mechanism to accelerate LLM applications where a large portion of the input prompt is fixed. We first leverage K-means clustering offline to group the keys for the fixed context based on semantic similarity and represent each cluster with a single centroid value. During inference, we compare query tokens from the user input with the centroids to predict which of the keys from the fixed context are semantically relevant and need to be loaded during inference. We then compute exact attention using only these important keys from the fixed context, thereby reducing bandwidth and computational costs. We also extend our method to use a hierarchical centroid lookup to identify important keys, which can reduce the complexity of attention from linear to logarithmic with respect to the context length. We implement optimized Triton kernels for centroid comparison and sparse FlashAttention with important keys, achieving more than 4x speedups during both the prefill and generation phases for long-context inference. Furthermore, we have extensively evaluated our method on various long-context benchmarks including LongBench, where it achieves a 3x reduction in KV cache budget without accuracy loss and up to an 8x reduction with <0.5 point accuracy gap for various models.

Candidate generation is the first stage in recommendation systems, where a light-weight system is used to retrieve potentially relevant items for an input user. These candidate items are then ranked and pruned in later stages of recommender systems using a more complex ranking model. Since candidate generation is the top of the recommendation funnel, it is important to retrieve a high-recall candidate set to feed into downstream ranking models. A common approach for candidate generation is to leverage approximate nearest neighbor (ANN) search from a single dense query embedding; however, this approach this can yield a low-diversity result set with many near duplicates. As users often have multiple interests, candidate retrieval should ideally return a diverse set of candidates reflective of the user's multiple interests. To this end, we introduce kNN-Embed, a general approach to improving diversity in dense ANN-based retrieval. kNN-Embed represents each user as a smoothed mixture over learned item clusters that represent distinct `interests' of the user. By querying each of a user's mixture component in proportion to their mixture weights, we retrieve a high-diversity set of candidates reflecting elements from each of a user's interests. We experimentally compare kNN-Embed to standard ANN candidate retrieval, and show significant improvements in overall recall and improved diversity across three datasets. Accompanying this work, we open source a large Twitter follow-graph dataset, to spur further research in graph-mining and representation learning for recommender systems.

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.

Language model performance depends on identifying the optimal mixture of data groups to train on (e.g., law, code, math). Prior work has proposed a diverse set of methods to efficiently learn mixture proportions, ranging from fitting regression models over training runs to dynamically updating proportions throughout training. Surprisingly, we find that no existing method consistently outperforms a simple stratified sampling baseline in terms of average test perplexity. To understand this inconsistency, we unify existing methods into a standard framework, showing they are equivalent to solving a common optimization problem: minimize average loss subject to a method-specific mixing law -- an implicit assumption on the relationship between loss and mixture proportions. This framework suggests that measuring the fidelity of a method's mixing law can offer insights into its performance. Empirically, we find that existing methods set their mixing law parameters inaccurately, resulting in the inconsistent mixing performance we observe. Using this insight, we derive a new online method named Aioli, which directly estimates the mixing law parameters throughout training and uses them to dynamically adjust proportions. Aioli outperforms stratified sampling on 6 out of 6 datasets by an average of 0.27 test perplexity points, whereas existing methods fail to consistently beat stratified sampling, doing up to 6.9 points worse. Moreover, in a practical setting where proportions are learned on shorter runs due to computational constraints, Aioli can dynamically adjust these proportions over the full training run, consistently improving performance over existing methods by up to 12.012 test perplexity points.

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

We 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.

Clustering is a widely deployed unsupervised learning tool. Model-based clustering is a flexible framework to tackle data heterogeneity when the clusters have different shapes. Likelihood-based inference for mixture distributions often involves non-convex and high-dimensional objective functions, imposing difficult computational and statistical challenges. The classic expectation-maximization (EM) algorithm is a computationally thrifty iterative method that maximizes a surrogate function minorizing the log-likelihood of observed data in each iteration, which however suffers from bad local maxima even in the special case of the standard Gaussian mixture model with common isotropic covariance matrices. On the other hand, recent studies reveal that the unique global solution of a semidefinite programming (SDP) relaxed K-means achieves the information-theoretically sharp threshold for perfectly recovering the cluster labels under the standard Gaussian mixture model. In this paper, we extend the SDP approach to a general setting by integrating cluster labels as model parameters and propose an iterative likelihood adjusted SDP (iLA-SDP) method that directly maximizes the exact observed likelihood in the presence of data heterogeneity. By lifting the cluster assignment to group-specific membership matrices, iLA-SDP avoids centroids estimation -- a key feature that allows exact recovery under well-separateness of centroids without being trapped by their adversarial configurations. Thus iLA-SDP is less sensitive than EM to initialization and more stable on high-dimensional data. Our numeric experiments demonstrate that iLA-SDP can achieve lower mis-clustering errors over several widely used clustering methods including K-means, SDP and EM algorithms.

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.

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.

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

The data used to pretrain large language models has a decisive impact on a model's downstream performance, which has led to a large body of work on data selection methods that aim to automatically determine the most suitable data to use for pretraining. Existing data selection methods suffer from slow and computationally expensive processes, a problem amplified by the increasing size of models and of pretraining datasets. Data mixing, on the other hand, reduces the complexity of data selection by grouping data points together and determining sampling probabilities across entire groups. However, data mixing proportions are typically fixed before training and therefore cannot adapt to changing training dynamics. To address these limitations, we develop an efficient algorithm for Online Data Mixing (ODM) that combines elements from both data selection and data mixing. Based on multi-armed bandit algorithms, our online approach optimizes the data mixing proportions during training. Remarkably, our method trains a model that reaches the final perplexity of the next best method with 19\% fewer training iterations, and improves performance on the 5-shot MMLU benchmark by 1.9% relative accuracy, while adding negligible wall-clock time during pretraining.

Long-context LLMs have enabled numerous downstream applications but also introduced significant challenges related to computational and memory efficiency. To address these challenges, optimizations for long-context inference have been developed, centered around the KV cache. However, existing benchmarks often evaluate in single-request, neglecting the full lifecycle of the KV cache in real-world use. This oversight is particularly critical, as KV cache reuse has become widely adopted in LLMs inference frameworks, such as vLLM and SGLang, as well as by LLM providers, including OpenAI, Microsoft, Google, and Anthropic. To address this gap, we introduce SCBench(SharedContextBench), a comprehensive benchmark for evaluating long-context methods from a KV cachecentric perspective: 1) KV cache generation, 2) KV cache compression, 3) KV cache retrieval, 4) KV cache loading. Specifically, SCBench uses test examples with shared context, ranging 12 tasks with two shared context modes, covering four categories of long-context capabilities: string retrieval, semantic retrieval, global information, and multi-task. With it, we provide an extensive KV cache-centric analysis of eight categories long-context solutions, including Gated Linear RNNs, Mamba-Attention hybrids, and efficient methods such as sparse attention, KV cache dropping, quantization, retrieval, loading, and prompt compression. The evaluation is conducted on 8 long-context LLMs. Our findings show that sub-O(n) memory methods suffer in multi-turn scenarios, while sparse encoding with O(n) memory and sub-O(n^2) pre-filling computation perform robustly. Dynamic sparsity yields more expressive KV caches than static patterns, and layer-level sparsity in hybrid architectures reduces memory usage with strong performance. Additionally, we identify attention distribution shift issues in long-generation scenarios. https://aka.ms/SCBench.

Knowledge distillation (KD) is a widely used framework for training compact, task-specific models by leveraging the knowledge of teacher models. However, its application to active learning (AL), which aims to minimize annotation costs through iterative sample selection, remains underexplored. This gap stems from the fact that KD typically assumes access to sufficient labeled data, whereas AL operates in data-scarce scenarios where task-specific teacher models are often unavailable. In this paper, we introduce ActiveKD, a framework that integrates AL with KD by leveraging the zero- and few-shot capabilities of large vision-language models (VLMs). A key aspect of ActiveKD is the structured prediction bias of VLMs -- i.e., their predictions form clusters in the probability space. We regard this structure as an inductive bias of the teacher model, capturing generalizable output patterns beneficial to student learning. To exploit this bias, we propose Probabilistic CoreSet (PCoreSet), a selection strategy that maximizes coverage in the probability space rather than the feature space. PCoreSet strategically selects categorically diverse unlabeled samples, facilitating more efficient transfer of teacher knowledge under limited annotation budgets. Evaluations on 11 datasets show that PCoreSet consistently outperforms existing selection methods within the ActiveKD framework, advancing research at the intersection of AL and KD.

Recently, the retrieval models based on dense representations have been gradually applied in the first stage of the document retrieval tasks, showing better performance than traditional sparse vector space models. To obtain high efficiency, the basic structure of these models is Bi-encoder in most cases. However, this simple structure may cause serious information loss during the encoding of documents since the queries are agnostic. To address this problem, we design a method to mimic the queries on each of the documents by an iterative clustering process and represent the documents by multiple pseudo queries (i.e., the cluster centroids). To boost the retrieval process using approximate nearest neighbor search library, we also optimize the matching function with a two-step score calculation procedure. Experimental results on several popular ranking and QA datasets show that our model can achieve state-of-the-art results.

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

Motivated by concerns about making online decisions that incur undue amount of risk at each time step, in this paper, we formulate the probably anytime-safe stochastic combinatorial semi-bandits problem. In this problem, the agent is given the option to select a subset of size at most K from a set of L ground items. Each item is associated to a certain mean reward as well as a variance that represents its risk. To mitigate the risk that the agent incurs, we require that with probability at least 1-delta, over the entire horizon of time T, each of the choices that the agent makes should contain items whose sum of variances does not exceed a certain variance budget. We call this probably anytime-safe constraint. Under this constraint, we design and analyze an algorithm {\sc PASCombUCB} that minimizes the regret over the horizon of time T. By developing accompanying information-theoretic lower bounds, we show that under both the problem-dependent and problem-independent paradigms, {\sc PASCombUCB} is almost asymptotically optimal. Experiments are conducted to corroborate our theoretical findings. Our problem setup, the proposed {\sc PASCombUCB} algorithm, and novel analyses are applicable to domains such as recommendation systems and transportation in which an agent is allowed to choose multiple items at a single time step and wishes to control the risk over the whole time horizon.

We give the first efficient algorithm for learning halfspaces in the testable learning model recently defined by Rubinfeld and Vasilyan (2023). In this model, a learner certifies that the accuracy of its output hypothesis is near optimal whenever the training set passes an associated test, and training sets drawn from some target distribution -- e.g., the Gaussian -- must pass the test. This model is more challenging than distribution-specific agnostic or Massart noise models where the learner is allowed to fail arbitrarily if the distributional assumption does not hold. We consider the setting where the target distribution is Gaussian (or more generally any strongly log-concave distribution) in d dimensions and the noise model is either Massart or adversarial (agnostic). For Massart noise, our tester-learner runs in polynomial time and outputs a hypothesis with (information-theoretically optimal) error opt + epsilon for any strongly log-concave target distribution. For adversarial noise, our tester-learner obtains error O(opt) + epsilon in polynomial time when the target distribution is Gaussian; for strongly log-concave distributions, we obtain O(opt) + epsilon in quasipolynomial time. Prior work on testable learning ignores the labels in the training set and checks that the empirical moments of the covariates are close to the moments of the base distribution. Here we develop new tests of independent interest that make critical use of the labels and combine them with the moment-matching approach of Gollakota et al. (2023). This enables us to simulate a variant of the algorithm of Diakonikolas et al. (2020) for learning noisy halfspaces using nonconvex SGD but in the testable learning setting.

We introduce HyperCLOVA X THINK, the first reasoning-focused large language model in the HyperCLOVA X family, pre-trained on roughly 6 trillion high-quality Korean, and English tokens, augmented with targeted synthetic Korean data. It was implemented as a compute-memory-balanced Peri-LN Transformer scaled with muP, pre-trained through a three-stage curriculum that expands the context window to 128K tokens, and post-trained via supervised fine-tuning with Reinforcement Learning from Verifiable Rewards supports both detailed rationale and concise-answer modes. It delivers competitive performance against similarly sized models on Korea-focused benchmarks such as KMMLU, CSAT, KoBALT-700, HAERAE-1.0, and KoBigBench, while preserving robust bilingual consistency and translation quality. In addition, a vision-augmented variant matches or exceeds GPT-4.1 on the KCSAT STEM benchmark, all of which are achieved with substantially lower training compute than existing models of similar sizes. We also present a pruning and distillation technique that will soon be applied to HyperCLOVA X THINK for an open-source and business-friendly foundation model. Altogether, these capabilities position HyperCLOVA X THINK as a robust foundation for Korean AI innovation and a valuable resource for the global research community.

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

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

Large Language models (LLMs) have become a research hotspot. To accelerate the inference of LLMs, storing computed caches in memory has become the standard technique. However, as the inference length increases, growing KV caches might lead to out-of-memory issues. Many existing methods address this issue through KV cache compression, primarily by preserving key tokens throughout all layers to reduce information loss. Most of them allocate a uniform budget size for each layer to retain. However, we observe that the minimum budget sizes needed to retain essential information vary across layers and models based on the perspectives of attention and hidden state output. Building on this observation, this paper proposes a simple yet effective KV cache compression method that leverages layer uncertainty to allocate budget size for each layer. Experimental results show that the proposed method can reduce memory usage of the KV caches to only sim20\% when compared to Full KV inference while achieving nearly lossless performance.

Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers, which is commonly used in the optimization literature due to its fast convergence. In contrast to distributed optimization, distributed sampling allows for uncertainty quantification in Bayesian inference tasks. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. For our theoretical results, we use convex optimization tools to establish a fundamental inequality on the generated local sample iterates. This inequality enables us to show convergence of the distribution associated with these iterates to the underlying target distribution in Wasserstein distance. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.

With the emergence of Mixture-of-Experts (MoE), the efficient scaling of model size has accelerated the development of large language models in recent years. However, their high memory requirements prevent their use in resource-constrained environments. While knowledge distillation (KD) has been a proven method for model compression, its application to MoE teacher models remains underexplored. Through our investigation, we discover that non-activated experts in MoE models possess valuable knowledge that benefits student models. We further demonstrate that existing KD methods are not optimal for compressing MoE models, as they fail to leverage this knowledge effectively. To address this, we propose two intuitive MoE-specific KD methods for the first time: Knowledge Augmentation (KA) and Student-Aware Router (SAR), both designed to effectively extract knowledge from all experts. Specifically, KA augments knowledge by sampling experts multiple times, while SAR uses all experts and adjusts the expert weights through router training to provide optimal knowledge. Extensive experiments show that our methods outperform conventional KD methods, demonstrating their effectiveness for MoE teacher models.

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.

One-shot coreset selection aims to select a representative subset of the training data, given a pruning rate, that can later be used to train future models while retaining high accuracy. State-of-the-art coreset selection methods pick the highest importance examples based on an importance metric and are found to perform well at low pruning rates. However, at high pruning rates, they suffer from a catastrophic accuracy drop, performing worse than even random sampling. This paper explores the reasons behind this accuracy drop both theoretically and empirically. We first propose a novel metric to measure the coverage of a dataset on a specific distribution by extending the classical geometric set cover problem to a distribution cover problem. This metric helps explain why coresets selected by SOTA methods at high pruning rates perform poorly compared to random sampling because of worse data coverage. We then propose a novel one-shot coreset selection method, Coverage-centric Coreset Selection (CCS), that jointly considers overall data coverage upon a distribution as well as the importance of each example. We evaluate CCS on five datasets and show that, at high pruning rates (e.g., 90%), it achieves significantly better accuracy than previous SOTA methods (e.g., at least 19.56% higher on CIFAR10) as well as random selection (e.g., 7.04% higher on CIFAR10) and comparable accuracy at low pruning rates. We make our code publicly available at https://github.com/haizhongzheng/Coverage-centric-coreset-selection.

We aim to identify how different components in the KD pipeline affect the resulting performance and how much the optimal KD pipeline varies across different datasets/tasks, such as the data augmentation policy, the loss function, and the intermediate representation for transferring the knowledge between teacher and student. To tease apart their effects, we propose Distiller, a meta KD framework that systematically combines a broad range of techniques across different stages of the KD pipeline, which enables us to quantify each component's contribution. Within Distiller, we unify commonly used objectives for distillation of intermediate representations under a universal mutual information (MI) objective and propose a class of MI-alpha objective functions with better bias/variance trade-off for estimating the MI between the teacher and the student. On a diverse set of NLP datasets, the best Distiller configurations are identified via large-scale hyperparameter optimization. Our experiments reveal the following: 1) the approach used to distill the intermediate representations is the most important factor in KD performance, 2) among different objectives for intermediate distillation, MI-alpha performs the best, and 3) data augmentation provides a large boost for small training datasets or small student networks. Moreover, we find that different datasets/tasks prefer different KD algorithms, and thus propose a simple AutoDistiller algorithm that can recommend a good KD pipeline for a new dataset.

The choice of embedding model is a crucial step in the design of Retrieval Augmented Generation (RAG) systems. Given the sheer volume of available options, identifying clusters of similar models streamlines this model selection process. Relying solely on benchmark performance scores only allows for a weak assessment of model similarity. Thus, in this study, we evaluate the similarity of embedding models within the context of RAG systems. Our assessment is two-fold: We use Centered Kernel Alignment to compare embeddings on a pair-wise level. Additionally, as it is especially pertinent to RAG systems, we evaluate the similarity of retrieval results between these models using Jaccard and rank similarity. We compare different families of embedding models, including proprietary ones, across five datasets from the popular Benchmark Information Retrieval (BEIR). Through our experiments we identify clusters of models corresponding to model families, but interestingly, also some inter-family clusters. Furthermore, our analysis of top-k retrieval similarity reveals high-variance at low k values. We also identify possible open-source alternatives to proprietary models, with Mistral exhibiting the highest similarity to OpenAI models.

Temperature sampling is a conventional approach to diversify large language model predictions. As temperature increases, the prediction becomes diverse but also vulnerable to hallucinations -- generating tokens that are sensible but not factual. One common approach to mitigate hallucinations is to provide source/grounding documents and the model is trained to produce predictions that bind to and are attributable to the provided source. It appears that there is a trade-off between diversity and attribution. To mitigate any such trade-off, we propose to relax the constraint of having a fixed temperature over decoding steps, and a mechanism to guide the dynamic temperature according to its relevance to the source through KL-divergence. Our experiments justifies the trade-off, and shows that our sampling algorithm outperforms the conventional top-k and top-p algorithms in conversational question-answering and summarization tasks.

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

In recent years, the challenge of extracting information from business documents has emerged as a critical task, finding applications across numerous domains. This effort has attracted substantial interest from both industry and academy, highlighting its significance in the current technological landscape. Most datasets in this area are primarily focused on Key Information Extraction (KIE), where the extraction process revolves around extracting information using a specific, predefined set of keys. Unlike most existing datasets and benchmarks, our focus is on discovering key-value pairs (KVPs) without relying on predefined keys, navigating through an array of diverse templates and complex layouts. This task presents unique challenges, primarily due to the absence of comprehensive datasets and benchmarks tailored for non-predetermined KVP extraction. To address this gap, we introduce KVP10k , a new dataset and benchmark specifically designed for KVP extraction. The dataset contains 10707 richly annotated images. In our benchmark, we also introduce a new challenging task that combines elements of KIE as well as KVP in a single task. KVP10k sets itself apart with its extensive diversity in data and richly detailed annotations, paving the way for advancements in the field of information extraction from complex business documents.

Finding the mode of a high dimensional probability distribution D is a fundamental algorithmic problem in statistics and data analysis. There has been particular interest in efficient methods for solving the problem when D is represented as a mixture model or kernel density estimate, although few algorithmic results with worst-case approximation and runtime guarantees are known. In this work, we significantly generalize a result of (LeeLiMusco:2021) on mode approximation for Gaussian mixture models. We develop randomized dimensionality reduction methods for mixtures involving a broader class of kernels, including the popular logistic, sigmoid, and generalized Gaussian kernels. As in Lee et al.'s work, our dimensionality reduction results yield quasi-polynomial algorithms for mode finding with multiplicative accuracy (1-epsilon) for any epsilon > 0. Moreover, when combined with gradient descent, they yield efficient practical heuristics for the problem. In addition to our positive results, we prove a hardness result for box kernels, showing that there is no polynomial time algorithm for finding the mode of a kernel density estimate, unless P = NP. Obtaining similar hardness results for kernels used in practice (like Gaussian or logistic kernels) is an interesting future direction.

The ecological validity of soundscape studies usually rests on a choice of soundscapes that are representative of the perceptual space under investigation. For example, a soundscape pleasantness study might investigate locations with soundscapes ranging from "pleasant" to "annoying". The choice of soundscapes is typically researcher-led, but a participant-led process can reduce selection bias and improve result reliability. Hence, we propose a robust participant-led method to pinpoint characteristic soundscapes possessing arbitrary perceptual attributes. We validate our method by identifying Singaporean soundscapes spanning the perceptual quadrants generated from the "Pleasantness" and "Eventfulness" axes of the ISO 12913-2 circumplex model of soundscape perception, as perceived by local experts. From memory and experience, 67 participants first selected locations corresponding to each perceptual quadrant in each major planning region of Singapore. We then performed weighted k-means clustering on the selected locations, with weights for each location derived from previous frequencies and durations spent in each location by each participant. Weights hence acted as proxies for participant confidence. In total, 62 locations were thereby identified as suitable locations with characteristic soundscapes for further research utilizing the ISO 12913-2 perceptual quadrants. Audio-visual recordings and acoustic characterization of the soundscapes will be made in a future study.

Transformer-based large language models (LLMs) cache context as key-value (KV) pairs during inference. As context length grows, KV cache sizes expand, leading to substantial memory overhead and increased attention latency. This paper introduces KVzip, a query-agnostic KV cache eviction method enabling effective reuse of compressed KV caches across diverse queries. KVzip quantifies the importance of a KV pair using the underlying LLM to reconstruct original contexts from cached KV pairs, subsequently evicting pairs with lower importance. Extensive empirical evaluations demonstrate that KVzip reduces KV cache size by 3-4times and FlashAttention decoding latency by approximately 2times, with negligible performance loss in question-answering, retrieval, reasoning, and code comprehension tasks. Evaluations include various models such as LLaMA3.1-8B, Qwen2.5-14B, and Gemma3-12B, with context lengths reaching up to 170K tokens. KVzip significantly outperforms existing query-aware KV eviction methods, which suffer from performance degradation even at a 90% cache budget ratio under multi-query scenarios.

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.

How to efficiently serve Large Language Models (LLMs) has become a pressing issue because of their huge computational cost in their autoregressive generation process. To mitigate computational costs, LLMs often employ the KV Cache technique to improve the generation speed. While improving the computational efficiency, the storage requirements of the KV cache are substantial, particularly in long-context scenarios, leading to significant memory consumption. Existing KV cache eviction methods often degrade the performance of LLMs in long-context scenarios due to the information loss introduced by eviction. In this paper, we propose a novel KV cache merging approach, called KVMerger, to achieve adaptive KV cache compression for long-context tasks without significant performance degradation under constrained memory budgets. Our approach is inspired by the intriguing observation that key states exhibit high similarity at the token level within a single sequence. To facilitate merging, we develop an effective yet straightforward merging set identification algorithm to identify suitable KV states for merging. Our merging set identification algorithm stimulates the second observation that KV cache sparsity, from similarity perspective, is independent of the dataset and remains persistent at the model level. Subsequently, we propose a Gaussian kernel weighted merging algorithm to selectively merge all states within each merging set. We conduct extensive experiments to demonstrate the effectiveness of KVMerger for long-context tasks under constrained memory budgets, applying it to models including Llama2-7B-chat and Llama2-13B-chat. Using the LongBench and ZeroScroll benchmarks, we compare our method with other KV cache compression techniques, including H2O and CaM, showing that our method achieves superior performance across tasks with both 50% and 35% KV cache budgets.

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.

Efficiently serving large language models (LLMs) requires batching many requests together to reduce the cost per request. Yet, the key-value (KV) cache, which stores attention keys and values to avoid re-computations, significantly increases memory demands and becomes the new bottleneck in speed and memory usage. This memory demand increases with larger batch sizes and longer context lengths. Additionally, the inference speed is limited by the size of KV cache, as the GPU's SRAM must load the entire KV cache from the main GPU memory for each token generated, causing the computational core to be idle during this process. A straightforward and effective solution to reduce KV cache size is quantization, which decreases the total bytes taken by KV cache. However, there is a lack of in-depth studies that explore the element distribution of KV cache to understand the hardness and limitation of KV cache quantization. To fill the gap, we conducted a comprehensive study on the element distribution in KV cache of popular LLMs. Our findings indicate that the key cache should be quantized per-channel, i.e., group elements along the channel dimension and quantize them together. In contrast, the value cache should be quantized per-token. From this analysis, we developed a tuning-free 2bit KV cache quantization algorithm, named KIVI. With the hardware-friendly implementation, KIVI can enable Llama (Llama-2), Falcon, and Mistral models to maintain almost the same quality while using 2.6times less peak memory usage (including the model weight). This reduction in memory usage enables up to 4times larger batch size, bringing 2.35times sim 3.47times throughput on real LLM inference workload. The source code is available at https://github.com/jy-yuan/KIVI.

Exponential increases in scientific experimental data are outstripping the rate of progress in silicon technology. As a result, heterogeneous combinations of architectures and process or device technologies are increasingly important to meet the computing demands of future scientific experiments. However, the complexity of heterogeneous computing systems requires systematic modeling to understand performance. We present a model which addresses this need by framing key aspects of data collection pipelines and constraints, and combines them with the important vectors of technology that shape alternatives, computing metrics that allow complex alternatives to be compared. For instance, a data collection pipeline may be characterized by parameters such as sensor sampling rates, amount of data collected, and the overall relevancy of retrieved samples. Alternatives to this pipeline are enabled by hardware development vectors including advancing CMOS, GPUs, neuromorphic computing, and edge computing. By calculating metrics for each alternative such as overall F1 score, power, hardware cost, and energy expended per relevant sample, this model allows alternate data collection systems to be rigorously compared. To demonstrate this model's capability, we apply it to the CMS experiment (and planned HL-LHC upgrade) to evaluate and compare the application of novel technologies in the data acquisition system (DAQ). We demonstrate that improvements to early stages in the DAQ are highly beneficial, greatly reducing the resources required at later stages of processing (such as a 60% power reduction) and increasing the amount of relevant data retrieved from the experiment per unit power (improving from 0.065 to 0.31 samples/kJ) However, we predict further advances will be required in order to meet overall power and cost constraints for the DAQ.

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.

Ranking has always been one of the top concerns in information retrieval researches. For decades, the lexical matching signal has dominated the ad-hoc retrieval process, but solely using this signal in retrieval may cause the vocabulary mismatch problem. In recent years, with the development of representation learning techniques, many researchers turn to Dense Retrieval (DR) models for better ranking performance. Although several existing DR models have already obtained promising results, their performance improvement heavily relies on the sampling of training examples. Many effective sampling strategies are not efficient enough for practical usage, and for most of them, there still lacks theoretical analysis in how and why performance improvement happens. To shed light on these research questions, we theoretically investigate different training strategies for DR models and try to explain why hard negative sampling performs better than random sampling. Through the analysis, we also find that there are many potential risks in static hard negative sampling, which is employed by many existing training methods. Therefore, we propose two training strategies named a Stable Training Algorithm for dense Retrieval (STAR) and a query-side training Algorithm for Directly Optimizing Ranking pErformance (ADORE), respectively. STAR improves the stability of DR training process by introducing random negatives. ADORE replaces the widely-adopted static hard negative sampling method with a dynamic one to directly optimize the ranking performance. Experimental results on two publicly available retrieval benchmark datasets show that either strategy gains significant improvements over existing competitive baselines and a combination of them leads to the best performance.

Large Language Models (LLMs) have been widely adopted to process long-context tasks. However, the large memory overhead of the key-value (KV) cache poses significant challenges in long-context scenarios. Existing training-free KV cache compression methods typically focus on quantization and token pruning, which have compression limits, and excessive sparsity can lead to severe performance degradation. Other methods design new architectures with less KV overhead but require significant training overhead. To address the above two drawbacks, we further explore the redundancy in the channel dimension and apply an architecture-level design with minor training costs. Therefore, we introduce CSKV, a training-efficient Channel Shrinking technique for KV cache compression: (1) We first analyze the singular value distribution of the KV cache, revealing significant redundancy and compression potential along the channel dimension. Based on this observation, we propose using low-rank decomposition for key and value layers and storing the low-dimension features. (2) To preserve model performance, we introduce a bi-branch KV cache, including a window-based full-precision KV cache and a low-precision compressed KV cache. (3) To reduce the training costs, we minimize the layer-wise reconstruction loss for the compressed KV cache instead of retraining the entire LLMs. Extensive experiments show that CSKV can reduce the memory overhead of the KV cache by 80% while maintaining the model's long-context capability. Moreover, we show that our method can be seamlessly combined with quantization to further reduce the memory overhead, achieving a compression ratio of up to 95%.

A critical approach for efficiently deploying computationally demanding large language models (LLMs) is Key-Value (KV) caching. The KV cache stores key-value states of previously generated tokens, significantly reducing the need for repetitive computations and thereby lowering latency in autoregressive generation. However, the size of the KV cache grows linearly with sequence length, posing challenges for applications requiring long context input and extensive sequence generation. In this paper, we present a simple yet effective approach, called MiniCache, to compress the KV cache across layers from a novel depth perspective, significantly reducing the memory footprint for LLM inference. Our approach is based on the observation that KV cache states exhibit high similarity between the adjacent layers in the middle-to-deep portion of LLMs. To facilitate merging, we propose disentangling the states into the magnitude and direction components, interpolating the directions of the state vectors while preserving their lengths unchanged. Furthermore, we introduce a token retention strategy to keep highly distinct state pairs unmerged, thus preserving the information with minimal additional storage overhead. Our MiniCache is training-free and general, complementing existing KV cache compression strategies, such as quantization and sparsity. We conduct a comprehensive evaluation of MiniCache utilizing various models including LLaMA-2, LLaMA-3, Phi-3, Mistral, and Mixtral across multiple benchmarks, demonstrating its exceptional performance in achieving superior compression ratios and high throughput. On the ShareGPT dataset, LLaMA-2-7B with 4-bit MiniCache achieves a remarkable compression ratio of up to 5.02x, enhances inference throughput by approximately 5x, and reduces the memory footprint by 41% compared to the FP16 full cache baseline, all while maintaining near-lossless performance.

Large language models (LLMs) have demonstrated exceptional capabilities in generating text, images, and video content. However, as context length grows, the computational cost of attention increases quadratically with the number of tokens, presenting significant efficiency challenges. This paper presents an analysis of various Key-Value (KV) cache compression strategies, offering a comprehensive taxonomy that categorizes these methods by their underlying principles and implementation techniques. Furthermore, we evaluate their impact on performance and inference latency, providing critical insights into their effectiveness. Our findings highlight the trade-offs involved in KV cache compression and its influence on handling long-context scenarios, paving the way for more efficient LLM implementations.

Multimodal Large Language Models (MLLMs) have achieved remarkable success across various applications, yet their computational overhead during deployment remains a critical challenge. While Key-Value (KV) caching improves inference efficiency by trading memory for computation, the growing memory footprint from storing extensive KV caches reduces throughput and limits long-term execution on devices with constrained GPU memory. Existing approaches primarily focus on dropping unimportant tokens to reduce the KV cache size, mitigating memory constraints at the cost of potential information loss. In contrast, we propose a simple yet effective visual quantization strategy that preserves all visual tokens while significantly reducing memory consumption. To achieve an extreme quantization ratio, i.e., 1-bit quantization, we propose group-specific quantization and quantile-based quantization approaches, motivated by the inherent patterns of the KV cache. Our method is plug-and-play, enabling seamless integration into various MLLMs to improve memory efficiency without architectural modifications. Extensive experiments demonstrate that our approach effectively reduces memory overhead while maintaining computational efficiency and preserving multimodal performance.

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.

Inference with transformer-based language models begins with a prompt processing step. In this step, the model generates the first output token and stores the KV cache needed for future generation steps. This prompt processing step can be computationally expensive, taking 10s of seconds or more for billion-parameter models on edge devices when prompt lengths or batch sizes rise. This degrades user experience by introducing significant latency into the model's outputs. To reduce the time spent producing the first output (known as the ``time to first token'', or TTFT) of a pretrained model, we introduce a novel method called KV Prediction. In our method, a small auxiliary model is used to process the prompt and produce an approximation of the KV cache used by a base model. This approximated KV cache is then used with the base model for autoregressive generation without the need to query the auxiliary model again. We demonstrate that our method produces a pareto-optimal efficiency-accuracy trade-off when compared to baselines. On TriviaQA, we demonstrate relative accuracy improvements in the range of 15%-50% across a range of TTFT FLOPs budgets. We also demonstrate accuracy improvements of up to 30% on HumanEval python code completion at fixed TTFT FLOPs budgets. Additionally, we benchmark models on an Apple M2 Pro CPU and demonstrate that our improvement in FLOPs translates to a TTFT speedup on hardware. We release our code at https://github.com/apple/corenet/tree/main/projects/kv-prediction .

Synthetic high-quality multi-step reasoning data can significantly enhance the performance of large language models on various tasks. However, most existing methods rely on rejection sampling, which generates trajectories independently and suffers from inefficiency and imbalanced sampling across problems of varying difficulty. In this work, we introduce FastMCTS, an innovative data synthesis strategy inspired by Monte Carlo Tree Search. FastMCTS provides a more efficient sampling method for multi-step reasoning data, offering step-level evaluation signals and promoting balanced sampling across problems of different difficulty levels. Experiments on both English and Chinese reasoning datasets demonstrate that FastMCTS generates over 30\% more correct reasoning paths compared to rejection sampling as the number of generated tokens scales up. Furthermore, under comparable synthetic data budgets, models trained on FastMCTS-generated data outperform those trained on rejection sampling data by 3.9\% across multiple benchmarks. As a lightweight sampling strategy, FastMCTS offers a practical and efficient alternative for synthesizing high-quality reasoning data. Our code will be released soon.

Test-time compute scaling has emerged as a new axis along which to improve model accuracy, where additional computation is used at inference time to allow the model to think longer for more challenging problems. One promising approach for test-time compute scaling is search against a process reward model, where a model generates multiple potential candidates at each step of the search, and these partial trajectories are then scored by a separate reward model in order to guide the search process. The diversity of trajectories in the tree search process affects the accuracy of the search, since increasing diversity promotes more exploration. However, this diversity comes at a cost, as divergent trajectories have less KV sharing, which means they consume more memory and slow down the search process. Previous search methods either do not perform sufficient exploration, or else explore diverse trajectories but have high latency. We address this challenge by proposing Efficient Tree Search (ETS), which promotes KV sharing by pruning redundant trajectories while maintaining necessary diverse trajectories. ETS incorporates a linear programming cost model to promote KV cache sharing by penalizing the number of nodes retained, while incorporating a semantic coverage term into the cost model to ensure that we retain trajectories which are semantically different. We demonstrate how ETS can achieve 1.8times reduction in average KV cache size during the search process, leading to 1.4times increased throughput relative to prior state-of-the-art methods, with minimal accuracy degradation and without requiring any custom kernel implementation. Code is available at: https://github.com/SqueezeAILab/ETS.

We propose a novel speculative decoding method tailored for multi-sample reasoning scenarios, such as self-consistency and Best-of-N sampling. Our method exploits the intrinsic consensus of parallel generation paths to synthesize high-quality draft tokens without requiring auxiliary models or external databases. By dynamically analyzing structural patterns across parallel reasoning paths through a probabilistic aggregation mechanism, it identifies consensus token sequences that align with the decoding distribution. Evaluations on mathematical reasoning benchmarks demonstrate a substantial improvement in draft acceptance rates over baselines, while reducing the latency in draft token construction. This work establishes a paradigm shift for efficient multi-sample inference, enabling seamless integration of speculative decoding with sampling-based reasoning techniques.

As large language models (LLMs) are applied to more use cases, creating high quality, task-specific datasets for fine-tuning becomes a bottleneck for model improvement. Using high quality human data has been the most common approach to unlock model performance, but is prohibitively expensive in many scenarios. Several alternative methods have also emerged, such as generating synthetic or hybrid data, but the effectiveness of these approaches remain unclear, especially in resource-constrained scenarios and tasks that are not easily verified. To investigate this, we group various synthetic data generation strategies into three representative categories -- Answer Augmentation, Question Rephrase and New Question -- and study the performance of student LLMs trained under various constraints, namely seed instruction set size and query budget. We demonstrate that these strategies are not equally effective across settings. Notably, the optimal data generation strategy depends strongly on the ratio between the available teacher query budget and the size of the seed instruction set. When this ratio is low, generating new answers to existing questions proves most effective, but as this ratio increases, generating new questions becomes optimal. Across all tasks, we find that choice of augmentation method and other design choices matter substantially more in low to mid data regimes than in high data regimes. We provide a practical framework for selecting the appropriate augmentation method across settings, taking into account additional factors such as the scalability of each method, the importance of verifying synthetic data, and the use of different LLMs for synthetic data generation.

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.

Knowledge distillation (KD) has been widely adopted to compress large language models (LLMs). Existing KD methods investigate various divergence measures including the Kullback-Leibler (KL), reverse Kullback-Leibler (RKL), and Jensen-Shannon (JS) divergences. However, due to limitations inherent in their assumptions and definitions, these measures fail to deliver effective supervision when few distribution overlap exists between the teacher and the student. In this paper, we show that the aforementioned KL, RKL, and JS divergences respectively suffer from issues of mode-averaging, mode-collapsing, and mode-underestimation, which deteriorates logits-based KD for diverse NLP tasks. We propose the Sinkhorn Knowledge Distillation (SinKD) that exploits the Sinkhorn distance to ensure a nuanced and precise assessment of the disparity between teacher and student distributions. Besides, profit by properties of the Sinkhorn metric, we can get rid of sample-wise KD that restricts the perception of divergence in each teacher-student sample pair. Instead, we propose a batch-wise reformulation to capture geometric intricacies of distributions across samples in the high-dimensional space. Comprehensive evaluation on GLUE and SuperGLUE, in terms of comparability, validity, and generalizability, highlights our superiority over state-of-the-art methods on all kinds of LLMs with encoder-only, encoder-decoder, and decoder-only architectures.

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

Designing recommendation systems with limited or no available training data remains a challenge. To that end, a new combinatorial optimization problem is formulated to generate optimized item selection for experimentation with the goal to shorten the time for collecting randomized training data. We first present an overview of the optimized item selection problem and a multi-level optimization framework to solve it. The approach integrates techniques from discrete optimization, unsupervised clustering, and latent text embeddings. We then discuss how to incorporate optimized item selection with active learning as part of randomized exploration in an ongoing fashion.

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

Retrieval-augmented Generation (RAG) has primarily been studied in limited settings, such as factoid question answering; more challenging, reasoning-intensive benchmarks have seen limited success from minimal RAG. In this work, we challenge this prevailing view on established, reasoning-intensive benchmarks: MMLU, MMLU Pro, AGI Eval, GPQA, and MATH. We identify a key missing component in prior work: a usable, web-scale datastore aligned with the breadth of pretraining data. To this end, we introduce CompactDS: a diverse, high-quality, web-scale datastore that achieves high retrieval accuracy and subsecond latency on a single-node. The key insights are (1) most web content can be filtered out without sacrificing coverage, and a compact, high-quality subset is sufficient; and (2) combining in-memory approximate nearest neighbor (ANN) retrieval and on-disk exact search balances speed and recall. Using CompactDS, we show that a minimal RAG pipeline achieves consistent accuracy improvements across all benchmarks and model sizes (8B--70B), with relative gains of 10% on MMLU, 33% on MMLU Pro, 14% on GPQA, and 19% on MATH. No single data source suffices alone, highlighting the importance of diversity of sources (web crawls, curated math, academic papers, textbooks). Finally, we show that our carefully designed in-house datastore matches or outperforms web search engines such as Google Search, as well as recently proposed, complex agent-based RAG systems--all while maintaining simplicity, reproducibility, and self-containment. We release CompactDS and our retrieval pipeline, supporting future research exploring retrieval-based AI systems.

Knowledge distillation (KD) is a general neural network training approach that uses a teacher model to guide the student model. Existing works mainly study KD from the network output side (e.g., trying to design a better KD loss function), while few have attempted to understand it from the input side. Especially, its interplay with data augmentation (DA) has not been well understood. In this paper, we ask: Why do some DA schemes (e.g., CutMix) inherently perform much better than others in KD? What makes a "good" DA in KD? Our investigation from a statistical perspective suggests that a good DA scheme should reduce the covariance of the teacher-student cross-entropy. A practical metric, the stddev of teacher's mean probability (T. stddev), is further presented and well justified empirically. Besides the theoretical understanding, we also introduce a new entropy-based data-mixing DA scheme, CutMixPick, to further enhance CutMix. Extensive empirical studies support our claims and demonstrate how we can harvest considerable performance gains simply by using a better DA scheme in knowledge distillation.

We present any4, a learned 4-bit weight quantization solution for large language models (LLMs) providing arbitrary numeric representations without requiring pre-processing of weights or activations. any4 yields higher accuracy compared to other related 4-bit numeric representation types: int4, fp4 and nf4, as evaluated on a range of model sizes, generations and families (Llama 2, Llama 3, Mistral and Mixtral). While any4 does not require preprocessing of weights or activations, it is also competitive with orthogonal techniques that require such preprocessing (e.g., AWQ and GPTQ). We also experiment with any3 and any2 and show competitiveness at lower bits. Additionally, we show that we can calibrate using a single curated diverse sample rather than hundreds of samples from a dataset as done in most quantization approaches. We also open source tinygemm, a latency optimized GPU matrix multiplication library for LLMs, that implements any4 using a GPU-efficient lookup table strategy along with other common quantization methods. We open source our code at https://github.com/facebookresearch/any4 .

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.

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 .

The pre-training of large language models usually requires massive amounts of resources, both in terms of computation and data. Frequently used web sources such as Common Crawl might contain enough noise to make this pre-training sub-optimal. In this work, we experiment with different sampling methods from the Spanish version of mC4, and present a novel data-centric technique which we name perplexity sampling that enables the pre-training of language models in roughly half the amount of steps and using one fifth of the data. The resulting models are comparable to the current state-of-the-art, and even achieve better results for certain tasks. Our work is proof of the versatility of Transformers, and paves the way for small teams to train their models on a limited budget. Our models are available at this https://huggingface.co/bertin-project{URL}.

We introduce KodCode, a synthetic dataset that addresses the persistent challenge of acquiring high-quality, verifiable training data across diverse difficulties and domains for training Large Language Models for coding. Existing code-focused resources typically fail to ensure either the breadth of coverage (e.g., spanning simple coding tasks to advanced algorithmic problems) or verifiable correctness (e.g., unit tests). In contrast, KodCode comprises question-solution-test triplets that are systematically validated via a self-verification procedure. Our pipeline begins by synthesizing a broad range of coding questions, then generates solutions and test cases with additional attempts allocated to challenging problems. Finally, post-training data synthesis is done by rewriting questions into diverse formats and generating responses under a test-based reject sampling procedure from a reasoning model (DeepSeek R1). This pipeline yields a large-scale, robust and diverse coding dataset. KodCode is suitable for supervised fine-tuning and the paired unit tests also provide great potential for RL tuning. Fine-tuning experiments on coding benchmarks (HumanEval(+), MBPP(+), BigCodeBench, and LiveCodeBench) demonstrate that KodCode-tuned models achieve state-of-the-art performance, surpassing models like Qwen2.5-Coder-32B-Instruct and DeepSeek-R1-Distill-Llama-70B.

Recent efforts in fine-tuning language models often rely on automatic data selection, commonly using Nearest Neighbors retrieval from large datasets. However, we theoretically show that this approach tends to select redundant data, limiting its effectiveness or even hurting performance. To address this, we introduce SIFT, a data selection algorithm designed to reduce uncertainty about the model's response given a prompt, which unifies ideas from retrieval and active learning. Whereas Nearest Neighbor retrieval typically fails in the presence of information duplication, SIFT accounts for information duplication and optimizes the overall information gain of the selected examples. We focus our evaluations on fine-tuning at test-time for prompt-specific language modeling on the Pile dataset, and show that SIFT consistently outperforms Nearest Neighbor retrieval, with minimal computational overhead. Moreover, we show that our uncertainty estimates can predict the performance gain of test-time fine-tuning, and use this to develop an adaptive algorithm that invests test-time compute proportional to realized performance gains. We provide the activeft (Active Fine-Tuning) library which can be used as a drop-in replacement for Nearest Neighbor retrieval.

Speculative decoding reduces the inference latency of a target large language model via utilizing a smaller and faster draft model. Its performance depends on a hyperparameter K -- the candidate length, i.e., the number of candidate tokens for the target model to verify in each round. However, previous methods often use simple heuristics to choose K, which may result in sub-optimal performance. We study the choice of the candidate length K and formulate it as a Markov Decision Process. We theoretically show that the optimal policy of this Markov decision process takes the form of a threshold policy, i.e., the current speculation should stop and be verified when the probability of getting a rejection exceeds a threshold value. Motivated by this theory, we propose SpecDec++, an enhanced version of speculative decoding that adaptively determines the candidate length on the fly. We augment the draft model with a trained acceptance prediction head to predict the conditional acceptance probability of the candidate tokens. SpecDec++ will stop the current speculation when the predicted probability that at least one token gets rejected exceeds a threshold. We implement SpecDec++ and apply it to the llama-2-chat 7B & 70B model pair. Our adaptive method achieves a 2.04x speedup on the Alpaca dataset (an additional 7.2% improvement over the baseline speculative decoding). On the GSM8K and HumanEval datasets, our method achieves a 2.26x speedup (9.4% improvement) and 2.23x speedup (11.1% improvement), respectively.

Long context large language models (LLMs) pose significant challenges for efficient serving due to the large memory footprint and high access overhead of KV cache. Retrieval-based KV cache reduction methods can mitigate these challenges, typically by offloading the complete KV cache to CPU and retrieving necessary tokens on demand during inference. However, these methods still suffer from unsatisfactory accuracy degradation and extra retrieval overhead. To address these limitations, this paper proposes A^2ATS, a novel retrieval-based KV cache reduction method. A^2ATS aims to obtain an accurate approximation of attention scores by applying the vector quantization technique to key states, thereby enabling efficient and precise retrieval of the top-K tokens. First, we propose Windowed Rotary Position Embedding, which decouples the positional dependency from query and key states after position embedding. Then, we propose query-aware vector quantization that optimizes the objective of attention score approximation directly. Finally, we design the heterogeneous inference architecture for KV cache offloading, enabling long context serving with larger batch sizes. Experimental results demonstrate that A^2ATS can achieve a lower performance degradation with similar or lower overhead compared to existing methods, thereby increasing long context serving throughput by up to 2.7 times.

Large language models have achieved notable success across various domains, yet efficient inference is still limited by the quadratic computation complexity of the attention mechanism. The inference consists of prefilling and decoding phases. Although several attempts have been made to accelerate decoding, the inefficiency of the prefilling phase, especially for long-context tasks, remains a challenge. In this paper, we observe a locality in query criticality during the prefilling phase of long-context processing: adjacent query tokens tend to focus on similar subsets of the past Key-Value (KV) cache. Based on this observation, we propose CritiPrefill, a criticality-based segment-wise prefilling method. This method partitions the input sequence's queries and KV cache into segments and blocks, utilizing a segment-wise algorithm to estimate the query criticality. By pruning non-critical computations between query segments and cache blocks in the self-attention mechanism, the prefilling process can be significantly accelerated. Extensive evaluations on multiple long-context datasets show up to 2.7x speedup on Llama3-8B and 3.0x speedup on Yi-9B for 128K context length on a single A100 GPU, with minimal quality degradation.

We give an improved theoretical analysis of score-based generative modeling. Under a score estimate with small L^2 error (averaged across timesteps), we provide efficient convergence guarantees for any data distribution with second-order moment, by either employing early stopping or assuming smoothness condition on the score function of the data distribution. Our result does not rely on any log-concavity or functional inequality assumption and has a logarithmic dependence on the smoothness. In particular, we show that under only a finite second moment condition, approximating the following in reverse KL divergence in epsilon-accuracy can be done in tilde Oleft(d log (1/delta){epsilon}right) steps: 1) the variance-delta Gaussian perturbation of any data distribution; 2) data distributions with 1/delta-smooth score functions. Our analysis also provides a quantitative comparison between different discrete approximations and may guide the choice of discretization points in practice.

In this paper, we find a sample complexity bound for learning a simplex from noisy samples. Assume a dataset of size n is given which includes i.i.d. samples drawn from a uniform distribution over an unknown simplex in R^K, where samples are assumed to be corrupted by a multi-variate additive Gaussian noise of an arbitrary magnitude. We prove the existence of an algorithm that with high probability outputs a simplex having a ell_2 distance of at most varepsilon from the true simplex (for any varepsilon>0). Also, we theoretically show that in order to achieve this bound, it is sufficient to have ngeleft(K^2/varepsilon^2right)e^{Omegaleft(K/SNR^2right)} samples, where SNR stands for the signal-to-noise ratio. This result solves an important open problem and shows as long as SNRgeOmegaleft(K^{1/2}right), the sample complexity of the noisy regime has the same order to that of the noiseless case. Our proofs are a combination of the so-called sample compression technique in ashtiani2018nearly, mathematical tools from high-dimensional geometry, and Fourier analysis. In particular, we have proposed a general Fourier-based technique for recovery of a more general class of distribution families from additive Gaussian noise, which can be further used in a variety of other related problems.

Clustering is an unsupervised learning problem that aims to partition unlabelled data points into groups with similar features. Traditional clustering algorithms provide limited insight into the groups they find as their main focus is accuracy and not the interpretability of the group assignments. This has spurred a recent line of work on explainable machine learning for clustering. In this paper we focus on the cluster description problem where, given a dataset and its partition into clusters, the task is to explain the clusters. We introduce a new approach to explain clusters by constructing polyhedra around each cluster while minimizing either the complexity of the resulting polyhedra or the number of features used in the description. We formulate the cluster description problem as an integer program and present a column generation approach to search over an exponential number of candidate half-spaces that can be used to build the polyhedra. To deal with large datasets, we introduce a novel grouping scheme that first forms smaller groups of data points and then builds the polyhedra around the grouped data, a strategy which out-performs simply sub-sampling data. Compared to state of the art cluster description algorithms, our approach is able to achieve competitive interpretability with improved description accuracy.

Existing KBQA methods have traditionally relied on multi-stage methodologies, involving tasks such as entity linking, subgraph retrieval and query structure generation. However, multi-stage approaches are dependent on the accuracy of preceding steps, leading to cascading errors and increased inference time. Although a few studies have explored the use of end-to-end models, they often suffer from lower accuracy and generate inoperative query that is not supported by the underlying data. Furthermore, most prior approaches are limited to the static training data, potentially overlooking the evolving nature of knowledge bases over time. To address these challenges, we present a novel end-to-end natural language to SPARQL framework, SPARKLE. Notably SPARKLE leverages the structure of knowledge base directly during the decoding, effectively integrating knowledge into the query generation. Our study reveals that simply referencing knowledge base during inference significantly reduces the occurrence of inexecutable query generations. SPARKLE achieves new state-of-the-art results on SimpleQuestions-Wiki and highest F1 score on LCQuAD 1.0 (among models not using gold entities), while getting slightly lower result on the WebQSP dataset. Finally, we demonstrate SPARKLE's fast inference speed and its ability to adapt when the knowledge base differs between the training and inference stages.

We introduce marginalization models (MaMs), a new family of generative models for high-dimensional discrete data. They offer scalable and flexible generative modeling with tractable likelihoods by explicitly modeling all induced marginal distributions. Marginalization models enable fast evaluation of arbitrary marginal probabilities with a single forward pass of the neural network, which overcomes a major limitation of methods with exact marginal inference, such as autoregressive models (ARMs). We propose scalable methods for learning the marginals, grounded in the concept of "marginalization self-consistency". Unlike previous methods, MaMs support scalable training of any-order generative models for high-dimensional problems under the setting of energy-based training, where the goal is to match the learned distribution to a given desired probability (specified by an unnormalized (log) probability function such as energy function or reward function). We demonstrate the effectiveness of the proposed model on a variety of discrete data distributions, including binary images, language, physical systems, and molecules, for maximum likelihood and energy-based training settings. MaMs achieve orders of magnitude speedup in evaluating the marginal probabilities on both settings. For energy-based training tasks, MaMs enable any-order generative modeling of high-dimensional problems beyond the capability of previous methods. Code is at https://github.com/PrincetonLIPS/MaM.

Compared with full client participation, partial client participation is a more practical scenario in federated learning, but it may amplify some challenges in federated learning, such as data heterogeneity. The lack of inactive clients' updates in partial client participation makes it more likely for the model aggregation to deviate from the aggregation based on full client participation. Training with large batches on individual clients is proposed to address data heterogeneity in general, but their effectiveness under partial client participation is not clear. Motivated by these challenges, we propose to develop a novel federated learning framework, referred to as FedAMD, for partial client participation. The core idea is anchor sampling, which separates partial participants into anchor and miner groups. Each client in the anchor group aims at the local bullseye with the gradient computation using a large batch. Guided by the bullseyes, clients in the miner group steer multiple near-optimal local updates using small batches and update the global model. By integrating the results of the two groups, FedAMD is able to accelerate the training process and improve the model performance. Measured by epsilon-approximation and compared to the state-of-the-art methods, FedAMD achieves the convergence by up to O(1/epsilon) fewer communication rounds under non-convex objectives. Empirical studies on real-world datasets validate the effectiveness of FedAMD and demonstrate the superiority of the proposed algorithm: Not only does it considerably save computation and communication costs, but also the test accuracy significantly improves.

Given a (machine learning) classifier and a collection of unlabeled data, how can we efficiently identify misclassification patterns presented in this dataset? To address this problem, we propose a human-machine collaborative framework that consists of a team of human annotators and a sequential recommendation algorithm. The recommendation algorithm is conceptualized as a stochastic sampler that, in each round, queries the annotators a subset of samples for their true labels and obtains the feedback information on whether the samples are misclassified. The sampling mechanism needs to balance between discovering new patterns of misclassification (exploration) and confirming the potential patterns of classification (exploitation). We construct a determinantal point process, whose intensity balances the exploration-exploitation trade-off through the weighted update of the posterior at each round to form the generator of the stochastic sampler. The numerical results empirically demonstrate the competitive performance of our framework on multiple datasets at various signal-to-noise ratios.

Reasoning large language models (LLMs) heavily rely on scaling test-time compute to perform complex reasoning tasks by generating extensive "thinking" chains. While demonstrating impressive results, this approach incurs significant computational costs and inference time. In this work, we challenge the assumption that long thinking chains results in better reasoning capabilities. We first demonstrate that shorter reasoning chains within individual questions are significantly more likely to yield correct answers - up to 34.5% more accurate than the longest chain sampled for the same question. Based on these results, we suggest short-m@k, a novel reasoning LLM inference method. Our method executes k independent generations in parallel and halts computation once the first m thinking processes are done. The final answer is chosen using majority voting among these m chains. Basic short-1@k demonstrates similar or even superior performance over standard majority voting in low-compute settings - using up to 40% fewer thinking tokens. short-3@k, while slightly less efficient than short-1@k, consistently surpasses majority voting across all compute budgets, while still being substantially faster (up to 33% wall time reduction). Inspired by our results, we finetune an LLM using short, long, and randomly selected reasoning chains. We then observe that training on the shorter ones leads to better performance. Our findings suggest rethinking current methods of test-time compute in reasoning LLMs, emphasizing that longer "thinking" does not necessarily translate to improved performance and can, counter-intuitively, lead to degraded results.

The emergence of LLMs has ignited a fresh surge of breakthroughs in NLP applications, particularly in domains such as question-answering systems and text generation. As the need for longer context grows, a significant bottleneck in model deployment emerges due to the linear expansion of the Key-Value (KV) cache with the context length. Existing methods primarily rely on various hypotheses, such as sorting the KV cache based on attention scores for replacement or eviction, to compress the KV cache and improve model throughput. However, heuristics used by these strategies may wrongly evict essential KV cache, which can significantly degrade model performance. In this paper, we propose QAQ, a Quality Adaptive Quantization scheme for the KV cache. We theoretically demonstrate that key cache and value cache exhibit distinct sensitivities to quantization, leading to the formulation of separate quantization strategies for their non-uniform quantization. Through the integration of dedicated outlier handling, as well as an improved attention-aware approach, QAQ achieves up to 10x the compression ratio of the KV cache size with a neglectable impact on model performance. QAQ significantly reduces the practical hurdles of deploying LLMs, opening up new possibilities for longer-context applications. The code is available at github.com/ClubieDong/KVCacheQuantization.

A simple and effective method for the alignment of generative models is the best-of-n policy, where n samples are drawn from a base policy, and ranked based on a reward function, and the highest ranking one is selected. A commonly used analytical expression in the literature claims that the KL divergence between the best-of-n policy and the base policy is equal to log (n) - (n-1)/n. We disprove the validity of this claim, and show that it is an upper bound on the actual KL divergence. We also explore the tightness of this upper bound in different regimes. Finally, we propose a new estimator for the KL divergence and empirically show that it provides a tight approximation through a few examples.

Entity resolution (record linkage, microclustering) systems are notoriously difficult to evaluate. Looking for a needle in a haystack, traditional evaluation methods use sophisticated, application-specific sampling schemes to find matching pairs of records among an immense number of non-matches. We propose an alternative that facilitates the creation of representative, reusable benchmark data sets without necessitating complex sampling schemes. These benchmark data sets can then be used for model training and a variety of evaluation tasks. Specifically, we propose an entity-centric data labeling methodology that integrates with a unified framework for monitoring summary statistics, estimating key performance metrics such as cluster and pairwise precision and recall, and analyzing root causes for errors. We validate the framework in an application to inventor name disambiguation and through simulation studies. Software: https://github.com/OlivierBinette/er-evaluation/

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.

Active learning is able to reduce the amount of labelling effort by using a machine learning model to query the user for specific inputs. While there are many papers on new active learning techniques, these techniques rarely satisfy the constraints of a real-world project. In this paper, we analyse the main drawbacks of current active learning techniques and we present approaches to alleviate them. We do a systematic study on the effects of the most common issues of real-world datasets on the deep active learning process: model convergence, annotation error, and dataset imbalance. We derive two techniques that can speed up the active learning loop such as partial uncertainty sampling and larger query size. Finally, we present our open-source Bayesian active learning library, BaaL.

Key-value (KV) caching has emerged as a crucial optimization technique for accelerating inference in large language models (LLMs). By allowing the attention operation to scale linearly rather than quadratically with the total sequence length, KV caching significantly enhances generation throughput. However, due to large context lengths in the modern LLMs, the memory footprint of the KV is a huge bottleneck for model deployment directly impacting the model's batch size, hindering its ability to deliver high-throughput. Existing research addresses this challenge using several techniques, such as discarding low-attention tokens, quantization, and matrix approximation which typically lead to a negative impact on the model accuracy. In this paper, We propose KVCrush technology which can be combined with many KV compression technologies to improve the model accuracy at a much smaller memory. KVCrush provides an alternate representation scheme for key-value states, along with a low-overhead token pruning algorithm that accounts for the token distribution in the KV cache, which in turn allows for a a smaller footprint while maintaining the accuracy of the model. Based on our results, KVCrush reduces LongBench KV Cache size by 4x with less than 1% accuracy drop and achieves state-of-the-art average accuracy with minimal overhead, incurring less than 0.5% total inference latency. KVCrush not only outperforms the accuracy of state-of-the-art importance-based token retention schemes but is also compatible with typical practical LLM deployments using KV cache paging schemes such as vLLM and mixed precision quantization.

Given a matrix Min R^{mtimes n}, the low rank matrix completion problem asks us to find a rank-k approximation of M as UV^top for Uin R^{mtimes k} and Vin R^{ntimes k} by only observing a few entries specified by a set of entries Omegasubseteq [m]times [n]. In particular, we examine an approach that is widely used in practice -- the alternating minimization framework. Jain, Netrapalli and Sanghavi~jns13 showed that if M has incoherent rows and columns, then alternating minimization provably recovers the matrix M by observing a nearly linear in n number of entries. While the sample complexity has been subsequently improved~glz17, alternating minimization steps are required to be computed exactly. This hinders the development of more efficient algorithms and fails to depict the practical implementation of alternating minimization, where the updates are usually performed approximately in favor of efficiency. In this paper, we take a major step towards a more efficient and error-robust alternating minimization framework. To this end, we develop an analytical framework for alternating minimization that can tolerate moderate amount of errors caused by approximate updates. Moreover, our algorithm runs in time widetilde O(|Omega| k), which is nearly linear in the time to verify the solution while preserving the sample complexity. This improves upon all prior known alternating minimization approaches which require widetilde O(|Omega| k^2) time.

Recent advancements in large language models (LLMs) have raised concerns about inference costs, increasing the need for research into model compression. While knowledge distillation (KD) is a prominent method for this, research on KD for generative language models like LLMs is relatively sparse, and the approach of distilling student-friendly knowledge, which has shown promising performance in KD for classification models, remains unexplored in generative language models. To explore this approach, we propose PromptKD, a simple yet effective method that utilizes prompt tuning - for the first time in KD - to enable generative language models to transfer student-friendly knowledge. Unlike previous works in classification that require fine-tuning the entire teacher model for extracting student-friendly knowledge, PromptKD achieves similar effects by adding a small number of prompt tokens and tuning only the prompt with student guidance. Extensive experiments on instruction-following datasets using the GPT-2 model family show that PromptKD achieves state-of-the-art performance while adding only 0.0007% of the teacher's parameters as prompts. Further analysis suggests that distilling student-friendly knowledge alleviates exposure bias effectively throughout the entire training process, leading to performance enhancements.

Score-based generative models (SGMs) sample from a target distribution by iteratively transforming noise using the score function of the perturbed target. For any finite training set, this score function can be evaluated in closed form, but the resulting SGM memorizes its training data and does not generate novel samples. In practice, one approximates the score by training a neural network via score-matching. The error in this approximation promotes generalization, but neural SGMs are costly to train and sample, and the effective regularization this error provides is not well-understood theoretically. In this work, we instead explicitly smooth the closed-form score to obtain an SGM that generates novel samples without training. We analyze our model and propose an efficient nearest-neighbor-based estimator of its score function. Using this estimator, our method achieves competitive sampling times while running on consumer-grade CPUs.

LLMs are seeing growing use for applications such as document analysis and summarization which require large context windows, and with these large context windows KV cache activations surface as the dominant contributor to memory consumption during inference. Quantization is a promising approach for compressing KV cache activations; however, existing solutions fail to represent activations accurately in ultra-low precisions, such as sub-4-bit. In this work, we present KVQuant, which addresses this problem by incorporating novel methods for quantizing cached KV activations, including: (i) Per-Channel Key Quantization, where we adjust the dimension along which we quantize the Key activations to better match the distribution; (ii) Pre-RoPE Key Quantization, where we quantize Key activations before the rotary positional embedding to mitigate its impact on quantization; (iii) Non-Uniform KV Cache Quantization, where we derive per-layer sensitivity-weighted non-uniform datatypes that better represent the distributions; (iv) Per-Vector Dense-and-Sparse Quantization, where we isolate outliers separately for each vector to minimize skews in quantization ranges; and (v) Q-Norm, where we normalize quantization centroids in order to mitigate distribution shift, providing additional benefits for 2-bit quantization. By applying our method to the LLaMA, LLaMA-2, and Mistral models, we achieve <0.1 perplexity degradation with 3-bit quantization on both Wikitext-2 and C4, outperforming existing approaches. Our method enables serving the LLaMA-7B model with a context length of up to 1 million on a single A100-80GB GPU and up to 10 million on an 8-GPU system.

Efficient KV cache management in LLMs is crucial for long-context tasks like RAG and summarization. Existing KV cache compression methods enforce a fixed pattern, neglecting task-specific characteristics and reducing the retention of essential information. However, we observe distinct activation patterns across layers in various tasks, highlighting the need for adaptive strategies tailored to each task's unique demands. Based on this insight, we propose DynamicKV, a method that dynamically optimizes token retention by adjusting the number of tokens retained at each layer to adapt to the specific task. DynamicKV establishes global and per-layer maximum KV cache budgets, temporarily retaining the maximum budget for the current layer, and periodically updating the KV cache sizes of all preceding layers during inference. Our method retains only 1.7% of the KV cache size while achieving ~85% of the Full KV cache performance on LongBench. Notably, even under extreme compression (0.9%), DynamicKV surpasses state-of-the-art (SOTA) methods by 11% in the Needle-in-a-Haystack test using Mistral-7B-Instruct-v0.2. The code will be released.

With the increasing size of datasets used for training neural networks, data pruning becomes an attractive field of research. However, most current data pruning algorithms are limited in their ability to preserve accuracy compared to models trained on the full data, especially in high pruning regimes. In this paper we explore the application of data pruning while incorporating knowledge distillation (KD) when training on a pruned subset. That is, rather than relying solely on ground-truth labels, we also use the soft predictions from a teacher network pre-trained on the complete data. By integrating KD into training, we demonstrate significant improvement across datasets, pruning methods, and on all pruning fractions. We first establish a theoretical motivation for employing self-distillation to improve training on pruned data. Then, we empirically make a compelling and highly practical observation: using KD, simple random pruning is comparable or superior to sophisticated pruning methods across all pruning regimes. On ImageNet for example, we achieve superior accuracy despite training on a random subset of only 50% of the data. Additionally, we demonstrate a crucial connection between the pruning factor and the optimal knowledge distillation weight. This helps mitigate the impact of samples with noisy labels and low-quality images retained by typical pruning algorithms. Finally, we make an intriguing observation: when using lower pruning fractions, larger teachers lead to accuracy degradation, while surprisingly, employing teachers with a smaller capacity than the student's may improve results. Our code will be made available.

Despite the significant success of large language models (LLMs), their extensive memory requirements pose challenges for deploying them in long-context token generation. The substantial memory footprint of LLM decoders arises from the necessity to store all previous tokens in the attention module, a requirement imposed by key-value (KV) caching. In this work, our focus is on developing an efficient compression technique for the KV cache. Empirical evidence indicates a significant clustering tendency within key embeddings in the attention module. Building on this key insight, we have devised a novel caching method with sublinear complexity, employing online clustering on key tokens and online ell_2 sampling on values. The result is a provably accurate and efficient attention decoding algorithm, termed SubGen. Not only does this algorithm ensure a sublinear memory footprint and sublinear time complexity, but we also establish a tight error bound for our approach. Empirical evaluations on long-context question-answering tasks demonstrate that SubGen significantly outperforms existing and state-of-the-art KV cache compression methods in terms of performance and efficiency.

Training data compositions for Large Language Models (LLMs) can significantly affect their downstream performance. However, a thorough data ablation study exploring large sets of candidate data mixtures is typically prohibitively expensive since the full effect is seen only after training the models; this can lead practitioners to settle for sub-optimal data mixtures. We propose an efficient method for approximating data ablations which trains individual models on subsets of a training corpus and reuses them across evaluations of combinations of subsets. In continued pre-training experiments, we find that, given an arbitrary evaluation set, the perplexity score of a single model trained on a candidate set of data is strongly correlated with perplexity scores of parameter averages of models trained on distinct partitions of that data. From this finding, we posit that researchers and practitioners can conduct inexpensive simulations of data ablations by maintaining a pool of models that were each trained on partitions of a large training corpus, and assessing candidate data mixtures by evaluating parameter averages of combinations of these models. This approach allows for substantial improvements in amortized training efficiency -- scaling only linearly with respect to new data -- by enabling reuse of previous training computation, opening new avenues for improving model performance through rigorous, incremental data assessment and mixing.

The estimation of repeatedly nested expectations is a challenging task that arises in many real-world systems. However, existing methods generally suffer from high computational costs when the number of nestings becomes large. Fix any non-negative integer D for the total number of nestings. Standard Monte Carlo methods typically cost at least O(varepsilon^{-(2+D)}) and sometimes O(varepsilon^{-2(1+D)}) to obtain an estimator up to varepsilon-error. More advanced methods, such as multilevel Monte Carlo, currently only exist for D = 1. In this paper, we propose a novel Monte Carlo estimator called READ, which stands for "Recursive Estimator for Arbitrary Depth.'' Our estimator has an optimal computational cost of O(varepsilon^{-2}) for every fixed D under suitable assumptions, and a nearly optimal computational cost of O(varepsilon^{-2(1 + delta)}) for any 0 < delta < frac12 under much more general assumptions. Our estimator is also unbiased, which makes it easy to parallelize. The key ingredients in our construction are an observation of the problem's recursive structure and the recursive use of the randomized multilevel Monte Carlo method.

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.

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.

Making text-to-image (T2I) generative model sample both fast and well represents a promising research direction. Previous studies have typically focused on either enhancing the visual quality of synthesized images at the expense of sampling efficiency or dramatically accelerating sampling without improving the base model's generative capacity. Moreover, nearly all inference methods have not been able to ensure stable performance simultaneously on both diffusion models (DMs) and visual autoregressive models (ARMs). In this paper, we introduce a novel plug-and-play inference paradigm, CoRe^2, which comprises three subprocesses: Collect, Reflect, and Refine. CoRe^2 first collects classifier-free guidance (CFG) trajectories, and then use collected data to train a weak model that reflects the easy-to-learn contents while reducing number of function evaluations during inference by half. Subsequently, CoRe^2 employs weak-to-strong guidance to refine the conditional output, thereby improving the model's capacity to generate high-frequency and realistic content, which is difficult for the base model to capture. To the best of our knowledge, CoRe^2 is the first to demonstrate both efficiency and effectiveness across a wide range of DMs, including SDXL, SD3.5, and FLUX, as well as ARMs like LlamaGen. It has exhibited significant performance improvements on HPD v2, Pick-of-Pic, Drawbench, GenEval, and T2I-Compbench. Furthermore, CoRe^2 can be seamlessly integrated with the state-of-the-art Z-Sampling, outperforming it by 0.3 and 0.16 on PickScore and AES, while achieving 5.64s time saving using SD3.5.Code is released at https://github.com/xie-lab-ml/CoRe/tree/main.

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

Efficient k-nearest neighbor search is a fundamental task, foundational for many problems in NLP. When the similarity is measured by dot-product between dual-encoder vectors or ell_2-distance, there already exist many scalable and efficient search methods. But not so when similarity is measured by more accurate and expensive black-box neural similarity models, such as cross-encoders, which jointly encode the query and candidate neighbor. The cross-encoders' high computational cost typically limits their use to reranking candidates retrieved by a cheaper model, such as dual encoder or TF-IDF. However, the accuracy of such a two-stage approach is upper-bounded by the recall of the initial candidate set, and potentially requires additional training to align the auxiliary retrieval model with the cross-encoder model. In this paper, we present an approach that avoids the use of a dual-encoder for retrieval, relying solely on the cross-encoder. Retrieval is made efficient with CUR decomposition, a matrix decomposition approach that approximates all pairwise cross-encoder distances from a small subset of rows and columns of the distance matrix. Indexing items using our approach is computationally cheaper than training an auxiliary dual-encoder model through distillation. Empirically, for k > 10, our approach provides test-time recall-vs-computational cost trade-offs superior to the current widely-used methods that re-rank items retrieved using a dual-encoder or TF-IDF.

Combining several (sample approximations of) distributions, which we term sub-posteriors, into a single distribution proportional to their product, is a common challenge. Occurring, for instance, in distributed 'big data' problems, or when working under multi-party privacy constraints. Many existing approaches resort to approximating the individual sub-posteriors for practical necessity, then find either an analytical approximation or sample approximation of the resulting (product-pooled) posterior. The quality of the posterior approximation for these approaches is poor when the sub-posteriors fall out-with a narrow range of distributional form, such as being approximately Gaussian. Recently, a Fusion approach has been proposed which finds an exact Monte Carlo approximation of the posterior, circumventing the drawbacks of approximate approaches. Unfortunately, existing Fusion approaches have a number of computational limitations, particularly when unifying a large number of sub-posteriors. In this paper, we generalise the theory underpinning existing Fusion approaches, and embed the resulting methodology within a recursive divide-and-conquer sequential Monte Carlo paradigm. This ultimately leads to a competitive Fusion approach, which is robust to increasing numbers of sub-posteriors.

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

As large language models (LLMs) continue to advance, the demand for higher quality and faster processing of long contexts across various applications is growing. KV cache is widely adopted as it stores previously generated key and value tokens, effectively reducing redundant computations during inference. However, as memory overhead becomes a significant concern, efficient compression of KV cache has gained increasing attention. Most existing methods perform compression from two perspectives: identifying important tokens and designing compression strategies. However, these approaches often produce biased distributions of important tokens due to the influence of accumulated attention scores or positional encoding. Furthermore, they overlook the sparsity and redundancy across different heads, which leads to difficulties in preserving the most effective information at the head level. To this end, we propose EMS to overcome these limitations, while achieving better KV cache compression under extreme compression ratios. Specifically, we introduce a Global-Local score that combines accumulated attention scores from both global and local KV tokens to better identify the token importance. For the compression strategy, we design an adaptive and unified Evict-then-Merge framework that accounts for the sparsity and redundancy of KV tokens across different heads. Additionally, we implement the head-wise parallel compression through a zero-class mechanism to enhance efficiency. Extensive experiments demonstrate our SOTA performance even under extreme compression ratios. EMS consistently achieves the lowest perplexity, improves scores by over 1.28 points across four LLMs on LongBench under a 256 cache budget, and preserves 95% retrieval accuracy with a cache budget less than 2% of the context length in the Needle-in-a-Haystack task.

Key-Value (KV) caching is a common technique to enhance the computational efficiency of Large Language Models (LLMs), but its memory overhead grows rapidly with input length. Prior work has shown that not all tokens are equally important for text generation, proposing layer-level KV cache compression to selectively retain key information. Recognizing the distinct roles of attention heads in generation, we propose HeadKV, a head-level KV cache compression method, and HeadKV-R2, which leverages a novel contextual reasoning ability estimation for compression. Our approach operates at the level of individual heads, estimating their importance for contextual QA tasks that require both retrieval and reasoning capabilities. Extensive experiments across diverse benchmarks (LongBench, LooGLE), model architectures (e.g., Llama-3-8B-Instruct, Mistral-7B-Instruct), and long-context abilities tests demonstrate that our head-level KV cache compression significantly outperforms strong baselines, particularly in low-resource settings (KV size = 64 & 128). Notably, our method retains just 1.5% of the KV cache while achieving 97% of the performance of the full KV cache on the contextual question answering benchmark.

This paper introduces an information-aware quantization framework that adaptively compresses the key-value (KV) cache in large language models (LLMs). Although prior work has underscored the distinct roles of key and value cache during inference, our systematic analysis -- examining singular value distributions, spectral norms, and Frobenius norms -- reveals, for the first time, that key matrices consistently exhibit higher norm values and are more sensitive to quantization than value matrices. Furthermore, our theoretical analysis shows that matrices with higher spectral norms amplify quantization errors more significantly. Motivated by these insights, we propose a mixed-precision quantization strategy, KV-AdaQuant, which allocates more bit-width for keys and fewer for values since key matrices have higher norm values. With the same total KV bit budget, this approach effectively mitigates error propagation across transformer layers while achieving significant memory savings. Our extensive experiments on multiple LLMs (1B--70B) demonstrate that our mixed-precision quantization scheme maintains high model accuracy even under aggressive compression. For instance, using 4-bit for Key and 2-bit for Value achieves an accuracy of 75.2%, whereas reversing the assignment (2-bit for Key and 4-bit for Value) yields only 54.7% accuracy. The code is available at https://tinyurl.com/kv-adaquant

We study the classic Text-to-Pattern Hamming Distances problem: given a pattern P of length m and a text T of length n, both over a polynomial-size alphabet, compute the Hamming distance between P and T[i, ., . , i+m-1] for every shift i, under the standard Word-RAM model with Theta(log n)-bit words. - We provide an O(nm) time Las Vegas randomized algorithm for this problem, beating the decades-old O(n m log m) running time [Abrahamson, SICOMP 1987]. We also obtain a deterministic algorithm, with a slightly higher O(nm(log mloglog m)^{1/4}) running time. Our randomized algorithm extends to the k-bounded setting, with running time Obig(n+nk{m}big), removing all the extra logarithmic factors from earlier algorithms [Gawrychowski and Uzna\'{n}ski, ICALP 2018; Chan, Golan, Kociumaka, Kopelowitz and Porat, STOC 2020]. - For the (1+epsilon)-approximate version of Text-to-Pattern Hamming Distances, we give an O(epsilon^{-0.93}n) time Monte Carlo randomized algorithm, beating the previous O(epsilon^{-1}n) running time [Kopelowitz and Porat, FOCS 2015; Kopelowitz and Porat, SOSA 2018]. Our approximation algorithm exploits a connection with 3SUM, and uses a combination of Fredman's trick, equality matrix product, and random sampling; in particular, we obtain new results on approximate counting versions of 3SUM and Exact Triangle, which may be of independent interest. Our exact algorithms use a novel combination of hashing, bit-packed FFT, and recursion; in particular, we obtain a faster algorithm for computing the sumset of two integer sets, in the regime when the universe size is close to quadratic in the number of elements. We also prove a fine-grained equivalence between the exact Text-to-Pattern Hamming Distances problem and a range-restricted, counting version of 3SUM.

AutoML systems build machine learning models automatically by performing a search over valid data transformations and learners, along with hyper-parameter optimization for each learner. Many AutoML systems use meta-learning to guide search for optimal pipelines. In this work, we present a novel meta-learning system called KGpip which, (1) builds a database of datasets and corresponding pipelines by mining thousands of scripts with program analysis, (2) uses dataset embeddings to find similar datasets in the database based on its content instead of metadata-based features, (3) models AutoML pipeline creation as a graph generation problem, to succinctly characterize the diverse pipelines seen for a single dataset. KGpip's meta-learning is a sub-component for AutoML systems. We demonstrate this by integrating KGpip with two AutoML systems. Our comprehensive evaluation using 126 datasets, including those used by the state-of-the-art systems, shows that KGpip significantly outperforms these systems.

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.

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 demand for inference on extremely large scale LLMs has seen enormous growth in the recent months. It made evident the colossal shortage of dedicated hardware capable of efficient and fast processing of the involved compute and memory movement. The problem is aggravated by the exploding raise in the lengths of the sequences being processed, since those require efficient on-chip storage of the KV-cache of size proportional to the sequence length. To make the required compute feasible and fit the involved data into available memory, numerous quantization techniques have been proposed that allow accurate quantization for both weights and activations. One of the main recent breakthroughs in this direction was introduction of the family of Block Floating Point (BFP) formats characterized by a block of mantissas with a shared scale factor. These enable memory- power-, and compute- efficient hardware support of the tensor operations and provide extremely good quantization accuracy. The main issues preventing widespread application of block formats is caused by the presence of outliers in weights and activations since those affect the accuracy of the other values in the same block. In this paper, we focus on the most critical problem of limited KV-cache storage. We propose a novel approach enabling usage of low precision BFP formats without compromising the resulting model accuracy. We exploit the common channel-wise patterns exhibited by the outliers to rearrange them in such a way, that their quantization quality is significantly improved. The methodology yields 2x savings in the memory footprint without significant degradation of the model's accuracy. Importantly, the rearrangement of channels happens at the compile time and thus has no impact on the inference latency.

Knowledge distillation (KD) is widely used to train small, high-performing student language models (LMs) using large teacher LMs. While effective in fine-tuning, KD during pre-training faces challenges in efficiency, flexibility, and effectiveness. Existing methods either incur high computational costs due to online teacher inference, require tokenization matching between teacher and student LMs, or risk losing the difficulty and diversity of the teacher-generated training data. To address these issues, we propose MiniPLM, a KD framework for pre-training LMs by refining the training data distribution with the teacher's knowledge. For efficiency, MiniPLM performs offline teacher LM inference, allowing KD for multiple student LMs without adding training-time costs. For flexibility, MiniPLM operates solely on the training corpus, enabling KD across model families. For effectiveness, MiniPLM leverages the differences between large and small LMs to enhance the difficulty and diversity of the training data, helping student LMs acquire versatile and sophisticated knowledge. Extensive experiments demonstrate that MiniPLM boosts the student LMs' performance on 9 widely used downstream tasks, improves the language modeling capabilities, and reduces pre-training computation. The benefit of MiniPLM extends to large pre-training scales, evidenced by the extrapolation of the scaling curves. Further analysis reveals that MiniPLM supports KD across model families and enhances the utilization of pre-training data. Our model, code, and data are available at https://github.com/thu-coai/MiniPLM.

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.

Recent LLMs have significantly improved reasoning capabilities, primarily by including an explicit, lengthy Thinking process as part of generation. In this paper, we question whether this explicit thinking is necessary. Using the state-of-the-art DeepSeek-R1-Distill-Qwen, we find that bypassing the thinking process via simple prompting, denoted as NoThinking, can be surprisingly effective. When controlling for the number of tokens, NoThinking outperforms Thinking across a diverse set of seven challenging reasoning datasets--including mathematical problem solving, formal theorem proving, and coding--especially in low-budget settings, e.g., 51.3 vs. 28.9 on ACM 23 with 700 tokens. Notably, the performance of NoThinking becomes more competitive with pass@k as k increases. Building on this observation, we demonstrate that a parallel scaling approach that uses NoThinking to generate N outputs independently and aggregates them is highly effective. For aggregation, we use task-specific verifiers when available, or we apply simple best-of-N strategies such as confidence-based selection. Our method outperforms a range of baselines with similar latency using Thinking, and is comparable to Thinking with significantly longer latency (up to 9x). Together, our research encourages a reconsideration of the necessity of lengthy thinking processes, while also establishing a competitive reference for achieving strong reasoning performance in low-budget settings or at low latency using parallel scaling.

Retrieval-augmented generation (RAG) and long-context language models (LCLMs) both address context limitations of LLMs in open-domain question answering (QA). However, optimal external context to retrieve remains an open problem: fixing the retrieval size risks either wasting tokens or omitting key evidence. Existing adaptive methods like Self-RAG and Self-Route rely on iterative LLM prompting and perform well on factoid QA, but struggle with aggregation QA, where the optimal context size is both unknown and variable. We present Adaptive-k retrieval, a simple and effective single-pass method that adaptively selects the number of passages based on the distribution of the similarity scores between the query and the candidate passages. It does not require model fine-tuning, extra LLM inferences or changes to existing retriever-reader pipelines. On both factoid and aggregation QA benchmarks, Adaptive-k matches or outperforms fixed-k baselines while using up to 10x fewer tokens than full-context input, yet still retrieves 70% of relevant passages. It improves accuracy across five LCLMs and two embedding models, highlighting that dynamically adjusting context size leads to more efficient and accurate QA.

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

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.

Large Language Models (LLMs) have shown promising performance in knowledge-intensive reasoning tasks that require a compound understanding of knowledge. However, deployment of the LLMs in real-world applications can be challenging due to their high computational requirements and concerns on data privacy. Previous studies have focused on building task-specific small language models (LMs) by fine-tuning them with labeled data or distilling LLMs. However, these approaches are ill-suited for knowledge-intensive reasoning tasks due to the limited capacity of small LMs in memorizing the knowledge required. Motivated by our theoretical analysis on memorization, we propose Knowledge-Augmented Reasoning Distillation (KARD), a novel method that fine-tunes small LMs to generate rationales with augmented knowledge retrieved from an external knowledge base. Moreover, we further propose a neural reranker to obtain documents relevant to rationale generation. We empirically show that KARD significantly improves the performance of small T5 and Flan-T5 models on the challenging knowledge-intensive reasoning datasets, namely MedQA-USMLE and StrategyQA. Notably, our method makes the 250M models achieve superior performance against the fine-tuned 3B models, having 12 times larger parameters, on both MedQA-USMLE and StrategyQA benchmarks.

We introduce Filter Like You Test (FLYT), a method for curating large-scale vision-language datasets that learns the usefulness of each data point as a pretraining example. FLYT trains a scoring model that learns to weigh each example using gradient signals from downstream tasks training sets. Using the same training methodology, we develop Mixing-FLYT (M-FLYT), which takes the per-example scores generated by different scoring methods and learns to unify them into a single score. Our training methodology naturally produces a distribution over the training examples, which we leverage through Soft Cap Sampling (SCS), a strategy for obtaining a filtered pretraining dataset from per-example probabilities that samples examples while preventing over-representation through a repetition penalty. Using all three methods, we achieve 40.1% ImageNet zero-shot accuracy on the DataComp medium scale filtering benchmark, a 1.9% absolute accuracy increase over all previous results and a 5.5% increase over results that -- like us -- use only public resources.

We study the task of agnostically learning halfspaces under the Gaussian distribution. Specifically, given labeled examples (x,y) from an unknown distribution on R^n times { pm 1}, whose marginal distribution on x is the standard Gaussian and the labels y can be arbitrary, the goal is to output a hypothesis with 0-1 loss OPT+epsilon, where OPT is the 0-1 loss of the best-fitting halfspace. We prove a near-optimal computational hardness result for this task, under the widely believed sub-exponential time hardness of the Learning with Errors (LWE) problem. Prior hardness results are either qualitatively suboptimal or apply to restricted families of algorithms. Our techniques extend to yield near-optimal lower bounds for related problems, including ReLU regression.

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

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 .

Knowledge distillation (KD) is a common approach to compress a teacher model to reduce its inference cost and memory footprint, by training a smaller student model. However, in the context of autoregressive language models (LMs), we empirically find that larger teacher LMs might dramatically result in a poorer student. In response to this problem, we conduct a series of analyses and reveal that different tokens have different teaching modes, neglecting which will lead to performance degradation. Motivated by this, we propose a simple yet effective adaptive teaching approach (ATKD) to improve the KD. The core of ATKD is to reduce rote learning and make teaching more diverse and flexible. Extensive experiments on 8 LM tasks show that, with the help of ATKD, various baseline KD methods can achieve consistent and significant performance gains (up to +3.04% average score) across all model types and sizes. More encouragingly, ATKD can improve the student model generalization effectively.

Software repositories is one of the sources of data in Empirical Software Engineering, primarily in the Mining Software Repositories field, aimed at extracting knowledge from the dynamics and practice of software projects. With the emergence of social coding platforms such as GitHub, researchers have now access to millions of software repositories to use as source data for their studies. With this massive amount of data, sampling techniques are needed to create more manageable datasets. The creation of these datasets is a crucial step, and researchers have to carefully select the repositories to create representative samples according to a set of variables of interest. However, current sampling methods are often based on random selection or rely on variables which may not be related to the research study (e.g., popularity or activity). In this paper, we present a methodology for creating representative samples of software repositories, where such representativeness is properly aligned with both the characteristics of the population of repositories and the requirements of the empirical study. We illustrate our approach with use cases based on Hugging Face repositories.

We introduce Kimi K2, a Mixture-of-Experts (MoE) large language model with 32 billion activated parameters and 1 trillion total parameters. We propose the MuonClip optimizer, which improves upon Muon with a novel QK-clip technique to address training instability while enjoying the advanced token efficiency of Muon. Based on MuonClip, K2 was pre-trained on 15.5 trillion tokens with zero loss spike. During post-training, K2 undergoes a multi-stage post-training process, highlighted by a large-scale agentic data synthesis pipeline and a joint reinforcement learning (RL) stage, where the model improves its capabilities through interactions with real and synthetic environments. Kimi K2 achieves state-of-the-art performance among open-source non-thinking models, with strengths in agentic capabilities. Notably, K2 obtains 66.1 on Tau2-Bench, 76.5 on ACEBench (En), 65.8 on SWE-Bench Verified, and 47.3 on SWE-Bench Multilingual -- surpassing most open and closed-sourced baselines in non-thinking settings. It also exhibits strong capabilities in coding, mathematics, and reasoning tasks, with a score of 53.7 on LiveCodeBench v6, 49.5 on AIME 2025, 75.1 on GPQA-Diamond, and 27.1 on OJBench, all without extended thinking. These results position Kimi K2 as one of the most capable open-source large language models to date, particularly in software engineering and agentic tasks. We release our base and post-trained model checkpoints to facilitate future research and applications of agentic intelligence.

Code generation with large language models has shown significant promise, especially when employing retrieval-augmented generation (RAG) with few-shot examples. However, selecting effective examples that enhance generation quality remains a challenging task, particularly when the target programming language (PL) is underrepresented. In this study, we present two key findings: (1) retrieving examples whose presented algorithmic plans can be referenced for generating the desired behavior significantly improves generation accuracy, and (2) converting code into pseudocode effectively captures such algorithmic plans, enhancing retrieval quality even when the source and the target PLs are different. Based on these findings, we propose Plan-as-query Example Retrieval for few-shot prompting in Code generation (PERC), a novel framework that utilizes algorithmic plans to identify and retrieve effective examples. We validate the effectiveness of PERC through extensive experiments on the CodeContests, HumanEval and MultiPL-E benchmarks: PERC consistently outperforms the state-of-the-art RAG methods in code generation, both when the source and target programming languages match or differ, highlighting its adaptability and robustness in diverse coding environments.

We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higher-order functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higher-order functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasi-Borel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasi-Borel counterpart to the Metropolis-Hastings-Green theorem.

Motivated by reducing the computational and storage costs of LLMs, model compression and KV cache compression have attracted much attention from researchers. However, current methods predominantly emphasize maintaining the performance of compressed LLMs, as measured by perplexity or simple accuracy on tasks of common sense knowledge QA and basic arithmetic reasoning. In this blog, we present a brief review of recent advancements in LLMs related to retrieval-augmented generation, multi-step reasoning, external tools, and computational expressivity, all of which substantially enhance LLM performance. Then, we propose a lottery LLM hypothesis suggesting that for a given LLM and task, there exists a smaller lottery LLM capable of producing the same performance as the original LLM with the assistance of multi-step reasoning and external tools. Based on the review of current progress in LLMs, we discuss and summarize the essential capabilities that the lottery LLM and KV cache compression must possess, which are currently overlooked in existing methods.

We study preferential Bayesian optimization (BO) where reliable feedback is limited to pairwise comparison called duels. An important challenge in preferential BO, which uses the preferential Gaussian process (GP) model to represent flexible preference structure, is that the posterior distribution is a computationally intractable skew GP. The most widely used approach for preferential BO is Gaussian approximation, which ignores the skewness of the true posterior. Alternatively, Markov chain Monte Carlo (MCMC) based preferential BO is also proposed. In this work, we first verify the accuracy of Gaussian approximation, from which we reveal the critical problem that the predictive probability of duels can be inaccurate. This observation motivates us to improve the MCMC-based estimation for skew GP, for which we show the practical efficiency of Gibbs sampling and derive the low variance MC estimator. However, the computational time of MCMC can still be a bottleneck in practice. Towards building a more practical preferential BO, we develop a new method that achieves both high computational efficiency and low sample complexity, and then demonstrate its effectiveness through extensive numerical experiments.

Key-Value (KV) cache has become a bottleneck of LLMs for long-context generation. Despite the numerous efforts in this area, the optimization for the decoding phase is generally ignored. However, we believe such optimization is crucial, especially for long-output generation tasks based on the following two observations: (i) Excessive compression during the prefill phase, which requires specific full context impairs the comprehension of the reasoning task; (ii) Deviation of heavy hitters occurs in the reasoning tasks with long outputs. Therefore, SCOPE, a simple yet efficient framework that separately performs KV cache optimization during the prefill and decoding phases, is introduced. Specifically, the KV cache during the prefill phase is preserved to maintain the essential information, while a novel strategy based on sliding is proposed to select essential heavy hitters for the decoding phase. Memory usage and memory transfer are further optimized using adaptive and discontinuous strategies. Extensive experiments on LongGenBench show the effectiveness and generalization of SCOPE and its compatibility as a plug-in to other prefill-only KV compression 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.

Given a database of bit strings A_1,ldots,A_min {0,1}^n, a fundamental data structure task is to estimate the distances between a given query Bin {0,1}^n with all the strings in the database. In addition, one might further want to ensure the integrity of the database by releasing these distance statistics in a secure manner. In this work, we propose differentially private (DP) data structures for this type of tasks, with a focus on Hamming and edit distance. On top of the strong privacy guarantees, our data structures are also time- and space-efficient. In particular, our data structure is epsilon-DP against any sequence of queries of arbitrary length, and for any query B such that the maximum distance to any string in the database is at most k, we output m distance estimates. Moreover, - For Hamming distance, our data structure answers any query in widetilde O(mk+n) time and each estimate deviates from the true distance by at most widetilde O(k/e^{epsilon/log k}); - For edit distance, our data structure answers any query in widetilde O(mk^2+n) time and each estimate deviates from the true distance by at most widetilde O(k/e^{epsilon/(log k log n)}). For moderate k, both data structures support sublinear query operations. We obtain these results via a novel adaptation of the randomized response technique as a bit flipping procedure, applied to the sketched strings.

With the advancements in long-context inference capabilities of large language models (LLMs), the KV cache has become one of the foundational components. However, its substantial GPU memory consumption makes KV cache compression a key technique for enabling efficient LLM inference in industrial scenarios. While recent studies have focused on optimizing the memory occupied by the KV cache, they overlook two critical factors: preserving semantic coherence and considering task-specific characteristic during compression. To address these limitations, we propose a novel task-adaptive KV cache window selection method, WindowKV. WindowKV dynamically selects local semantic windows consisting of consecutive tokens, according to task-specific characteristics, ensuring the retained KV cache captures continuous, essential context. Additionally, we introduce an intra-group layer KV cache indices sharing strategy to reduce computational overhead, achieving a balance between performance and efficiency. We rigorously evaluate WindowKV on the LongBench benchmark, and the results demonstrate that it maintains a performance comparable to full KV cache retention while using only 12% of the original KV cache, significantly reducing memory requirements. Furthermore, our method also achieves state-of-the-art results in the Needle-in-a-Haystack evaluation, highlighting its effectiveness and robustness.