Daily Papers

Using a fully Bayesian approach, Gaussian Process regression is extended to include marginalisation over the kernel choice and kernel hyperparameters. In addition, Bayesian model comparison via the evidence enables direct kernel comparison. The calculation of the joint posterior was implemented with a transdimensional sampler which simultaneously samples over the discrete kernel choice and their hyperparameters by embedding these in a higher-dimensional space, from which samples are taken using nested sampling. Kernel recovery and mean function inference were explored on synthetic data from exoplanet transit light curve simulations. Subsequently, the method was extended to marginalisation over mean functions and noise models and applied to the inference of the present-day Hubble parameter, H_0, from real measurements of the Hubble parameter as a function of redshift, derived from the cosmologically model-independent cosmic chronometer and ΛCDM-dependent baryon acoustic oscillation observations. The inferred H_0 values from the cosmic chronometers, baryon acoustic oscillations and combined datasets are H_0= 66 pm 6, km,s^{-1},Mpc^{-1}, H_0= 67 pm 10, km,s^{-1},Mpc^{-1} and H_0= 69 pm 6, km,s^{-1},Mpc^{-1}, respectively. The kernel posterior of the cosmic chronometers dataset prefers a non-stationary linear kernel. Finally, the datasets are shown to be not in tension with ln R=12.17pm 0.02.

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.

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.

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.

Determinantal point processes (DPPs) are distributions over sets of items that model diversity using kernels. Their applications in machine learning include summary extraction and recommendation systems. Yet, the cost of sampling from a DPP is prohibitive in large-scale applications, which has triggered an effort towards efficient approximate samplers. We build a novel MCMC sampler that combines ideas from combinatorial geometry, linear programming, and Monte Carlo methods to sample from DPPs with a fixed sample cardinality, also called projection DPPs. Our sampler leverages the ability of the hit-and-run MCMC kernel to efficiently move across convex bodies. Previous theoretical results yield a fast mixing time of our chain when targeting a distribution that is close to a projection DPP, but not a DPP in general. Our empirical results demonstrate that this extends to sampling projection DPPs, i.e., our sampler is more sample-efficient than previous approaches which in turn translates to faster convergence when dealing with costly-to-evaluate functions, such as summary extraction in our experiments.

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

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

Dimensionality reduction methods are unsupervised approaches which learn low-dimensional spaces where some properties of the initial space, typically the notion of "neighborhood", are preserved. Such methods usually require propagation on large k-NN graphs or complicated optimization solvers. On the other hand, self-supervised learning approaches, typically used to learn representations from scratch, rely on simple and more scalable frameworks for learning. In this paper, we propose TLDR, a dimensionality reduction method for generic input spaces that is porting the recent self-supervised learning framework of Zbontar et al. (2021) to the specific task of dimensionality reduction, over arbitrary representations. We propose to use nearest neighbors to build pairs from a training set and a redundancy reduction loss to learn an encoder that produces representations invariant across such pairs. TLDR is a method that is simple, easy to train, and of broad applicability; it consists of an offline nearest neighbor computation step that can be highly approximated, and a straightforward learning process. Aiming for scalability, we focus on improving linear dimensionality reduction, and show consistent gains on image and document retrieval tasks, e.g. gaining +4% mAP over PCA on ROxford for GeM- AP, improving the performance of DINO on ImageNet or retaining it with a 10x compression.

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

Diffusion models have been successful on a range of conditional generation tasks including molecular design and text-to-image generation. However, these achievements have primarily depended on task-specific conditional training or error-prone heuristic approximations. Ideally, a conditional generation method should provide exact samples for a broad range of conditional distributions without requiring task-specific training. To this end, we introduce the Twisted Diffusion Sampler, or TDS. TDS is a sequential Monte Carlo (SMC) algorithm that targets the conditional distributions of diffusion models through simulating a set of weighted particles. The main idea is to use twisting, an SMC technique that enjoys good computational efficiency, to incorporate heuristic approximations without compromising asymptotic exactness. We first find in simulation and in conditional image generation tasks that TDS provides a computational statistical trade-off, yielding more accurate approximations with many particles but with empirical improvements over heuristics with as few as two particles. We then turn to motif-scaffolding, a core task in protein design, using a TDS extension to Riemannian diffusion models. On benchmark test cases, TDS allows flexible conditioning criteria and often outperforms the state of the art.

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

In high dimension, low sample size (HDLSS) settings, classifiers based on Euclidean distances like the nearest neighbor classifier and the average distance classifier perform quite poorly if differences between locations of the underlying populations get masked by scale differences. To rectify this problem, several modifications of these classifiers have been proposed in the literature. However, existing methods are confined to location and scale differences only, and often fail to discriminate among populations differing outside of the first two moments. In this article, we propose some simple transformations of these classifiers resulting into improved performance even when the underlying populations have the same location and scale. We further propose a generalization of these classifiers based on the idea of grouping of variables. The high-dimensional behavior of the proposed classifiers is studied theoretically. Numerical experiments with a variety of simulated examples as well as an extensive analysis of real data sets exhibit advantages of the proposed methods.

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

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

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

In this paper, we study an under-explored but important factor of diffusion generative models, i.e., the combinatorial complexity. Data samples are generally high-dimensional, and for various structured generation tasks, additional attributes are combined to associate with data samples. We show that the space spanned by the combination of dimensions and attributes can be insufficiently covered by existing training schemes of diffusion generative models, potentially limiting test time performance. We present a simple fix to this problem by constructing stochastic processes that fully exploit the combinatorial structures, hence the name ComboStoc. Using this simple strategy, we show that network training is significantly accelerated across diverse data modalities, including images and 3D structured shapes. Moreover, ComboStoc enables a new way of test time generation which uses asynchronous time steps for different dimensions and attributes, thus allowing for varying degrees of control over them. Our code is available at: https://github.com/Xrvitd/ComboStoc

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.

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.

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.

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.

The standard practice in Generative Adversarial Networks (GANs) discards the discriminator during sampling. However, this sampling method loses valuable information learned by the discriminator regarding the data distribution. In this work, we propose a collaborative sampling scheme between the generator and the discriminator for improved data generation. Guided by the discriminator, our approach refines the generated samples through gradient-based updates at a particular layer of the generator, shifting the generator distribution closer to the real data distribution. Additionally, we present a practical discriminator shaping method that can smoothen the loss landscape provided by the discriminator for effective sample refinement. Through extensive experiments on synthetic and image datasets, we demonstrate that our proposed method can improve generated samples both quantitatively and qualitatively, offering a new degree of freedom in GAN sampling.

Despite high semantic alignment, modern text-to-image (T2I) generative models still struggle to synthesize diverse images from a given prompt. This lack of diversity not only restricts user choice, but also risks amplifying societal biases. In this work, we enhance the T2I diversity through a geometric lens. Unlike most existing methods that rely primarily on entropy-based guidance to increase sample dissimilarity, we introduce Geometry-Aware Spherical Sampling (GASS) to enhance diversity by explicitly controlling both prompt-dependent and prompt-independent sources of variation. Specifically, we decompose the diversity measure in CLIP embeddings using two orthogonal directions: the text embedding, which captures semantic variation related to the prompt, and an identified orthogonal direction that captures prompt-independent variation (e.g., backgrounds). Based on this decomposition, GASS increases the geometric projection spread of generated image embeddings along both axes and guides the T2I sampling process via expanded predictions along the generation trajectory. Our experiments on different frozen T2I backbones (U-Net and DiT, diffusion and flow) and benchmarks demonstrate the effectiveness of disentangled diversity enhancement with minimal impact on image fidelity and semantic alignment.

The recent success of distributed word representations has led to an increased interest in analyzing the properties of their spatial distribution. Several studies have suggested that contextualized word embedding models do not isotropically project tokens into vector space. However, current methods designed to measure isotropy, such as average random cosine similarity and the partition score, have not been thoroughly analyzed and are not appropriate for measuring isotropy. We propose IsoScore: a novel tool that quantifies the degree to which a point cloud uniformly utilizes the ambient vector space. Using rigorously designed tests, we demonstrate that IsoScore is the only tool available in the literature that accurately measures how uniformly distributed variance is across dimensions in vector space. Additionally, we use IsoScore to challenge a number of recent conclusions in the NLP literature that have been derived using brittle metrics of isotropy. We caution future studies from using existing tools to measure isotropy in contextualized embedding space as resulting conclusions will be misleading or altogether inaccurate.

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

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

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%.

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.

We propose a new sampler for robust estimators that always selects the sample with the highest probability of consisting only of inliers. After every unsuccessful iteration, the inlier probabilities are updated in a principled way via a Bayesian approach. The probabilities obtained by the deep network are used as prior (so-called neural guidance) inside the sampler. Moreover, we introduce a new loss that exploits, in a geometrically justifiable manner, the orientation and scale that can be estimated for any type of feature, e.g., SIFT or SuperPoint, to estimate two-view geometry. The new loss helps to learn higher-order information about the underlying scene geometry. Benefiting from the new sampler and the proposed loss, we combine the neural guidance with the state-of-the-art MAGSAC++. Adaptive Reordering Sampler with Neurally Guided MAGSAC (ARS-MAGSAC) is superior to the state-of-the-art in terms of accuracy and run-time on the PhotoTourism and KITTI datasets for essential and fundamental matrix estimation. The code and trained models are available at https://github.com/weitong8591/ars_magsac.

Diversity has been gaining interest in the NLP community in recent years. At the same time, state-of-the-art transformer models such as ModernBERT use very large pre-training datasets, which are driven by size rather than by diversity. This summons for an investigation of the impact of diversity on the ModernBERT pre-training. We do so in this study, with the express intent of reducing pre-training dataset size, while retaining at least comparable performance. We compare diversity-driven sampling algorithms, so as to pick the best one. We find that diversity-driven sampling allows in some tasks to gain 10 points relative to randomly-sampled pre-training data of commensurate size. We also see that a model pre-trained for 483h on a diversity-driven dataset of 150M tokens can yield a commensurate performance to a model pre-trained for 1,775h on a randomly-driven dataset of 2.4B tokens.

Rapid advancement of machine learning solutions has often coincided with the production of a test public data set. Such datasets reduce the largest barrier to entry for tackling a problem -- procuring data -- while also providing a benchmark to compare different solutions. Furthermore, large datasets have been used to train high-performing feature finders which are then used in new approaches to problems beyond that initially defined. In order to encourage the rapid development in the analysis of data collected using liquid argon time projection chambers, a class of particle detectors used in high energy physics experiments, we have produced the PILArNet, first 2D and 3D open dataset to be used for a couple of key analysis tasks. The initial dataset presented in this paper contains 300,000 samples simulated and recorded in three different volume sizes. The dataset is stored efficiently in sparse 2D and 3D matrix format with auxiliary information about simulated particles in the volume, and is made available for public research use. In this paper we describe the dataset, tasks, and the method used to procure the sample.

We present EuLearn, the first surface datasets equitably representing a diversity of topological types. We designed our embedded surfaces of uniformly varying genera relying on random knots, thus allowing our surfaces to knot with themselves. EuLearn contributes new topological datasets of meshes, point clouds, and scalar fields in 3D. We aim to facilitate the training of machine learning systems that can discern topological features. We experimented with specific emblematic 3D neural network architectures, finding that their vanilla implementations perform poorly on genus classification. To enhance performance, we developed a novel, non-Euclidean, statistical sampling method adapted to graph and manifold data. We also introduce adjacency-informed adaptations of PointNet and Transformer architectures that rely on our non-Euclidean sampling strategy. Our results demonstrate that incorporating topological information into deep learning workflows significantly improves performance on these otherwise challenging EuLearn datasets.

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.

We study sampling algorithms for β-ensembles with time complexity less than cubic in the cardinality of the ensemble. Following Dumitriu & Edelman (2002), we see the ensemble as the eigenvalues of a random tridiagonal matrix, namely a random Jacobi matrix. First, we provide a unifying and elementary treatment of the tridiagonal models associated to the three classical Hermite, Laguerre and Jacobi ensembles. For this purpose, we use simple changes of variables between successive reparametrizations of the coefficients defining the tridiagonal matrix. Second, we derive an approximate sampler for the simulation of β-ensembles, and illustrate how fast it can be for polynomial potentials. This method combines a Gibbs sampler on Jacobi matrices and the diagonalization of these matrices. In practice, even for large ensembles, only a few Gibbs passes suffice for the marginal distribution of the eigenvalues to fit the expected theoretical distribution. When the conditionals in the Gibbs sampler can be simulated exactly, the same fast empirical convergence is observed for the fluctuations of the largest eigenvalue. Our experimental results support a conjecture by Krishnapur et al. (2016), that the Gibbs chain on Jacobi matrices of size N mixes in O(log(N)).

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

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

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.

Precision and Recall are two prominent metrics of generative performance, which were proposed to separately measure the fidelity and diversity of generative models. Given their central role in comparing and improving generative models, understanding their limitations are crucially important. To that end, in this work, we identify a critical flaw in the common approximation of these metrics using k-nearest-neighbors, namely, that the very interpretations of fidelity and diversity that are assigned to Precision and Recall can fail in high dimensions, resulting in very misleading conclusions. Specifically, we empirically and theoretically show that as the number of dimensions grows, two model distributions with supports at equal point-wise distance from the support of the real distribution, can have vastly different Precision and Recall regardless of their respective distributions, hence an emergent asymmetry in high dimensions. Based on our theoretical insights, we then provide simple yet effective modifications to these metrics to construct symmetric metrics regardless of the number of dimensions. Finally, we provide experiments on real-world datasets to illustrate that the identified flaw is not merely a pathological case, and that our proposed metrics are effective in alleviating its impact.

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.

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

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.

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.

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

Recent advances in masked diffusion models (MDMs) have established them as powerful non-autoregressive alternatives for sequence generation. Nevertheless, our preliminary experiments reveal that the generation quality of MDMs is still highly sensitive to the choice of decoding strategy. In particular, widely adopted uncertainty-based samplers suffer from two key limitations: a lack of global trajectory control and a pronounced bias toward trivial tokens in the early stages of decoding. These shortcomings restrict the full potential of MDMs. In this work, we introduce Position-Aware Confidence-Calibrated Sampling (PC-Sampler), a novel decoding strategy that unifies global trajectory planning with content-aware informativeness maximization. PC-Sampler incorporates a position-aware weighting mechanism to regulate the decoding path and a calibrated confidence score to suppress the premature selection of trivial tokens. Extensive experiments on three advanced MDMs across seven challenging benchmarks-including logical reasoning and planning tasks-demonstrate that PC-Sampler consistently outperforms existing MDM decoding strategies by more than 10% on average, significantly narrowing the performance gap with state-of-the-art autoregressive models. All codes are available at https://github.com/NEUIR/PC-Sampler.

We tackle the problem of sampling from intractable high-dimensional density functions, a fundamental task that often appears in machine learning and statistics. We extend recent sampling-based approaches that leverage controlled stochastic processes to model approximate samples from these target densities. The main drawback of these approaches is that the training objective requires full trajectories to compute, resulting in sluggish credit assignment issues due to use of entire trajectories and a learning signal present only at the terminal time. In this work, we present Diffusion Generative Flow Samplers (DGFS), a sampling-based framework where the learning process can be tractably broken down into short partial trajectory segments, via parameterizing an additional "flow function". Our method takes inspiration from the theory developed for generative flow networks (GFlowNets), allowing us to make use of intermediate learning signals. Through various challenging experiments, we demonstrate that DGFS achieves more accurate estimates of the normalization constant than closely-related prior methods.

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

Mapping sequences of discrete data to a point in a continuous space makes it difficult to retrieve those sequences via random sampling. Mapping the input to a volume would make it easier to retrieve at test time, and that's the strategy followed by the family of approaches based on Variational Autoencoder. However the fact that they are at the same time optimizing for prediction and for smoothness of representation, forces them to trade-off between the two. We improve on the performance of some of the standard methods in deep learning to generate sentences by uniformly sampling a continuous space. We do it by proposing AriEL, that constructs volumes in a continuous space, without the need of encouraging the creation of volumes through the loss function. We first benchmark on a toy grammar, that allows to automatically evaluate the language learned and generated by the models. Then, we benchmark on a real dataset of human dialogues. Our results indicate that the random access to the stored information is dramatically improved, and our method AriEL is able to generate a wider variety of correct language by randomly sampling the latent space. VAE follows in performance for the toy dataset while, AE and Transformer follow for the real dataset. This partially supports to the hypothesis that encoding information into volumes instead of into points, can lead to improved retrieval of learned information with random sampling. This can lead to better generators and we also discuss potential disadvantages.

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.

Current recommender systems employ large-sized embedding tables with uniform dimensions for all features, leading to overfitting, high computational cost, and suboptimal generalizing performance. Many techniques aim to solve this issue by feature selection or embedding dimension search. However, these techniques typically select a fixed subset of features or embedding dimensions for all instances and feed all instances into one recommender model without considering heterogeneity between items or users. This paper proposes a novel instance-wise Hierarchical Architecture Search framework, iHAS, which automates neural architecture search at the instance level. Specifically, iHAS incorporates three stages: searching, clustering, and retraining. The searching stage identifies optimal instance-wise embedding dimensions across different field features via carefully designed Bernoulli gates with stochastic selection and regularizers. After obtaining these dimensions, the clustering stage divides samples into distinct groups via a deterministic selection approach of Bernoulli gates. The retraining stage then constructs different recommender models, each one designed with optimal dimensions for the corresponding group. We conduct extensive experiments to evaluate the proposed iHAS on two public benchmark datasets from a real-world recommender system. The experimental results demonstrate the effectiveness of iHAS and its outstanding transferability to widely-used deep recommendation models.

We present the task description of the Detection and Classification of Acoustic Scenes and Events (DCASE) 2023 Challenge Task 2: ``First-shot unsupervised anomalous sound detection (ASD) for machine condition monitoring''. The main goal is to enable rapid deployment of ASD systems for new kinds of machines without the need for hyperparameter tuning. In the past ASD tasks, developed methods tuned hyperparameters for each machine type, as the development and evaluation datasets had the same machine types. However, collecting normal and anomalous data as the development dataset can be infeasible in practice. In 2023 Task 2, we focus on solving the first-shot problem, which is the challenge of training a model on a completely novel machine type. Specifically, (i) each machine type has only one section (a subset of machine type) and (ii) machine types in the development and evaluation datasets are completely different. Analysis of 86 submissions from 23 teams revealed that the keys to outperform baselines were: 1) sampling techniques for dealing with class imbalances across different domains and attributes, 2) generation of synthetic samples for robust detection, and 3) use of multiple large pre-trained models to extract meaningful embeddings for the anomaly detector.

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.

We propose a fully data-driven approach to designing mutual information (MI) estimators. Since any MI estimator is a function of the observed sample from two random variables, we parameterize this function with a neural network (MIST) and train it end-to-end to predict MI values. Training is performed on a large meta-dataset of 625,000 synthetic joint distributions with known ground-truth MI. To handle variable sample sizes and dimensions, we employ a two-dimensional attention scheme ensuring permutation invariance across input samples. To quantify uncertainty, we optimize a quantile regression loss, enabling the estimator to approximate the sampling distribution of MI rather than return a single point estimate. This research program departs from prior work by taking a fully empirical route, trading universal theoretical guarantees for flexibility and efficiency. Empirically, the learned estimators largely outperform classical baselines across sample sizes and dimensions, including on joint distributions unseen during training. The resulting quantile-based intervals are well-calibrated and more reliable than bootstrap-based confidence intervals, while inference is orders of magnitude faster than existing neural baselines. Beyond immediate empirical gains, this framework yields trainable, fully differentiable estimators that can be embedded into larger learning pipelines. Moreover, exploiting MI's invariance to invertible transformations, meta-datasets can be adapted to arbitrary data modalities via normalizing flows, enabling flexible training for diverse target meta-distributions.

Modern neural networks are known to give overconfident prediction for out-of-distribution inputs when deployed in the open world. It is common practice to leverage a surrogate outlier dataset to regularize the model during training, and recent studies emphasize the role of uncertainty in designing the sampling strategy for outlier dataset. However, the OOD samples selected solely based on predictive uncertainty can be biased towards certain types, which may fail to capture the full outlier distribution. In this work, we empirically show that diversity is critical in sampling outliers for OOD detection performance. Motivated by the observation, we propose a straightforward and novel sampling strategy named DOS (Diverse Outlier Sampling) to select diverse and informative outliers. Specifically, we cluster the normalized features at each iteration, and the most informative outlier from each cluster is selected for model training with absent category loss. With DOS, the sampled outliers efficiently shape a globally compact decision boundary between ID and OOD data. Extensive experiments demonstrate the superiority of DOS, reducing the average FPR95 by up to 25.79% on CIFAR-100 with TI-300K.

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 .

We present Submatrix-wise Vector Embedding Learner (Swivel), a method for generating low-dimensional feature embeddings from a feature co-occurrence matrix. Swivel performs approximate factorization of the point-wise mutual information matrix via stochastic gradient descent. It uses a piecewise loss with special handling for unobserved co-occurrences, and thus makes use of all the information in the matrix. While this requires computation proportional to the size of the entire matrix, we make use of vectorized multiplication to process thousands of rows and columns at once to compute millions of predicted values. Furthermore, we partition the matrix into shards in order to parallelize the computation across many nodes. This approach results in more accurate embeddings than can be achieved with methods that consider only observed co-occurrences, and can scale to much larger corpora than can be handled with sampling methods.

We introduce a novel class of sample-based explanations we term high-dimensional representers, that can be used to explain the predictions of a regularized high-dimensional model in terms of importance weights for each of the training samples. Our workhorse is a novel representer theorem for general regularized high-dimensional models, which decomposes the model prediction in terms of contributions from each of the training samples: with positive (negative) values corresponding to positive (negative) impact training samples to the model's prediction. We derive consequences for the canonical instances of ell_1 regularized sparse models, and nuclear norm regularized low-rank models. As a case study, we further investigate the application of low-rank models in the context of collaborative filtering, where we instantiate high-dimensional representers for specific popular classes of models. Finally, we study the empirical performance of our proposed methods on three real-world binary classification datasets and two recommender system datasets. We also showcase the utility of high-dimensional representers in explaining model recommendations.

Uniform-state discrete diffusion models excel at few-step generation and guidance due to their ability to self-correct, making them preferred over autoregressive or Masked diffusion models in these settings. However, their sampling quality plateaus with ancestral samplers as the number of steps increases. We introduce a family of Predictor-Corrector (PC) samplers for discrete diffusion that generalize prior methods and apply to arbitrary noise processes. When paired with uniform-state diffusion, our samplers outperform ancestral sampling on both language and image modeling, achieving lower generative perplexity at matched unigram entropy on OpenWebText and better FID/IS scores on CIFAR10. Crucially, unlike conventional samplers, our PC methods continue to improve with more sampling steps. Taken together, these findings call into question the assumption that Masked diffusion is the inevitable future of diffusion-based language modeling. Beyond sampling, we develop a memory-efficient curriculum for the Gaussian relaxation training phase, reducing training time by 25% and memory by 33% compared to Duo while maintaining comparable perplexity on OpenWebText and LM1B and strong downstream performance. We release code, checkpoints, and a video-tutorial on: https://s-sahoo.com/duo-ch2

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

In this paper, we investigate the underexplored challenge of sample diversity in autoregressive (AR) generative models with bitwise visual tokenizers. We first analyze the factors that limit diversity in bitwise AR models and identify two key issues: (1) the binary classification nature of bitwise modeling, which restricts the prediction space, and (2) the overly sharp logits distribution, which causes sampling collapse and reduces diversity. Building on these insights, we propose DiverseAR, a principled and effective method that enhances image diversity without sacrificing visual quality. Specifically, we introduce an adaptive logits distribution scaling mechanism that dynamically adjusts the sharpness of the binary output distribution during sampling, resulting in smoother predictions and greater diversity. To mitigate potential fidelity loss caused by distribution smoothing, we further develop an energy-based generation path search algorithm that avoids sampling low-confidence tokens, thereby preserving high visual quality. Extensive experiments demonstrate that DiverseAR substantially improves sample diversity in bitwise autoregressive image generation.

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

Generative artificial intelligence (AI) has made unprecedented advances in vision language models over the past two years. During the generative process, new samples (images) are generated from an unknown high-dimensional distribution. Markov Chain Monte Carlo (MCMC) methods are particularly effective in drawing samples from such complex, high-dimensional distributions. This makes MCMC methods an integral component for models like EBMs, ensuring accurate sample generation. Gradient-based optimization is at the core of modern generative models. The update step during the optimization forms a Markov chain where the new update depends only on the current state. This allows exploration of the parameter space in a memoryless manner, thus combining the benefits of gradient-based optimization and MCMC sampling. MCMC methods have shown an equally important role in physically based rendering where complex light paths are otherwise quite challenging to sample from simple importance sampling techniques. A lot of research is dedicated towards bringing physical realism to samples (images) generated from diffusion-based generative models in a data-driven manner, however, a unified framework connecting these techniques is still missing. In this course, we take the first steps toward understanding each of these components and exploring how MCMC could potentially serve as a bridge, linking these closely related areas of research. Our course aims to provide necessary theoretical and practical tools to guide students, researchers and practitioners towards the common goal of generative physically based rendering. All Jupyter notebooks with demonstrations associated to this tutorial can be found on the project webpage: https://sinbag.github.io/mcmc/

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.

High-quality pre-training data is crutial for large language models, where quality captures factual reliability and semantic value, and diversity ensures broad coverage and distributional heterogeneity. Existing approaches typically rely on single or multiple-dimensional score-based selection. However, directly selecting top-scored data often degrades performance, and sampling from a broader range is required to recover results. The above non-monotonicity between dataset scores and downstream benchmark results reveals a fundamental bias: score-based methods collapse correlated dimensions, causing top-scored data to appear high-quality while systematically overlooking diversity. We argue that ensuring diversity requires decomposing correlated metrics into orthogonal feature dimensions, from which the top-scored data can be directly selected. Therefore, we proposed the Orthogonal Diversity-Aware Selection (ODiS) algorithm, which preserves both quality and diversity during data selection. First, ODiS evaluates data from multiple dimensions, covering language quality, knowledge quality, and comprehension difficulty. The multi-dimensional scores are then decorrelated via Principal Component Analysis (PCA), yielding orthogonal evaluation dimensions. For each dimension, a Roberta-based scorer is trained to regress the data onto PCA-projected scores, enabling scalable inference on large corpora. Finally, ODiS constructs the training dataset by selecting top-scored data within each orthogonal dimension, thereby ensuring both quality and diversity. Empirical results show that ODiS-selected data exhibit less than 2\% inter-dimension overlap, confirming orthogonality between dimensions. More importantly, models trained with ODiS-selected data significantly outperform other baselines on downstream benchmarks, highlighting the necessity of orthogonal, diversity-aware data selection for LLMs.

We present two large datasets of labelled plant-images that are suited towards the training of machine learning and computer vision models. The first dataset encompasses as the day of writing over 1.2 million images of indoor-grown crops and weeds common to the Canadian Prairies and many US states. The second dataset consists of over 540,000 images of plants imaged in farmland. All indoor plant images are labelled by species and we provide rich etadata on the level of individual images. This comprehensive database allows to filter the datasets under user-defined specifications such as for example the crop-type or the age of the plant. Furthermore, the indoor dataset contains images of plants taken from a wide variety of angles, including profile shots, top-down shots, and angled perspectives. The images taken from plants in fields are all from a top-down perspective and contain usually multiple plants per image. For these images metadata is also available. In this paper we describe both datasets' characteristics with respect to plant variety, plant age, and number of images. We further introduce an open-access sample of the indoor-dataset that contains 1,000 images of each species covered in our dataset. These, in total 14,000 images, had been selected, such that they form a representative sample with respect to plant age and ndividual plants per species. This sample serves as a quick entry point for new users to the dataset, allowing them to explore the data on a small scale and find the parameters of data most useful for their application without having to deal with hundreds of thousands of individual images.

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

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.

Social scientists are now using large language models to create "silicon samples" - synthetic datasets intended to stand in for human respondents, aimed at revolutionising human subjects research. However, there are many analytic choices which must be made to produce these samples. Though many of these choices are defensible, their impact on sample quality is poorly understood. I map out these analytic choices and demonstrate how a very small number of decisions can dramatically change the correspondence between silicon samples and human data. Configurations (N = 252) varied substantially in their capacity to estimate (i) rank ordering of participants, (ii) response distributions, and (iii) between-scale correlations. Most critically, configurations were not consistent in quality: those that performed well on one dimension often performed poorly on another, implying that there is no "one-size-fits-all" configuration that optimises the accuracy of these samples. I call for greater attention to the threat of analytic flexibility in using silicon samples.

We begin the study of list-decodable linear regression using batches. In this setting only an alpha in (0,1] fraction of the batches are genuine. Each genuine batch contains ge n i.i.d. samples from a common unknown distribution and the remaining batches may contain arbitrary or even adversarial samples. We derive a polynomial time algorithm that for any nge tilde Omega(1/alpha) returns a list of size mathcal O(1/alpha^2) such that one of the items in the list is close to the true regression parameter. The algorithm requires only mathcal{O}(d/alpha^2) genuine batches and works under fairly general assumptions on the distribution. The results demonstrate the utility of batch structure, which allows for the first polynomial time algorithm for list-decodable regression, which may be impossible for the non-batch setting, as suggested by a recent SQ lower bound diakonikolas2021statistical for the non-batch setting.

Across many scientific fields, measurements often represent the number of times an event occurs. For example, a document can be represented by word occurrence counts, neural activity by spike counts per time window, or online communication by daily email counts. These measurements yield high-dimensional count data that often approximate a Poisson distribution, frequently with low rates that produce substantial sparsity and complicate downstream analysis. A useful approach is to embed the data into a low-dimensional space that preserves meaningful structure, commonly termed dimensionality reduction. Yet existing dimensionality reduction methods, including both linear (e.g., PCA) and nonlinear approaches (e.g., t-SNE), often assume continuous Euclidean geometry, thereby misaligning with the discrete, sparse nature of low-rate count data. Here, we propose p-SNE (Poisson Stochastic Neighbor Embedding), a nonlinear neighbor embedding method designed around the Poisson structure of count data, using KL divergence between Poisson distributions to measure pairwise dissimilarity and Hellinger distance to optimize the embedding. We test p-SNE on synthetic Poisson data and demonstrate its ability to recover meaningful structure in real-world count datasets, including weekday patterns in email communication, research area clusters in OpenReview papers, and temporal drift and stimulus gradients in neural spike recordings.

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

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.

In generative models, two paradigms have gained attraction in various applications: next-set prediction-based Masked Generative Models and next-noise prediction-based Non-Autoregressive Models, e.g., Diffusion Models. In this work, we propose using discrete-state models to connect them and explore their scalability in the vision domain. First, we conduct a step-by-step analysis in a unified design space across two types of models including timestep-independence, noise schedule, temperature, guidance strength, etc in a scalable manner. Second, we re-cast typical discriminative tasks, e.g., image segmentation, as an unmasking process from [MASK]tokens on a discrete-state model. This enables us to perform various sampling processes, including flexible conditional sampling by only training once to model the joint distribution. All aforementioned explorations lead to our framework named Discrete Interpolants, which enables us to achieve state-of-the-art or competitive performance compared to previous discrete-state based methods in various benchmarks, like ImageNet256, MS COCO, and video dataset FaceForensics. In summary, by leveraging [MASK] in discrete-state models, we can bridge Masked Generative and Non-autoregressive Diffusion models, as well as generative and discriminative tasks.

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

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

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

Label noise is one of the key factors that lead to the poor generalization of deep learning models. Existing label-noise learning methods usually assume that the ground-truth classes of the training data are balanced. However, the real-world data is often imbalanced, leading to the inconsistency between observed and intrinsic class distribution with label noises. In this case, it is hard to distinguish clean samples from noisy samples on the intrinsic tail classes with the unknown intrinsic class distribution. In this paper, we propose a learning framework for label-noise learning with intrinsically long-tailed data. Specifically, we propose two-stage bi-dimensional sample selection (TABASCO) to better separate clean samples from noisy samples, especially for the tail classes. TABASCO consists of two new separation metrics that complement each other to compensate for the limitation of using a single metric in sample separation. Extensive experiments on benchmarks demonstrate the effectiveness of our method. Our code is available at https://github.com/Wakings/TABASCO.

Transductive Few-Shot Learning (TFSL) has recently attracted increasing attention since it typically outperforms its inductive peer by leveraging statistics of query samples. However, previous TFSL methods usually encode uniform prior that all the classes within query samples are equally likely, which is biased in imbalanced TFSL and causes severe performance degradation. Given this pivotal issue, in this work, we propose a novel Conditional Transport (CT) based imbalanced TFSL model called {\textbf P}rototypes-oriented {\textbf U}nbiased {\textbf T}ransfer {\textbf M}odel (PUTM) to fully exploit unbiased statistics of imbalanced query samples, which employs forward and backward navigators as transport matrices to balance the prior of query samples per class between uniform and adaptive data-driven distributions. For efficiently transferring statistics learned by CT, we further derive a closed form solution to refine prototypes based on MAP given the learned navigators. The above two steps of discovering and transferring unbiased statistics follow an iterative manner, formulating our EM-based solver. Experimental results on four standard benchmarks including miniImageNet, tieredImageNet, CUB, and CIFAR-FS demonstrate superiority of our model in class-imbalanced generalization.

Learning embedding table plays a fundamental role in Click-through rate(CTR) prediction from the view of the model performance and memory usage. The embedding table is a two-dimensional tensor, with its axes indicating the number of feature values and the embedding dimension, respectively. To learn an efficient and effective embedding table, recent works either assign various embedding dimensions for feature fields and reduce the number of embeddings respectively or mask the embedding table parameters. However, all these existing works cannot get an optimal embedding table. On the one hand, various embedding dimensions still require a large amount of memory due to the vast number of features in the dataset. On the other hand, decreasing the number of embeddings usually suffers from performance degradation, which is intolerable in CTR prediction. Finally, pruning embedding parameters will lead to a sparse embedding table, which is hard to be deployed. To this end, we propose an optimal embedding table learning framework OptEmbed, which provides a practical and general method to find an optimal embedding table for various base CTR models. Specifically, we propose pruning the redundant embeddings regarding corresponding features' importance by learnable pruning thresholds. Furthermore, we consider assigning various embedding dimensions as one single candidate architecture. To efficiently search the optimal embedding dimensions, we design a uniform embedding dimension sampling scheme to equally train all candidate architectures, meaning architecture-related parameters and learnable thresholds are trained simultaneously in one supernet. We then propose an evolution search method based on the supernet to find the optimal embedding dimensions for each field. Experiments on public datasets show that OptEmbed can learn a compact embedding table which can further improve the model performance.

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.

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

In healthcare, medical image segmentation is crucial for accurate disease diagnosis and the development of effective treatment strategies. Early detection can significantly aid in managing diseases and potentially prevent their progression. Machine learning, particularly deep convolutional neural networks, has emerged as a promising approach to addressing segmentation challenges. Traditional methods like U-Net use encoding blocks for local representation modeling and decoding blocks to uncover semantic relationships. However, these models often struggle with multi-scale objects exhibiting significant variations in texture and shape, and they frequently fail to capture long-range dependencies in the input data. Transformers designed for sequence-to-sequence predictions have been proposed as alternatives, utilizing global self-attention mechanisms. Yet, they can sometimes lack precise localization due to insufficient granular details. To overcome these limitations, we introduce TransDAE: a novel approach that reimagines the self-attention mechanism to include both spatial and channel-wise associations across the entire feature space, while maintaining computational efficiency. Additionally, TransDAE enhances the skip connection pathway with an inter-scale interaction module, promoting feature reuse and improving localization accuracy. Remarkably, TransDAE outperforms existing state-of-the-art methods on the Synaps multi-organ dataset, even without relying on pre-trained weights.

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.

Despite the success of deep neural networks, there are still many challenges in deep representation learning due to the data scarcity issues such as data imbalance, unseen distribution, and domain shift. To address the above-mentioned issues, a variety of methods have been devised to explore the sample relationships in a vanilla way (i.e., from the perspectives of either the input or the loss function), failing to explore the internal structure of deep neural networks for learning with sample relationships. Inspired by this, we propose to enable deep neural networks themselves with the ability to learn the sample relationships from each mini-batch. Specifically, we introduce a batch transformer module or BatchFormer, which is then applied into the batch dimension of each mini-batch to implicitly explore sample relationships during training. By doing this, the proposed method enables the collaboration of different samples, e.g., the head-class samples can also contribute to the learning of the tail classes for long-tailed recognition. Furthermore, to mitigate the gap between training and testing, we share the classifier between with or without the BatchFormer during training, which can thus be removed during testing. We perform extensive experiments on over ten datasets and the proposed method achieves significant improvements on different data scarcity applications without any bells and whistles, including the tasks of long-tailed recognition, compositional zero-shot learning, domain generalization, and contrastive learning. Code will be made publicly available at https://github.com/zhihou7/BatchFormer.

We might hope that when faced with unexpected inputs, well-designed software systems would fire off warnings. Machine learning (ML) systems, however, which depend strongly on properties of their inputs (e.g. the i.i.d. assumption), tend to fail silently. This paper explores the problem of building ML systems that fail loudly, investigating methods for detecting dataset shift, identifying exemplars that most typify the shift, and quantifying shift malignancy. We focus on several datasets and various perturbations to both covariates and label distributions with varying magnitudes and fractions of data affected. Interestingly, we show that across the dataset shifts that we explore, a two-sample-testing-based approach, using pre-trained classifiers for dimensionality reduction, performs best. Moreover, we demonstrate that domain-discriminating approaches tend to be helpful for characterizing shifts qualitatively and determining if they are harmful.

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 explore a generative machine learning-based approach for estimating multi-dimensional probability density functions (PDFs) in a target sample using a statistically independent but related control sample - a common challenge in particle physics data analysis. The generative model must accurately reproduce individual observable distributions while preserving the correlations between them, based on the input multidimensional distribution from the control sample. Here we present a conditional normalizing flow model (CNF) based on a chain of bijectors which learns to transform unpaired simulation events to data events. We assess the performance of the CNF model in the context of LHC Higgs to diphoton analysis, where we use the CNF model to convert a Monte Carlo diphoton sample to one that models data. We show that the CNF model can accurately model complex data distributions and correlations. We also leverage the recently popularized Modified Differential Multiplier Method (MDMM) to improve the convergence of our model and assign physical meaning to usually arbitrary loss-function parameters.

Accurate predictions using sequential spatiotemporal data are crucial for various applications. Utilizing real-world data, we aim to learn the intent of a smart device user within confined areas of a vehicle's surroundings. However, in real-world scenarios, environmental factors and sensor limitations result in non-stationary and irregularly sampled data, posing significant challenges. To address these issues, we developed a Transformer-based approach, STaRFormer, which serves as a universal framework for sequential modeling. STaRFormer employs a novel, dynamic attention-based regional masking scheme combined with semi-supervised contrastive learning to enhance task-specific latent representations. Comprehensive experiments on 15 datasets varying in types (including non-stationary and irregularly sampled), domains, sequence lengths, training samples, and applications, demonstrate the efficacy and practicality of STaRFormer. We achieve notable improvements over state-of-the-art approaches. Code and data will be made available.

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

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.

Estimating post-click conversion rate (CVR) accurately is crucial for ranking systems in industrial applications such as recommendation and advertising. Conventional CVR modeling applies popular deep learning methods and achieves state-of-the-art performance. However it encounters several task-specific problems in practice, making CVR modeling challenging. For example, conventional CVR models are trained with samples of clicked impressions while utilized to make inference on the entire space with samples of all impressions. This causes a sample selection bias problem. Besides, there exists an extreme data sparsity problem, making the model fitting rather difficult. In this paper, we model CVR in a brand-new perspective by making good use of sequential pattern of user actions, i.e., impression -> click -> conversion. The proposed Entire Space Multi-task Model (ESMM) can eliminate the two problems simultaneously by i) modeling CVR directly over the entire space, ii) employing a feature representation transfer learning strategy. Experiments on dataset gathered from Taobao's recommender system demonstrate that ESMM significantly outperforms competitive methods. We also release a sampling version of this dataset to enable future research. To the best of our knowledge, this is the first public dataset which contains samples with sequential dependence of click and conversion labels for CVR modeling.

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

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

Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible in closed form, so prior methods resort to imprecise approximations of the score matching training objective that degrade performance and preclude applications in high dimensions. In this work, we reexamine these approximations and propose several practical improvements. Our key observation is that most relevant manifolds are symmetric spaces, which are much more amenable to computation. By leveraging and combining various ans\"{a}tze, we can quickly compute relevant quantities to high precision. On low dimensional datasets, our correction produces a noticeable improvement, allowing diffusion to compete with other methods. Additionally, we show that our method enables us to scale to high dimensional tasks on nontrivial manifolds. In particular, we model QCD densities on SU(n) lattices and contrastively learned embeddings on high dimensional hyperspheres.

Diffusion-based samplers learn to sample complex, high-dimensional distributions using energies or log densities alone, without training data. Yet, they remain impractical for molecular sampling because they are often slower than molecular dynamics and miss thermodynamically relevant modes. Inspired by enhanced sampling, we encourage exploration by introducing a sequential bias along bespoke, information-rich, low-dimensional projections of atomic coordinates known as collective variables (CVs). We introduce a repulsive potential centered on the CVs from recent samples, which pushes future samples towards novel CV regions and effectively increases the temperature in the projected space. Our resulting method improves efficiency, mode discovery, enables the estimation of free energy differences, and retains independent sampling from the approximate Boltzmann distribution via reweighting by the bias. On standard peptide conformational sampling benchmarks, the method recovers diverse conformational states and accurate free energy profiles. We are the first to demonstrate reactive sampling using a diffusion-based sampler, capturing bond breaking and formation with universal interatomic potentials at near-first-principles accuracy. The approach resolves reactive energy landscapes at a fraction of the wall-clock time of standard sampling methods, advancing diffusion-based sampling towards practical use in molecular sciences.

Dense retrieval represents queries and documents as high-dimensional embeddings, but these representations can be redundant at the query level: for a given information need, only a subset of dimensions is consistently helpful for ranking. Prior work addresses this via pseudo-relevance feedback (PRF) based dimension importance estimation, which can produce query-aware masks without labeled data but often relies on noisy pseudo signals and heuristic test-time procedures. In contrast, supervised adapter methods leverage relevance labels to improve embedding quality, yet they learn global transformations shared across queries and do not explicitly model query-aware dimension importance. We propose a Query-Aware Adaptive Dimension Selection framework that learns to predict per-dimension importance directly from query embedding. We first construct oracle dimension importance distributions over embedding dimensions using supervised relevance labels, and then train a predictor to map a query embedding to these label-distilled importance scores. At inference, the predictor selects a query-aware subset of dimensions for similarity computation based solely on the query embedding, without pseudo-relevance feedback. Experiments across multiple dense retrievers and benchmarks show that our learned dimension selector improves retrieval effectiveness over the full-dimensional baseline as well as PRF-based masking and supervised adapter baselines.

Colloquially speaking, image generation models based upon diffusion processes are frequently said to exhibit "hallucinations," samples that could never occur in the training data. But where do such hallucinations come from? In this paper, we study a particular failure mode in diffusion models, which we term mode interpolation. Specifically, we find that diffusion models smoothly "interpolate" between nearby data modes in the training set, to generate samples that are completely outside the support of the original training distribution; this phenomenon leads diffusion models to generate artifacts that never existed in real data (i.e., hallucinations). We systematically study the reasons for, and the manifestation of this phenomenon. Through experiments on 1D and 2D Gaussians, we show how a discontinuous loss landscape in the diffusion model's decoder leads to a region where any smooth approximation will cause such hallucinations. Through experiments on artificial datasets with various shapes, we show how hallucination leads to the generation of combinations of shapes that never existed. Finally, we show that diffusion models in fact know when they go out of support and hallucinate. This is captured by the high variance in the trajectory of the generated sample towards the final few backward sampling process. Using a simple metric to capture this variance, we can remove over 95% of hallucinations at generation time while retaining 96% of in-support samples. We conclude our exploration by showing the implications of such hallucination (and its removal) on the collapse (and stabilization) of recursive training on synthetic data with experiments on MNIST and 2D Gaussians dataset. We release our code at https://github.com/locuslab/diffusion-model-hallucination.

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

Benefiting from prompt tuning, recent years have witnessed the promising performance of pre-trained vision-language models, e.g., CLIP, on versatile downstream tasks. In this paper, we focus on a particular setting of learning adaptive prompts on the fly for each test sample from an unseen new domain, which is known as test-time prompt tuning (TPT). Existing TPT methods typically rely on data augmentation and confidence selection. However, conventional data augmentation techniques, e.g., random resized crops, suffers from the lack of data diversity, while entropy-based confidence selection alone is not sufficient to guarantee prediction fidelity. To address these issues, we propose a novel TPT method, named DiffTPT, which leverages pre-trained diffusion models to generate diverse and informative new data. Specifically, we incorporate augmented data by both conventional method and pre-trained stable diffusion to exploit their respective merits, improving the models ability to adapt to unknown new test data. Moreover, to ensure the prediction fidelity of generated data, we introduce a cosine similarity-based filtration technique to select the generated data with higher similarity to the single test sample. Our experiments on test datasets with distribution shifts and unseen categories demonstrate that DiffTPT improves the zero-shot accuracy by an average of 5.13\% compared to the state-of-the-art TPT method. Our code and models will be publicly released.

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.

In this paper, we present our novel systems developed for the SemEval-2024 hallucination detection task. Our investigation spans a range of strategies to compare model predictions with reference standards, encompassing diverse baselines, the refinement of pre-trained encoders through supervised learning, and an ensemble approaches utilizing several high-performing models. Through these explorations, we introduce three distinct methods that exhibit strong performance metrics. To amplify our training data, we generate additional training samples from unlabelled training subset. Furthermore, we provide a detailed comparative analysis of our approaches. Notably, our premier method achieved a commendable 9th place in the competition's model-agnostic track and 17th place in model-aware track, highlighting its effectiveness and potential.

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.

Recent advances in neural rendering have shown that, albeit slow, implicit compact models can learn a scene's geometries and view-dependent appearances from multiple views. To maintain such a small memory footprint but achieve faster inference times, recent works have adopted `sampler' networks that adaptively sample a small subset of points along each ray in the implicit neural radiance fields. Although these methods achieve up to a 10times reduction in rendering time, they still suffer from considerable quality degradation compared to the vanilla NeRF. In contrast, we propose ProNeRF, which provides an optimal trade-off between memory footprint (similar to NeRF), speed (faster than HyperReel), and quality (better than K-Planes). ProNeRF is equipped with a novel projection-aware sampling (PAS) network together with a new training strategy for ray exploration and exploitation, allowing for efficient fine-grained particle sampling. Our ProNeRF yields state-of-the-art metrics, being 15-23x faster with 0.65dB higher PSNR than NeRF and yielding 0.95dB higher PSNR than the best published sampler-based method, HyperReel. Our exploration and exploitation training strategy allows ProNeRF to learn the full scenes' color and density distributions while also learning efficient ray sampling focused on the highest-density regions. We provide extensive experimental results that support the effectiveness of our method on the widely adopted forward-facing and 360 datasets, LLFF and Blender, respectively.

t-distributed Stochastic Neighborhood Embedding (t-SNE) is a method for dimensionality reduction and visualization that has become widely popular in recent years. Efficient implementations of t-SNE are available, but they scale poorly to datasets with hundreds of thousands to millions of high dimensional data-points. We present Fast Fourier Transform-accelerated Interpolation-based t-SNE (FIt-SNE), which dramatically accelerates the computation of t-SNE. The most time-consuming step of t-SNE is a convolution that we accelerate by interpolating onto an equispaced grid and subsequently using the fast Fourier transform to perform the convolution. We also optimize the computation of input similarities in high dimensions using multi-threaded approximate nearest neighbors. We further present a modification to t-SNE called "late exaggeration," which allows for easier identification of clusters in t-SNE embeddings. Finally, for datasets that cannot be loaded into the memory, we present out-of-core randomized principal component analysis (oocPCA), so that the top principal components of a dataset can be computed without ever fully loading the matrix, hence allowing for t-SNE of large datasets to be computed on resource-limited machines.

Scaling visual generation models is essential for real-world content creation, yet requires substantial training and computational expenses. Alternatively, test-time scaling has garnered growing attention due to resource efficiency and promising performance. In this work, we present TTS-VAR, the first general test-time scaling framework for visual auto-regressive (VAR) models, modeling the generation process as a path searching problem. To dynamically balance computational efficiency with exploration capacity, we first introduce an adaptive descending batch size schedule throughout the causal generation process. Besides, inspired by VAR's hierarchical coarse-to-fine multi-scale generation, our framework integrates two key components: (i) At coarse scales, we observe that generated tokens are hard for evaluation, possibly leading to erroneous acceptance of inferior samples or rejection of superior samples. Noticing that the coarse scales contain sufficient structural information, we propose clustering-based diversity search. It preserves structural variety through semantic feature clustering, enabling later selection on samples with higher potential. (ii) In fine scales, resampling-based potential selection prioritizes promising candidates using potential scores, which are defined as reward functions incorporating multi-scale generation history. Experiments on the powerful VAR model Infinity show a notable 8.7% GenEval score improvement (from 0.69 to 0.75). Key insights reveal that early-stage structural features effectively influence final quality, and resampling efficacy varies across generation scales. Code is available at https://github.com/ali-vilab/TTS-VAR.

In semi-supervised learning, unlabeled samples can be utilized through augmentation and consistency regularization. However, we observed certain samples, even undergoing strong augmentation, are still correctly classified with high confidence, resulting in a loss close to zero. It indicates that these samples have been already learned well and do not provide any additional optimization benefits to the model. We refer to these samples as ``naive samples". Unfortunately, existing SSL models overlook the characteristics of naive samples, and they just apply the same learning strategy to all samples. To further optimize the SSL model, we emphasize the importance of giving attention to naive samples and augmenting them in a more diverse manner. Sample adaptive augmentation (SAA) is proposed for this stated purpose and consists of two modules: 1) sample selection module; 2) sample augmentation module. Specifically, the sample selection module picks out {naive samples} based on historical training information at each epoch, then the naive samples will be augmented in a more diverse manner in the sample augmentation module. Thanks to the extreme ease of implementation of the above modules, SAA is advantageous for being simple and lightweight. We add SAA on top of FixMatch and FlexMatch respectively, and experiments demonstrate SAA can significantly improve the models. For example, SAA helped improve the accuracy of FixMatch from 92.50% to 94.76% and that of FlexMatch from 95.01% to 95.31% on CIFAR-10 with 40 labels.

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

Flow matching has emerged as a powerful generative modeling approach with flexible choices of source distribution. While Gaussian distributions are commonly used, the potential for better alternatives in high-dimensional data generation remains largely unexplored. In this paper, we propose a novel 2D simulation that captures high-dimensional geometric properties in an interpretable 2D setting, enabling us to analyze the learning dynamics of flow matching during training. Based on this analysis, we derive several key insights about flow matching behavior: (1) density approximation can paradoxically degrade performance due to mode discrepancy, (2) directional alignment suffers from path entanglement when overly concentrated, (3) Gaussian's omnidirectional coverage ensures robust learning, and (4) norm misalignment incurs substantial learning costs. Building on these insights, we propose a practical framework that combines norm-aligned training with directionally-pruned sampling. This approach maintains the robust omnidirectional supervision essential for stable flow learning, while eliminating initializations in data-sparse regions during inference. Importantly, our pruning strategy can be applied to any flow matching model trained with a Gaussian source, providing immediate performance gains without the need for retraining. Empirical evaluations demonstrate consistent improvements in both generation quality and sampling efficiency. Our findings provide practical insights and guidelines for source distribution design and introduce a readily applicable technique for improving existing flow matching models. Our code is available at https://github.com/kwanseokk/SourceFM.

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

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

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

We study the problem of visualizing large-scale and high-dimensional data in a low-dimensional (typically 2D or 3D) space. Much success has been reported recently by techniques that first compute a similarity structure of the data points and then project them into a low-dimensional space with the structure preserved. These two steps suffer from considerable computational costs, preventing the state-of-the-art methods such as the t-SNE from scaling to large-scale and high-dimensional data (e.g., millions of data points and hundreds of dimensions). We propose the LargeVis, a technique that first constructs an accurately approximated K-nearest neighbor graph from the data and then layouts the graph in the low-dimensional space. Comparing to t-SNE, LargeVis significantly reduces the computational cost of the graph construction step and employs a principled probabilistic model for the visualization step, the objective of which can be effectively optimized through asynchronous stochastic gradient descent with a linear time complexity. The whole procedure thus easily scales to millions of high-dimensional data points. Experimental results on real-world data sets demonstrate that the LargeVis outperforms the state-of-the-art methods in both efficiency and effectiveness. The hyper-parameters of LargeVis are also much more stable over different data sets.

Selecting a suitable training dataset is crucial for both general-domain (e.g., GPT-3) and domain-specific (e.g., Codex) language models (LMs). We formalize this data selection problem as selecting a subset of a large raw unlabeled dataset to match a desired target distribution, given some unlabeled target samples. Due to the large scale and dimensionality of the raw text data, existing methods use simple heuristics to select data that are similar to a high-quality reference corpus (e.g., Wikipedia), or leverage experts to manually curate data. Instead, we extend the classic importance resampling approach used in low-dimensions for LM data selection. Crucially, we work in a reduced feature space to make importance weight estimation tractable over the space of text. To determine an appropriate feature space, we first show that KL reduction, a data metric that measures the proximity between selected data and the target in a feature space, has high correlation with average accuracy on 8 downstream tasks (r=0.89) when computed with simple n-gram features. From this observation, we present Data Selection with Importance Resampling (DSIR), an efficient and scalable algorithm that estimates importance weights in a reduced feature space (e.g., n-gram features in our instantiation) and selects data with importance resampling according to these weights. When training general-domain models (target is Wikipedia + books), DSIR improves over random selection and heuristic filtering baselines by 2--2.5% on the GLUE benchmark. When performing continued pretraining towards a specific domain, DSIR performs comparably to expert curated data across 8 target distributions.

Modern machine learning research relies on relatively few carefully curated datasets. Even in these datasets, and typically in `untidy' or raw data, practitioners are faced with significant issues of data quality and diversity which can be prohibitively labor intensive to address. Existing methods for dealing with these challenges tend to make strong assumptions about the particular issues at play, and often require a priori knowledge or metadata such as domain labels. Our work is orthogonal to these methods: we instead focus on providing a unified and efficient framework for Metadata Archaeology -- uncovering and inferring metadata of examples in a dataset. We curate different subsets of data that might exist in a dataset (e.g. mislabeled, atypical, or out-of-distribution examples) using simple transformations, and leverage differences in learning dynamics between these probe suites to infer metadata of interest. Our method is on par with far more sophisticated mitigation methods across different tasks: identifying and correcting mislabeled examples, classifying minority-group samples, prioritizing points relevant for training and enabling scalable human auditing of relevant examples.

Transfer learning with a small amount of target data is an effective and common approach to adapting a pre-trained model to distribution shifts. In some situations, target data labels may be expensive to obtain, so we may only have access to a limited number of target data points. To make the most of a very small target dataset, we propose a lightweight, sample-efficient approach that learns a diverse set of features and adapts to a target distribution by interpolating these features. Our approach, Project and Probe (Pro^2), first learns a linear projection that maps a pre-trained embedding onto orthogonal directions while being predictive of labels in the source dataset. The goal of this step is to learn a variety of predictive features, so that at least some of them remain useful after distribution shift. Pro^2 then learns a linear classifier on top of these projected features using a small target dataset. Theoretically, we find that Pro^2 results in more sample-efficient generalization by inducing a favorable bias-variance tradeoff. Our experiments on four datasets, with multiple distribution shift settings for each, show that Pro^2 improves performance by 5-15% when given limited target data compared to prior methods such as standard linear probing.

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.

Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible high-dimensional data modeling, and act as a sampler for generating new samples under active guidance towards task-desired properties. Despite the significant empirical success, theory of diffusion models is very limited, potentially slowing down principled methodological innovations for further harnessing and improving diffusion models. In this paper, we review emerging applications of diffusion models, understanding their sample generation under various controls. Next, we overview the existing theories of diffusion models, covering their statistical properties and sampling capabilities. We adopt a progressive routine, beginning with unconditional diffusion models and connecting to conditional counterparts. Further, we review a new avenue in high-dimensional structured optimization through conditional diffusion models, where searching for solutions is reformulated as a conditional sampling problem and solved by diffusion models. Lastly, we discuss future directions about diffusion models. The purpose of this paper is to provide a well-rounded theoretical exposure for stimulating forward-looking theories and methods of diffusion models.

Recent progress in single-image 3D generation highlights the importance of multi-view coherency, leveraging 3D priors from large-scale diffusion models pretrained on Internet-scale images. However, the aspect of novel-view diversity remains underexplored within the research landscape due to the ambiguity in converting a 2D image into 3D content, where numerous potential shapes can emerge. Here, we aim to address this research gap by simultaneously addressing both consistency and diversity. Yet, striking a balance between these two aspects poses a considerable challenge due to their inherent trade-offs. This work introduces HarmonyView, a simple yet effective diffusion sampling technique adept at decomposing two intricate aspects in single-image 3D generation: consistency and diversity. This approach paves the way for a more nuanced exploration of the two critical dimensions within the sampling process. Moreover, we propose a new evaluation metric based on CLIP image and text encoders to comprehensively assess the diversity of the generated views, which closely aligns with human evaluators' judgments. In experiments, HarmonyView achieves a harmonious balance, demonstrating a win-win scenario in both consistency and diversity.

In autoregressive language models, each token is sampled by conditioning on all the past tokens; the overall string has thus been sampled from the correct underlying joint distribution represented by the model. In contrast, masked diffusion language models generate text by unmasking tokens out of order and potentially in parallel. Generating an overall string sampled from the correct underlying joint distribution would (again) require exactly one token unmasking in every full-model forward pass. The more tokens unmasked in parallel, the further away the string is from the true joint; this can be seen in the resulting drop in accuracy (but, increase in speed). In this paper we devise a way to {\em approximately} sample multiple tokens from the joint distribution in a single full-model forward pass; we do so by developing a new lightweight single-layer ``sampler" on top of an existing large diffusion LM. One forward pass of the full model can now be followed by multiple forward passes of only this sampler layer, to yield multiple unmasked tokens. Our sampler is trained to mimic exact joint sampling from the (frozen) full model. We show the effectiveness of our approximate joint sampling for both pretrained-only (Dream-7B-Base) and instruction-tuned (Dream-7B-Instruct) models on language modeling and math \& coding tasks. When four tokens are unmasked for each full-model denoising step, our sampling algorithm achieves a MAUVE score of 0.87 (vs marginal baseline of 0.31) with respect to the true joint distribution.

Traditional deep learning models rely on methods such as softmax cross-entropy and ArcFace loss for tasks like classification and face recognition. These methods mainly explore angular features in a hyperspherical space, often resulting in entangled inter-class features due to dense angular data across many classes. In this paper, a new field of feature exploration is proposed known as HyperSpaceX which enhances class discrimination by exploring both angular and radial dimensions in multi-hyperspherical spaces, facilitated by a novel DistArc loss. The proposed DistArc loss encompasses three feature arrangement components: two angular and one radial, enforcing intra-class binding and inter-class separation in multi-radial arrangement, improving feature discriminability. Evaluation of HyperSpaceX framework for the novel representation utilizes a proposed predictive measure that accounts for both angular and radial elements, providing a more comprehensive assessment of model accuracy beyond standard metrics. Experiments across seven object classification and six face recognition datasets demonstrate state-of-the-art (SoTA) results obtained from HyperSpaceX, achieving up to a 20% performance improvement on large-scale object datasets in lower dimensions and up to 6% gain in higher dimensions.

Encouraged by the growing availability of pre-trained 2D diffusion models, image-to-3D generation by leveraging Score Distillation Sampling (SDS) is making remarkable progress. Most existing methods combine novel-view lifting from 2D diffusion models which usually take the reference image as a condition while applying hard L2 image supervision at the reference view. Yet heavily adhering to the image is prone to corrupting the inductive knowledge of the 2D diffusion model leading to flat or distorted 3D generation frequently. In this work, we reexamine image-to-3D in a novel perspective and present Isotropic3D, an image-to-3D generation pipeline that takes only an image CLIP embedding as input. Isotropic3D allows the optimization to be isotropic w.r.t. the azimuth angle by solely resting on the SDS loss. The core of our framework lies in a two-stage diffusion model fine-tuning. Firstly, we fine-tune a text-to-3D diffusion model by substituting its text encoder with an image encoder, by which the model preliminarily acquires image-to-image capabilities. Secondly, we perform fine-tuning using our Explicit Multi-view Attention (EMA) which combines noisy multi-view images with the noise-free reference image as an explicit condition. CLIP embedding is sent to the diffusion model throughout the whole process while reference images are discarded once after fine-tuning. As a result, with a single image CLIP embedding, Isotropic3D is capable of generating multi-view mutually consistent images and also a 3D model with more symmetrical and neat content, well-proportioned geometry, rich colored texture, and less distortion compared with existing image-to-3D methods while still preserving the similarity to the reference image to a large extent. The project page is available at https://isotropic3d.github.io/. The code and models are available at https://github.com/pkunliu/Isotropic3D.

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