Daily Papers

Mixup is a highly successful technique to improve generalization of neural networks by augmenting the training data with combinations of random pairs. Selective mixup is a family of methods that apply mixup to specific pairs, e.g. only combining examples across classes or domains. These methods have claimed remarkable improvements on benchmarks with distribution shifts, but their mechanisms and limitations remain poorly understood. We examine an overlooked aspect of selective mixup that explains its success in a completely new light. We find that the non-random selection of pairs affects the training distribution and improve generalization by means completely unrelated to the mixing. For example in binary classification, mixup across classes implicitly resamples the data for a uniform class distribution - a classical solution to label shift. We show empirically that this implicit resampling explains much of the improvements in prior work. Theoretically, these results rely on a regression toward the mean, an accidental property that we identify in several datasets. We have found a new equivalence between two successful methods: selective mixup and resampling. We identify limits of the former, confirm the effectiveness of the latter, and find better combinations of their respective benefits.

Existing long-tailed recognition methods, aiming to train class-balanced models from long-tailed data, generally assume the models would be evaluated on the uniform test class distribution. However, practical test class distributions often violate this assumption (e.g., being either long-tailed or even inversely long-tailed), which may lead existing methods to fail in real applications. In this paper, we study a more practical yet challenging task, called test-agnostic long-tailed recognition, where the training class distribution is long-tailed while the test class distribution is agnostic and not necessarily uniform. In addition to the issue of class imbalance, this task poses another challenge: the class distribution shift between the training and test data is unknown. To tackle this task, we propose a novel approach, called Self-supervised Aggregation of Diverse Experts, which consists of two strategies: (i) a new skill-diverse expert learning strategy that trains multiple experts from a single and stationary long-tailed dataset to separately handle different class distributions; (ii) a novel test-time expert aggregation strategy that leverages self-supervision to aggregate the learned multiple experts for handling unknown test class distributions. We theoretically show that our self-supervised strategy has a provable ability to simulate test-agnostic class distributions. Promising empirical results demonstrate the effectiveness of our method on both vanilla and test-agnostic long-tailed recognition. Code is available at https://github.com/Vanint/SADE-AgnosticLT.

Existing losses used in deep metric learning (DML) for image retrieval often lead to highly non-uniform intra-class and inter-class representation structures across test classes and data distributions. When combined with the common practice of using a fixed threshold to declare a match, this gives rise to significant performance variations in terms of false accept rate (FAR) and false reject rate (FRR) across test classes and data distributions. We define this issue in DML as threshold inconsistency. In real-world applications, such inconsistency often complicates the threshold selection process when deploying commercial image retrieval systems. To measure this inconsistency, we propose a novel variance-based metric called Operating-Point-Inconsistency-Score (OPIS) that quantifies the variance in the operating characteristics across classes. Using the OPIS metric, we find that achieving high accuracy levels in a DML model does not automatically guarantee threshold consistency. In fact, our investigation reveals a Pareto frontier in the high-accuracy regime, where existing methods to improve accuracy often lead to degradation in threshold consistency. To address this trade-off, we introduce the Threshold-Consistent Margin (TCM) loss, a simple yet effective regularization technique that promotes uniformity in representation structures across classes by selectively penalizing hard sample pairs. Extensive experiments demonstrate TCM's effectiveness in enhancing threshold consistency while preserving accuracy, simplifying the threshold selection process in practical DML settings.

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.

Uniform random exploration in decision-making systems supports off-policy learning via supervision but incurs high regret, making it impractical for many applications. Conversely, non-uniform exploration offers better immediate performance but lacks support for off-policy learning. Recent research suggests that regression oracles can bridge this gap by combining non-uniform exploration with supervised learning. In this paper, we analyze these approaches within a real-world industrial context at Adyen, a large global payments processor characterized by batch logged delayed feedback, short-term memory, and dynamic action spaces under the Empirical Risk Minimization (ERM) framework. Our analysis reveals that while regression oracles significantly improve performance, they introduce challenges due to rigid algorithmic assumptions. Specifically, we observe that as a policy improves, subsequent generations may perform worse due to shifts in the reward distribution and increased class imbalance in the training data. This degradation occurs de spite improvements in other aspects of the training data, leading to decreased performance in successive policy iterations. We further explore the long-term impact of regression oracles, identifying a potential "oscillation effect." This effect arises when regression oracles influence probability estimates and the realizability of subsequent policy models, leading to fluctuations in performance across iterations. Our findings highlight the need for more adaptable algorithms that can leverage the benefits of regression oracles without introducing instability in policy performance over time.

The generalization and learning speed of a multi-class neural network can often be significantly improved by using soft targets that are a weighted average of the hard targets and the uniform distribution over labels. Smoothing the labels in this way prevents the network from becoming over-confident and label smoothing has been used in many state-of-the-art models, including image classification, language translation and speech recognition. Despite its widespread use, label smoothing is still poorly understood. Here we show empirically that in addition to improving generalization, label smoothing improves model calibration which can significantly improve beam-search. However, we also observe that if a teacher network is trained with label smoothing, knowledge distillation into a student network is much less effective. To explain these observations, we visualize how label smoothing changes the representations learned by the penultimate layer of the network. We show that label smoothing encourages the representations of training examples from the same class to group in tight clusters. This results in loss of information in the logits about resemblances between instances of different classes, which is necessary for distillation, but does not hurt generalization or calibration of the model's predictions.

In representation learning, uniformity refers to the uniform feature distribution in the latent space (i.e., unit hypersphere). Previous work has shown that improving uniformity contributes to the learning of under-represented classes. However, most of the previous work focused on classification; the representation space of imbalanced regression remains unexplored. Classification-based methods are not suitable for regression tasks because they cluster features into distinct groups without considering the continuous and ordered nature essential for regression. In a geometric aspect, we uniquely focus on ensuring uniformity in the latent space for imbalanced regression through two key losses: enveloping and homogeneity. The enveloping loss encourages the induced trace to uniformly occupy the surface of a hypersphere, while the homogeneity loss ensures smoothness, with representations evenly spaced at consistent intervals. Our method integrates these geometric principles into the data representations via a Surrogate-driven Representation Learning (SRL) framework. Experiments with real-world regression and operator learning tasks highlight the importance of uniformity in imbalanced regression and validate the efficacy of our geometry-based loss functions.

Real-world datasets follow an imbalanced distribution, which poses significant challenges in rare-category object detection. Recent studies tackle this problem by developing re-weighting and re-sampling methods, that utilise the class frequencies of the dataset. However, these techniques focus solely on the frequency statistics and ignore the distribution of the classes in image space, missing important information. In contrast to them, we propose FRActal CALibration (FRACAL): a novel post-calibration method for long-tailed object detection. FRACAL devises a logit adjustment method that utilises the fractal dimension to estimate how uniformly classes are distributed in image space. During inference, it uses the fractal dimension to inversely downweight the probabilities of uniformly spaced class predictions achieving balance in two axes: between frequent and rare categories, and between uniformly spaced and sparsely spaced classes. FRACAL is a post-processing method and it does not require any training, also it can be combined with many off-the-shelf models such as one-stage sigmoid detectors and two-stage instance segmentation models. FRACAL boosts the rare class performance by up to 8.6% and surpasses all previous methods on LVIS dataset, while showing good generalisation to other datasets such as COCO, V3Det and OpenImages. We provide the code at https://github.com/kostas1515/FRACAL.

Straight line equation y=mx with slope m, when singularly perturbed as ay^3+y=mx with a positive parameter a, results in S-shaped curves or S-curves on a real plane. As arightarrow 0, we get back y=mx which is a cumulative distribution function of a continuous uniform distribution that describes the occurrence of every event in an interval to be equally probable. As arightarrowinfty, the derivative of y has finite support only at y=0 resembling a degenerate distribution. Based on these arguments, in this work, we propose that these S-curves can represent maximum entropy uniform distribution to a zero entropy single value. We also argue that these S-curves are superposable as they are only parametrically nonlinear but fundamentally linear. So far, the superposed forms have been used to capture the patterns of natural systems such as nonlinear dynamics of biological growth and kinetics of enzyme reactions. Here, we attempt to use the S-curve and its superposed form as statistical models. We fit the models on a classical dataset containing flower measurements of iris plants and analyze their usefulness in pattern recognition. Based on these models, we claim that any non-uniform pattern can be represented as a singular perturbation to uniform distribution. However, our parametric estimation procedure have some limitations such as sensitivity to initial conditions depending on the data at hand.

The predictions of small transformers, trained to calculate the greatest common divisor (GCD) of two positive integers, can be fully characterized by looking at model inputs and outputs. As training proceeds, the model learns a list mathcal D of integers, products of divisors of the base used to represent integers and small primes, and predicts the largest element of mathcal D that divides both inputs. Training distributions impact performance. Models trained from uniform operands only learn a handful of GCD (up to 38 GCD leq100). Log-uniform operands boost performance to 73 GCD leq 100, and a log-uniform distribution of outcomes (i.e. GCD) to 91. However, training from uniform (balanced) GCD breaks explainability.

We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are assumed to concentrate around some low-dimensional structure. Estimating the distribution supported on this low-dimensional structure, such as a low-dimensional manifold, is challenging due to its singularity with respect to the Lebesgue measure in the ambient space. In the considered model, a usual likelihood approach can fail to estimate the target distribution consistently due to the singularity. We prove that a novel and effective solution exists by perturbing the data with an instance noise, which leads to consistent estimation of the underlying distribution with desirable convergence rates. We also characterize the class of distributions that can be efficiently estimated via deep generative models. This class is sufficiently general to contain various structured distributions such as product distributions, classically smooth distributions and distributions supported on a low-dimensional manifold. Our analysis provides some insights on how deep generative models can avoid the curse of dimensionality for nonparametric distribution estimation. We conduct a thorough simulation study and real data analysis to empirically demonstrate that the proposed data perturbation technique improves the estimation performance significantly.

Uniformity plays a crucial role in the assessment of learned representations, contributing to a deeper comprehension of self-supervised learning. The seminal work by Wang2020UnderstandingCR introduced a uniformity metric that quantitatively measures the collapse degree of learned representations. Directly optimizing this metric together with alignment proves to be effective in preventing constant collapse. However, we present both theoretical and empirical evidence revealing that this metric lacks sensitivity to dimensional collapse, highlighting its limitations. To address this limitation and design a more effective uniformity metric, this paper identifies five fundamental properties, some of which the existing uniformity metric fails to meet. We subsequently introduce a novel uniformity metric that satisfies all of these desiderata and exhibits sensitivity to dimensional collapse. When applied as an auxiliary loss in various established self-supervised methods, our proposed uniformity metric consistently enhances their performance in downstream tasks.Our code was released at https://github.com/sunset-clouds/WassersteinUniformityMetric.

When the performance of a machine learning model varies over groups defined by sensitive attributes (e.g., gender or ethnicity), the performance disparity can be expressed in terms of the probability distributions of the input and output variables over each group. In this paper, we exploit this fact to reduce the disparate impact of a fixed classification model over a population of interest. Given a black-box classifier, we aim to eliminate the performance gap by perturbing the distribution of input variables for the disadvantaged group. We refer to the perturbed distribution as a counterfactual distribution, and characterize its properties for common fairness criteria. We introduce a descent algorithm to learn a counterfactual distribution from data. We then discuss how the estimated distribution can be used to build a data preprocessor that can reduce disparate impact without training a new model. We validate our approach through experiments on real-world datasets, showing that it can repair different forms of disparity without a significant drop in accuracy.

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.

Feature attribution methods identify which features of an input most influence a model's output. Most widely-used feature attribution methods (such as SHAP, LIME, and Grad-CAM) are "class-dependent" methods in that they generate a feature attribution vector as a function of class. In this work, we demonstrate that class-dependent methods can "leak" information about the selected class, making that class appear more likely than it is. Thus, an end user runs the risk of drawing false conclusions when interpreting an explanation generated by a class-dependent method. In contrast, we introduce "distribution-aware" methods, which favor explanations that keep the label's distribution close to its distribution given all features of the input. We introduce SHAP-KL and FastSHAP-KL, two baseline distribution-aware methods that compute Shapley values. Finally, we perform a comprehensive evaluation of seven class-dependent and three distribution-aware methods on three clinical datasets of different high-dimensional data types: images, biosignals, and text.

Uniform-state discrete diffusion models hold the promise of fast text generation due to their inherent ability to self-correct. However, they are typically outperformed by autoregressive models and masked diffusion models. In this work, we narrow this performance gap by leveraging a key insight: Uniform-state diffusion processes naturally emerge from an underlying Gaussian diffusion. Our method, Duo, transfers powerful techniques from Gaussian diffusion to improve both training and sampling. First, we introduce a curriculum learning strategy guided by the Gaussian process, doubling training speed by reducing variance. Models trained with curriculum learning surpass autoregressive models in zero-shot perplexity on 3 of 7 benchmarks. Second, we present Discrete Consistency Distillation, which adapts consistency distillation from the continuous to the discrete setting. This algorithm unlocks few-step generation in diffusion language models by accelerating sampling by two orders of magnitude. We provide the code and model checkpoints on the project page: http://s-sahoo.github.io/duo

Arbitrary style transfer (AST) and domain generalization (DG) are important yet challenging visual learning tasks, which can be cast as a feature distribution matching problem. With the assumption of Gaussian feature distribution, conventional feature distribution matching methods usually match the mean and standard deviation of features. However, the feature distributions of real-world data are usually much more complicated than Gaussian, which cannot be accurately matched by using only the first-order and second-order statistics, while it is computationally prohibitive to use high-order statistics for distribution matching. In this work, we, for the first time to our best knowledge, propose to perform Exact Feature Distribution Matching (EFDM) by exactly matching the empirical Cumulative Distribution Functions (eCDFs) of image features, which could be implemented by applying the Exact Histogram Matching (EHM) in the image feature space. Particularly, a fast EHM algorithm, named Sort-Matching, is employed to perform EFDM in a plug-and-play manner with minimal cost. The effectiveness of our proposed EFDM method is verified on a variety of AST and DG tasks, demonstrating new state-of-the-art results. Codes are available at https://github.com/YBZh/EFDM.

In the real world, the frequency of occurrence of objects is naturally skewed forming long-tail class distributions, which results in poor performance on the statistically rare classes. A promising solution is to mine tail-class examples to balance the training dataset. However, mining tail-class examples is a very challenging task. For instance, most of the otherwise successful uncertainty-based mining approaches struggle due to distortion of class probabilities resulting from skewness in data. In this work, we propose an effective, yet simple, approach to overcome these challenges. Our framework enhances the subdued tail-class activations and, thereafter, uses a one-class data-centric approach to effectively identify tail-class examples. We carry out an exhaustive evaluation of our framework on three datasets spanning over two computer vision tasks. Substantial improvements in the minority-class mining and fine-tuned model's performance strongly corroborate the value of our proposed solution.

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

We 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.

Collections of probability distributions arise in a variety of applications ranging from user activity pattern analysis to brain connectomics. In practice these distributions can be defined over diverse domain types including finite intervals, circles, cylinders, spheres, other manifolds, and graphs. This paper introduces an approach for detecting differences between two collections of distributions over such general domains. To this end, we propose the intrinsic slicing construction that yields a novel class of Wasserstein distances on manifolds and graphs. These distances are Hilbert embeddable, allowing us to reduce the distribution collection comparison problem to a more familiar mean testing problem in a Hilbert space. We provide two testing procedures one based on resampling and another on combining p-values from coordinate-wise tests. Our experiments in various synthetic and real data settings show that the resulting tests are powerful and the p-values are well-calibrated.

Class imbalance (CI) is a longstanding problem in machine learning, slowing down training and reducing performances. Although empirical remedies exist, it is often unclear which ones work best and when, due to the lack of an overarching theory. We address a common case of imbalance, that of anomaly (or outlier) detection. We provide a theoretical framework to analyze, interpret and address CI. It is based on an exact solution of the teacher-student perceptron model, through replica theory. Within this framework, one can distinguish several sources of CI: either intrinsic, train or test imbalance. Our analysis reveals that the optimal train imbalance is generally different from 50%, with a non trivial dependence on the intrinsic imbalance, the abundance of data and on the noise in the learning. Moreover, there is a crossover between a small noise training regime where results are independent of the noise level to a high noise regime where performances quickly degrade with noise. Our results challenge some of the conventional wisdom on CI and offer practical guidelines to address it.

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

Prompt-based classifiers are an attractive approach for zero-shot classification. However, the precise choice of the prompt template and label words can largely influence performance, with semantically equivalent settings often showing notable performance difference. This discrepancy can be partly attributed to word biases, where the classifier may be biased towards classes. To address this problem, it is possible to optimise classification thresholds on a labelled data set, however, this mitigates some of the advantages of prompt-based classifiers. This paper instead approaches this problem by examining the expected marginal probabilities of the classes. Here, probabilities are reweighted to have a uniform prior over classes, in an unsupervised fashion. Further, we draw a theoretical connection between the class priors and the language models' word prior, and offer the ability to set a threshold in a zero-resource fashion. We show that matching class priors correlates strongly with the oracle upper bound performance and demonstrate large consistent performance gains for prompt settings over a range of NLP tasks.

Alignment and uniformity are fundamental principles within the domain of contrastive learning. In recommender systems, prior work has established that optimizing the Bayesian Personalized Ranking (BPR) loss contributes to the objectives of alignment and uniformity. Specifically, alignment aims to draw together the representations of interacting users and items, while uniformity mandates a uniform distribution of user and item embeddings across a unit hypersphere. This study revisits the alignment and uniformity properties within the context of multimodal recommender systems, revealing a proclivity among extant models to prioritize uniformity to the detriment of alignment. Our hypothesis challenges the conventional assumption of equitable item treatment through a uniformity loss, proposing a more nuanced approach wherein items with similar multimodal attributes converge toward proximal representations within the hyperspheric manifold. Specifically, we leverage the inherent similarity between items' multimodal data to calibrate their uniformity distribution, thereby inducing a more pronounced repulsive force between dissimilar entities within the embedding space. A theoretical analysis elucidates the relationship between this calibrated uniformity loss and the conventional uniformity function. Moreover, to enhance the fusion of multimodal features, we introduce a Spherical B\'ezier method designed to integrate an arbitrary number of modalities while ensuring that the resulting fused features are constrained to the same hyperspherical manifold. Empirical evaluations conducted on five real-world datasets substantiate the superiority of our approach over competing baselines. We also shown that the proposed methods can achieve up to a 5.4% increase in NDCG@20 performance via the integration of MLLM-extracted features. Source code is available at: https://github.com/enoche/CM3.

Conformal Prediction (CP) controls the prediction uncertainty of classification systems by producing a small prediction set, ensuring a predetermined probability that the true class lies within this set. This is commonly done by defining a score, based on the model predictions, and setting a threshold on this score using a validation set. In this study, we address the problem of CP calibration when we only have access to a calibration set with noisy labels. We show how we can estimate the noise-free conformal threshold based on the noisy labeled data. We derive a finite sample coverage guarantee for uniform noise that remains effective even in tasks with a large number of classes. We dub our approach Noise-Aware Conformal Prediction (NACP). We illustrate the performance of the proposed results on several standard image classification datasets with a large number of classes.

The Uniform Information Density (UID) hypothesis suggests that effective communication maintains a stable flow of information. In this work, we revisit this principle in the context of large language model (LLM) reasoning traces, asking whether step-level uniformity reflects reasoning quality. To this end, we propose an entropy-based stepwise information density metric and introduce two complementary measures of uniformity, local and global uniformity scores. Across the experiments on six different reasoning benchmarks, we find that step-level uniformity not only provides a strong theoretical lens but also yields practical performance benefits; for example, selecting reasoning traces with more uniform information density at the step-level improves accuracy by 10-32\% relative gains over baselines at AIME2025. Our analysis further reveals that correct reasoning traces tend to avoid sharp information density spikes, while incorrect traces exhibit irregular information bursts. These results demonstrate that UID-inspired information density measures outperform alternative internal signals as predictors of reasoning quality. Results highlight the uniformity of the information density as a robust diagnostic and selection criterion for building more reliable and accurate reasoning systems.

A sizeable fraction of gamma-ray burst (GRB) light curves (LCs) features a sequence of peaks, which holds information on the unknown way energy is dissipated into gamma-rays over time. Traditional searches for periodic signals in GRB LCs turned out to be inconclusive, partly because they are challenging as a consequence of the short-lived, coloured-noise, and non-stationary nature of the LCs themselves. Yet, recent claims have revived the issue. We searched for periodic components in GRB LCs through a new approach to GRBs, that avoids most of the issues faced by traditional techniques. We identified peaks through a well tested algorithm and selected GRBs with at least 10 peaks out of 5 GRB catalogues (Swift/BAT, CGRO/BATSE, Fermi/GBM, Insight-HXMT, BeppoSAX/GRBM). Each GRB was simply treated as a discrete point process, whose realisation coincides with the sequence of peak times. We searched for possible periodic recurrences based on the multinomial distribution, after accounting for the clustering of peaks due to the non-stationarity of the GRB signals. The best candidate has a p-value of 3e-4 that there is no periodic recurrence. However, accounting for the multiple trials of 555 searched GRBs, its statistical significance is demoted to 17%. The overall distribution of the p-values obtained for all GRBs is compatible with a uniform distribution in [0,1]. We found no robust evidence for multi-peaked GRBs with periodic recurrences. We can exclude that a sizeable fraction (>~ 0.75) of peaks of each GRB with at least 10 peaks are periodic. While our result does not necessarily clash with claimed periodicities based on Fourier techniques, it constrains the putative recurrent behaviour, which would not manifest itself through the sequence of peaks, but, evidently, in a more elusive way.

This article introduces Regression Discontinuity Design (RDD) with Distribution-Valued Outcomes (R3D), extending the standard RDD framework to settings where the outcome is a distribution rather than a scalar. Such settings arise when treatment is assigned at a higher level of aggregation than the outcome-for example, when a subsidy is allocated based on a firm-level revenue cutoff while the outcome of interest is the distribution of employee wages within the firm. Since standard RDD methods cannot accommodate such two-level randomness, I propose a novel approach based on random distributions. The target estimand is a "local average quantile treatment effect", which averages across random quantiles. To estimate this target, I introduce two related approaches: one that extends local polynomial regression to random quantiles and another based on local Fr\'echet regression, a form of functional regression. For both estimators, I establish asymptotic normality and develop uniform, debiased confidence bands together with a data-driven bandwidth selection procedure. Simulations validate these theoretical properties and show existing methods to be biased and inconsistent in this setting. I then apply the proposed methods to study the effects of gubernatorial party control on within-state income distributions in the US, using a close-election design. The results suggest a classic equality-efficiency tradeoff under Democratic governorship, driven by reductions in income at the top of the distribution.

The uniform information density (UID) hypothesis states that humans tend to distribute information roughly evenly across an utterance or discourse. Early evidence in support of the UID hypothesis came from Genzel & Charniak (2002), which proposed an entropy rate constancy principle based on the probability of English text under n-gram language models. We re-evaluate the claims of Genzel & Charniak (2002) with neural language models, failing to find clear evidence in support of entropy rate constancy. We conduct a range of experiments across datasets, model sizes, and languages and discuss implications for the uniform information density hypothesis and linguistic theories of efficient communication more broadly.

According to the generalized Polya theorem, the Gaussian distribution on the real line is characterized by the property of equidistribution of a monomial and a linear form of independent identically distributed random variables. We give a complete description of a-adic solenoids for which an analog of this theorem is true. The proof of the main theorem is reduced to solving some functional equation in the class of continuous positive definite functions on the character group of an a-adic solenoid

We show via a combination of mathematical arguments and empirical evidence that data distributions sampled from diffusion models satisfy a Concentration of Measure Property saying that any Lipschitz 1-dimensional projection of a random vector is not too far from its mean with high probability. This implies that such models are quite restrictive and gives an explanation for a fact previously observed in the literature that conventional diffusion models cannot capture "heavy-tailed" data (i.e. data x for which the norm |x|_2 does not possess a sub-Gaussian tail) well. We then proceed to train a generalized linear model using stochastic gradient descent (SGD) on the diffusion-generated data for a multiclass classification task and observe empirically that a Gaussian universality result holds for the test error. In other words, the test error depends only on the first and second order statistics of the diffusion-generated data in the linear setting. Results of such forms are desirable because they allow one to assume the data itself is Gaussian for analyzing performance of the trained classifier. Finally, we note that current approaches to proving universality do not apply to this case as the covariance matrices of the data tend to have vanishing minimum singular values for the diffusion-generated data, while the current proofs assume that this is not the case (see Subsection 3.4 for more details). This leaves extending previous mathematical universality results as an intriguing open question.

Customer Lifetime Value (CLTV) prediction is a critical task in business applications. Accurately predicting CLTV is challenging in real-world business scenarios, as the distribution of CLTV is complex and mutable. Firstly, there is a large number of users without any consumption consisting of a long-tailed part that is too complex to fit. Secondly, the small set of high-value users spent orders of magnitude more than a typical user leading to a wide range of the CLTV distribution which is hard to capture in a single distribution. Existing approaches for CLTV estimation either assume a prior probability distribution and fit a single group of distribution-related parameters for all samples, or directly learn from the posterior distribution with manually predefined buckets in a heuristic manner. However, all these methods fail to handle complex and mutable distributions. In this paper, we propose a novel optimal distribution selection model OptDist for CLTV prediction, which utilizes an adaptive optimal sub-distribution selection mechanism to improve the accuracy of complex distribution modeling. Specifically, OptDist trains several candidate sub-distribution networks in the distribution learning module (DLM) for modeling the probability distribution of CLTV. Then, a distribution selection module (DSM) is proposed to select the sub-distribution for each sample, thus making the selection automatically and adaptively. Besides, we design an alignment mechanism that connects both modules, which effectively guides the optimization. We conduct extensive experiments on both two public and one private dataset to verify that OptDist outperforms state-of-the-art baselines. Furthermore, OptDist has been deployed on a large-scale financial platform for customer acquisition marketing campaigns and the online experiments also demonstrate the effectiveness of OptDist.

Data collection is often difficult in critical fields such as medicine, physics, and chemistry. As a result, classification methods usually perform poorly with these small datasets, leading to weak predictive performance. Increasing the training set with additional synthetic data, similar to data augmentation in images, is commonly believed to improve downstream classification performance. However, current tabular generative methods that learn either the joint distribution p(x, y) or the class-conditional distribution p(x mid y) often overfit on small datasets, resulting in poor-quality synthetic data, usually worsening classification performance compared to using real data alone. To solve these challenges, we introduce TabEBM, a novel class-conditional generative method using Energy-Based Models (EBMs). Unlike existing methods that use a shared model to approximate all class-conditional densities, our key innovation is to create distinct EBM generative models for each class, each modelling its class-specific data distribution individually. This approach creates robust energy landscapes, even in ambiguous class distributions. Our experiments show that TabEBM generates synthetic data with higher quality and better statistical fidelity than existing methods. When used for data augmentation, our synthetic data consistently improves the classification performance across diverse datasets of various sizes, especially small ones. Code is available at https://github.com/andreimargeloiu/TabEBM.

The Sliced-Wasserstein distance (SW) is a computationally efficient and theoretically grounded alternative to the Wasserstein distance. Yet, the literature on its statistical properties -- or, more accurately, its generalization properties -- with respect to the distribution of slices, beyond the uniform measure, is scarce. To bring new contributions to this line of research, we leverage the PAC-Bayesian theory and a central observation that SW may be interpreted as an average risk, the quantity PAC-Bayesian bounds have been designed to characterize. We provide three types of results: i) PAC-Bayesian generalization bounds that hold on what we refer as adaptive Sliced-Wasserstein distances, i.e. SW defined with respect to arbitrary distributions of slices (among which data-dependent distributions), ii) a principled procedure to learn the distribution of slices that yields maximally discriminative SW, by optimizing our theoretical bounds, and iii) empirical illustrations of our theoretical findings.

The word embedding space in neural models is skewed, and correcting this can improve task performance. We point out that most approaches for modeling, correcting, and measuring the symmetry of an embedding space implicitly assume that the word frequencies are uniform; in reality, word frequencies follow a highly non-uniform distribution, known as Zipf's law. Surprisingly, simply performing PCA whitening weighted by the empirical word frequency that follows Zipf's law significantly improves task performance, surpassing established baselines. From a theoretical perspective, both our approach and existing methods can be clearly categorized: word representations are distributed according to an exponential family with either uniform or Zipfian base measures. By adopting the latter approach, we can naturally emphasize informative low-frequency words in terms of their vector norm, which becomes evident from the information-geometric perspective, and in terms of the loss functions for imbalanced classification. Additionally, our theory corroborates that popular natural language processing methods, such as skip-gram negative sampling, WhiteningBERT, and headless language models, work well just because their word embeddings encode the empirical word frequency into the underlying probabilistic model.

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

An oft-cited open problem of federated learning is the existence of data heterogeneity at the clients. One pathway to understanding the drastic accuracy drop in federated learning is by scrutinizing the behavior of the clients' deep models on data with different levels of "difficulty", which has been left unaddressed. In this paper, we investigate a different and rarely studied dimension of FL: ordered learning. Specifically, we aim to investigate how ordered learning principles can contribute to alleviating the heterogeneity effects in FL. We present theoretical analysis and conduct extensive empirical studies on the efficacy of orderings spanning three kinds of learning: curriculum, anti-curriculum, and random curriculum. We find that curriculum learning largely alleviates non-IIDness. Interestingly, the more disparate the data distributions across clients the more they benefit from ordered learning. We provide analysis explaining this phenomenon, specifically indicating how curriculum training appears to make the objective landscape progressively less convex, suggesting fast converging iterations at the beginning of the training procedure. We derive quantitative results of convergence for both convex and nonconvex objectives by modeling the curriculum training on federated devices as local SGD with locally biased stochastic gradients. Also, inspired by ordered learning, we propose a novel client selection technique that benefits from the real-world disparity in the clients. Our proposed approach to client selection has a synergic effect when applied together with ordered learning in FL.

Diffusion models are emerging expressive generative models, in which a large number of time steps (inference steps) are required for a single image generation. To accelerate such tedious process, reducing steps uniformly is considered as an undisputed principle of diffusion models. We consider that such a uniform assumption is not the optimal solution in practice; i.e., we can find different optimal time steps for different models. Therefore, we propose to search the optimal time steps sequence and compressed model architecture in a unified framework to achieve effective image generation for diffusion models without any further training. Specifically, we first design a unified search space that consists of all possible time steps and various architectures. Then, a two stage evolutionary algorithm is introduced to find the optimal solution in the designed search space. To further accelerate the search process, we employ FID score between generated and real samples to estimate the performance of the sampled examples. As a result, the proposed method is (i).training-free, obtaining the optimal time steps and model architecture without any training process; (ii). orthogonal to most advanced diffusion samplers and can be integrated to gain better sample quality. (iii). generalized, where the searched time steps and architectures can be directly applied on different diffusion models with the same guidance scale. Experimental results show that our method achieves excellent performance by using only a few time steps, e.g. 17.86 FID score on ImageNet 64 times 64 with only four steps, compared to 138.66 with DDIM. The code is available at https://github.com/lilijiangg/AutoDiffusion.

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

Although deep neural networks achieve tremendous success on various classification tasks, the generalization ability drops sheer when training datasets exhibit long-tailed distributions. One of the reasons is that the learned representations (i.e. features) from the imbalanced datasets are less effective than those from balanced datasets. Specifically, the learned representation under class-balanced distribution will present the Neural Collapse (NC) phenomena. NC indicates the features from the same category are close to each other and from different categories are maximally distant, showing an optimal linear separable state of classification. However, the pattern differs on imbalanced datasets and is partially responsible for the reduced performance of the model. In this work, we propose two explicit feature regularization terms to learn high-quality representation for class-imbalanced data. With the proposed regularization, NC phenomena will appear under the class-imbalanced distribution, and the generalization ability can be significantly improved. Our method is easily implemented, highly effective, and can be plugged into most existing methods. The extensive experimental results on widely-used benchmarks show the effectiveness of our method

The binary sum-of-digits function s returns the number of ones in the binary expansion of a nonnegative integer. Cusick's Hamming weight conjecture states that, for all integers tgeq 0, the set of nonnegative integers n such that s(n+t)geq s(n) has asymptotic density strictly larger than 1/2. We are concerned with the block-additive function r returning the number of (overlapping) occurrences of the block 11 in the binary expansion of n. The main result of this paper is a central limit-type theorem for the difference r(n+t)-r(n): the corresponding probability function is uniformly close to a Gaussian, where the uniform error tends to 0 as the number of blocks of ones in the binary expansion of t tends to infty.

Post-hoc out-of-distribution (OOD) detection has garnered intensive attention in reliable machine learning. Many efforts have been dedicated to deriving score functions based on logits, distances, or rigorous data distribution assumptions to identify low-scoring OOD samples. Nevertheless, these estimate scores may fail to accurately reflect the true data density or impose impractical constraints. To provide a unified perspective on density-based score design, we propose a novel theoretical framework grounded in Bregman divergence, which extends distribution considerations to encompass an exponential family of distributions. Leveraging the conjugation constraint revealed in our theorem, we introduce a ConjNorm method, reframing density function design as a search for the optimal norm coefficient p against the given dataset. In light of the computational challenges of normalization, we devise an unbiased and analytically tractable estimator of the partition function using the Monte Carlo-based importance sampling technique. Extensive experiments across OOD detection benchmarks empirically demonstrate that our proposed ConjNorm has established a new state-of-the-art in a variety of OOD detection setups, outperforming the current best method by up to 13.25% and 28.19% (FPR95) on CIFAR-100 and ImageNet-1K, respectively.

The infinitely wide neural network has been proven a useful and manageable mathematical model that enables the understanding of many phenomena appearing in deep learning. One example is the convergence of random deep networks to Gaussian processes that allows a rigorous analysis of the way the choice of activation function and network weights impacts the training dynamics. In this paper, we extend the seminal proof of Matthews et al. (2018) to a larger class of initial weight distributions (which we call PSEUDO-IID), including the established cases of IID and orthogonal weights, as well as the emerging low-rank and structured sparse settings celebrated for their computational speed-up benefits. We show that fully-connected and convolutional networks initialized with PSEUDO-IID distributions are all effectively equivalent up to their variance. Using our results, one can identify the Edge-of-Chaos for a broader class of neural networks and tune them at criticality in order to enhance their training. Moreover, they enable the posterior distribution of Bayesian Neural Networks to be tractable across these various initialization schemes.

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.

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.

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

While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the first rigorous analysis on approximation and generalization abilities of diffusion modeling for well-known function spaces. The highlight of this paper is that when the true density function belongs to the Besov space and the empirical score matching loss is properly minimized, the generated data distribution achieves the nearly minimax optimal estimation rates in the total variation distance and in the Wasserstein distance of order one. Furthermore, we extend our theory to demonstrate how diffusion models adapt to low-dimensional data distributions. We expect these results advance theoretical understandings of diffusion modeling and its ability to generate verisimilar outputs.

Long-tailed recognition with imbalanced class distribution naturally emerges in practical machine learning applications. Existing methods such as data reweighing, resampling, and supervised contrastive learning enforce the class balance with a price of introducing imbalance between instances of head class and tail class, which may ignore the underlying rich semantic substructures of the former and exaggerate the biases in the latter. We overcome these drawbacks by a novel ``subclass-balancing contrastive learning (SBCL)'' approach that clusters each head class into multiple subclasses of similar sizes as the tail classes and enforce representations to capture the two-layer class hierarchy between the original classes and their subclasses. Since the clustering is conducted in the representation space and updated during the course of training, the subclass labels preserve the semantic substructures of head classes. Meanwhile, it does not overemphasize tail class samples, so each individual instance contribute to the representation learning equally. Hence, our method achieves both the instance- and subclass-balance, while the original class labels are also learned through contrastive learning among subclasses from different classes. We evaluate SBCL over a list of long-tailed benchmark datasets and it achieves the state-of-the-art performance. In addition, we present extensive analyses and ablation studies of SBCL to verify its advantages.

Data heterogeneity in federated learning, characterized by a significant misalignment between local and global distributions, leads to divergent local optimization directions and hinders global model training. Existing studies mainly focus on optimizing local updates or global aggregation, but these indirect approaches demonstrate instability when handling highly heterogeneous data distributions, especially in scenarios where label skew and domain skew coexist. To address this, we propose a geometry-guided data generation method that centers on simulating the global embedding distribution locally. We first introduce the concept of the geometric shape of an embedding distribution and then address the challenge of obtaining global geometric shapes under privacy constraints. Subsequently, we propose GGEUR, which leverages global geometric shapes to guide the generation of new samples, enabling a closer approximation to the ideal global distribution. In single-domain scenarios, we augment samples based on global geometric shapes to enhance model generalization; in multi-domain scenarios, we further employ class prototypes to simulate the global distribution across domains. Extensive experimental results demonstrate that our method significantly enhances the performance of existing approaches in handling highly heterogeneous data, including scenarios with label skew, domain skew, and their coexistence. Code published at: https://github.com/WeiDai-David/2025CVPR_GGEUR

Recent advances in reinforcement learning (RL)-based post-training have led to notable improvements in large language models (LLMs), particularly in enhancing their reasoning capabilities to handle complex tasks. However, most existing methods treat the training data as a unified whole, overlooking the fact that modern LLM training often involves a mixture of data from diverse distributions-varying in both source and difficulty. This heterogeneity introduces a key challenge: how to adaptively schedule training across distributions to optimize learning efficiency. In this paper, we present a principled curriculum learning framework grounded in the notion of distribution-level learnability. Our core insight is that the magnitude of policy advantages reflects how much a model can still benefit from further training on a given distribution. Based on this, we propose a distribution-level curriculum learning framework for RL-based LLM post-training, which leverages the Upper Confidence Bound (UCB) principle to dynamically adjust sampling probabilities for different distrubutions. This approach prioritizes distributions with either high average advantage (exploitation) or low sample count (exploration), yielding an adaptive and theoretically grounded training schedule. We instantiate our curriculum learning framework with GRPO as the underlying RL algorithm and demonstrate its effectiveness on logic reasoning datasets with multiple difficulties and sources. Our experiments show that our framework significantly improves convergence speed and final performance, highlighting the value of distribution-aware curriculum strategies in LLM post-training. Code: https://github.com/ZhentingWang/DUMP.

Real-world data tends to follow a long-tailed distribution, where the class imbalance results in dominance of the head classes during training. In this paper, we propose a frustratingly simple but effective step-wise learning framework to gradually enhance the capability of the model in detecting all categories of long-tailed datasets. Specifically, we build smooth-tail data where the long-tailed distribution of categories decays smoothly to correct the bias towards head classes. We pre-train a model on the whole long-tailed data to preserve discriminability between all categories. We then fine-tune the class-agnostic modules of the pre-trained model on the head class dominant replay data to get a head class expert model with improved decision boundaries from all categories. Finally, we train a unified model on the tail class dominant replay data while transferring knowledge from the head class expert model to ensure accurate detection of all categories. Extensive experiments on long-tailed datasets LVIS v0.5 and LVIS v1.0 demonstrate the superior performance of our method, where we can improve the AP with ResNet-50 backbone from 27.0% to 30.3% AP, and especially for the rare categories from 15.5% to 24.9% AP. Our best model using ResNet-101 backbone can achieve 30.7% AP, which suppresses all existing detectors using the same backbone.

This paper studies the prediction of a target z from a pair of random variables (x,y), where the ground-truth predictor is additive E[z mid x,y] = f_star(x) +g_{star}(y). We study the performance of empirical risk minimization (ERM) over functions f+g, f in F and g in G, fit on a given training distribution, but evaluated on a test distribution which exhibits covariate shift. We show that, when the class F is "simpler" than G (measured, e.g., in terms of its metric entropy), our predictor is more resilient to heterogenous covariate shifts in which the shift in x is much greater than that in y. These results rely on a novel H\"older style inequality for the Dudley integral which may be of independent interest. Moreover, we corroborate our theoretical findings with experiments demonstrating improved resilience to shifts in "simpler" features across numerous domains.

We consider a number of graph kernels and proximity measures including commute time kernel, regularized Laplacian kernel, heat kernel, exponential diffusion kernel (also called "communicability"), etc., and the corresponding distances as applied to clustering nodes in random graphs and several well-known datasets. The model of generating random graphs involves edge probabilities for the pairs of nodes that belong to the same class or different predefined classes of nodes. It turns out that in most cases, logarithmic measures (i.e., measures resulting after taking logarithm of the proximities) perform better while distinguishing underlying classes than the "plain" measures. A comparison in terms of reject curves of inter-class and intra-class distances confirms this conclusion. A similar conclusion can be made for several well-known datasets. A possible origin of this effect is that most kernels have a multiplicative nature, while the nature of distances used in cluster algorithms is an additive one (cf. the triangle inequality). The logarithmic transformation is a tool to transform the first nature to the second one. Moreover, some distances corresponding to the logarithmic measures possess a meaningful cutpoint additivity property. In our experiments, the leader is usually the logarithmic Communicability measure. However, we indicate some more complicated cases in which other measures, typically, Communicability and plain Walk, can be the winners.

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.

Model attribution is a popular tool to explain the rationales behind model predictions. However, recent work suggests that the attributions are vulnerable to minute perturbations, which can be added to input samples to fool the attributions while maintaining the prediction outputs. Although empirical studies have shown positive performance via adversarial training, an effective certified defense method is eminently needed to understand the robustness of attributions. In this work, we propose to use uniform smoothing technique that augments the vanilla attributions by noises uniformly sampled from a certain space. It is proved that, for all perturbations within the attack region, the cosine similarity between uniformly smoothed attribution of perturbed sample and the unperturbed sample is guaranteed to be lower bounded. We also derive alternative formulations of the certification that is equivalent to the original one and provides the maximum size of perturbation or the minimum smoothing radius such that the attribution can not be perturbed. We evaluate the proposed method on three datasets and show that the proposed method can effectively protect the attributions from attacks, regardless of the architecture of networks, training schemes and the size of the datasets.

Ensuring equitable treatment (fairness) across protected attributes (such as gender or ethnicity) is a critical issue in machine learning. Most existing literature focuses on binary classification, but achieving fairness in regression tasks-such as insurance pricing or hiring score assessments-is equally important. Moreover, anti-discrimination laws also apply to continuous attributes, such as age, for which many existing methods are not applicable. In practice, multiple protected attributes can exist simultaneously; however, methods targeting fairness across several attributes often overlook so-called "fairness gerrymandering", thereby ignoring disparities among intersectional subgroups (e.g., African-American women or Hispanic men). In this paper, we propose a distance covariance regularisation framework that mitigates the association between model predictions and protected attributes, in line with the fairness definition of demographic parity, and that captures both linear and nonlinear dependencies. To enhance applicability in the presence of multiple protected attributes, we extend our framework by incorporating two multivariate dependence measures based on distance covariance: the previously proposed joint distance covariance (JdCov) and our novel concatenated distance covariance (CCdCov), which effectively address fairness gerrymandering in both regression and classification tasks involving protected attributes of various types. We discuss and illustrate how to calibrate regularisation strength, including a method based on Jensen-Shannon divergence, which quantifies dissimilarities in prediction distributions across groups. We apply our framework to the COMPAS recidivism dataset and a large motor insurance claims dataset.

This paper studies Kernel density estimation for a high-dimensional distribution rho(x). Traditional approaches have focused on the limit of large number of data points n and fixed dimension d. We analyze instead the regime where both the number n of data points y_i and their dimensionality d grow with a fixed ratio alpha=(log n)/d. Our study reveals three distinct statistical regimes for the kernel-based estimate of the density hat rho_h^{D}(x)=1{n h^d}sum_{i=1}^n Kleft(x-y_i{h}right), depending on the bandwidth h: a classical regime for large bandwidth where the Central Limit Theorem (CLT) holds, which is akin to the one found in traditional approaches. Below a certain value of the bandwidth, h_{CLT}(alpha), we find that the CLT breaks down. The statistics of hat rho_h^{D}(x) for a fixed x drawn from rho(x) is given by a heavy-tailed distribution (an alpha-stable distribution). In particular below a value h_G(alpha), we find that hat rho_h^{D}(x) is governed by extreme value statistics: only a few points in the database matter and give the dominant contribution to the density estimator. We provide a detailed analysis for high-dimensional multivariate Gaussian data. We show that the optimal bandwidth threshold based on Kullback-Leibler divergence lies in the new statistical regime identified in this paper. Our findings reveal limitations of classical approaches, show the relevance of these new statistical regimes, and offer new insights for Kernel density estimation in high-dimensional settings.

While score-based generative models (SGMs) have achieved remarkable success in enormous image generation tasks, their mathematical foundations are still limited. In this paper, we analyze the approximation and generalization of SGMs in learning a family of sub-Gaussian probability distributions. We introduce a notion of complexity for probability distributions in terms of their relative density with respect to the standard Gaussian measure. We prove that if the log-relative density can be locally approximated by a neural network whose parameters can be suitably bounded, then the distribution generated by empirical score matching approximates the target distribution in total variation with a dimension-independent rate. We illustrate our theory through examples, which include certain mixtures of Gaussians. An essential ingredient of our proof is to derive a dimension-free deep neural network approximation rate for the true score function associated with the forward process, which is interesting in its own right.

We study subsampling-based ridge ensembles in the proportional asymptotics regime, where the feature size grows proportionally with the sample size such that their ratio converges to a constant. By analyzing the squared prediction risk of ridge ensembles as a function of the explicit penalty lambda and the limiting subsample aspect ratio phi_s (the ratio of the feature size to the subsample size), we characterize contours in the (lambda, phi_s)-plane at any achievable risk. As a consequence, we prove that the risk of the optimal full ridgeless ensemble (fitted on all possible subsamples) matches that of the optimal ridge predictor. In addition, we prove strong uniform consistency of generalized cross-validation (GCV) over the subsample sizes for estimating the prediction risk of ridge ensembles. This allows for GCV-based tuning of full ridgeless ensembles without sample splitting and yields a predictor whose risk matches optimal ridge risk.

Finite symmetric groups S_n are essential in fields such as combinatorics, physics, and chemistry. However, learning a probability distribution over S_n poses significant challenges due to its intractable size and discrete nature. In this paper, we introduce SymmetricDiffusers, a novel discrete diffusion model that simplifies the task of learning a complicated distribution over S_n by decomposing it into learning simpler transitions of the reverse diffusion using deep neural networks. We identify the riffle shuffle as an effective forward transition and provide empirical guidelines for selecting the diffusion length based on the theory of random walks on finite groups. Additionally, we propose a generalized Plackett-Luce (PL) distribution for the reverse transition, which is provably more expressive than the PL distribution. We further introduce a theoretically grounded "denoising schedule" to improve sampling and learning efficiency. Extensive experiments show that our model achieves state-of-the-art or comparable performances on solving tasks including sorting 4-digit MNIST images, jigsaw puzzles, and traveling salesman problems. Our code is released at https://github.com/DSL-Lab/SymmetricDiffusers.

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

Mixed Integer Linear Programming (MILP) is a fundamental tool for modeling combinatorial optimization problems. Recently, a growing body of research has used machine learning to accelerate MILP solving. Despite the increasing popularity of this approach, there is a lack of a common repository that provides distributions of similar MILP instances across different domains, at different hardness levels, with standardized test sets. In this paper, we introduce Distributional MIPLIB, a multi-domain library of problem distributions for advancing ML-guided MILP methods. We curate MILP distributions from existing work in this area as well as real-world problems that have not been used, and classify them into different hardness levels. It will facilitate research in this area by enabling comprehensive evaluation on diverse and realistic domains. We empirically illustrate the benefits of using Distributional MIPLIB as a research vehicle in two ways. We evaluate the performance of ML-guided variable branching on previously unused distributions to identify potential areas for improvement. Moreover, we propose to learn branching policies from a mix of distributions, demonstrating that mixed distributions achieve better performance compared to homogeneous distributions when there is limited data and generalize well to larger instances. The dataset is publicly available at https://sites.google.com/usc.edu/distributional-miplib/home.

We present prompt distribution learning for effectively adapting a pre-trained vision-language model to address downstream recognition tasks. Our method not only learns low-bias prompts from a few samples but also captures the distribution of diverse prompts to handle the varying visual representations. In this way, we provide high-quality task-related content for facilitating recognition. This prompt distribution learning is realized by an efficient approach that learns the output embeddings of prompts instead of the input embeddings. Thus, we can employ a Gaussian distribution to model them effectively and derive a surrogate loss for efficient training. Extensive experiments on 12 datasets demonstrate that our method consistently and significantly outperforms existing methods. For example, with 1 sample per category, it relatively improves the average result by 9.1% compared to human-crafted prompts.

Class-incremental learning (CIL) is a particularly challenging variant of continual learning, where the goal is to learn to discriminate between all classes presented in an incremental fashion. Existing approaches often suffer from excessive forgetting and imbalance of the scores assigned to classes that have not been seen together during training. In this study, we introduce a novel approach, Prediction Error-based Classification (PEC), which differs from traditional discriminative and generative classification paradigms. PEC computes a class score by measuring the prediction error of a model trained to replicate the outputs of a frozen random neural network on data from that class. The method can be interpreted as approximating a classification rule based on Gaussian Process posterior variance. PEC offers several practical advantages, including sample efficiency, ease of tuning, and effectiveness even when data are presented one class at a time. Our empirical results show that PEC performs strongly in single-pass-through-data CIL, outperforming other rehearsal-free baselines in all cases and rehearsal-based methods with moderate replay buffer size in most cases across multiple benchmarks.

In physics and engineering literature, the distribution of the excursion-above-zero time distribution (exceedance distribution) for a stationary Gaussian process has been approximated by a stationary switching process with independently distributed switching times. The approach matched the covariance of the clipped Gaussian process with the one for the stationary switching process and the distribution of the latter was used as the so-called independent interval approximation (IIA). The approach successfully assessed the persistency exponent for many physically important processes but left an unanswered question when such an approach leads to a mathematically meaningful and proper exceedance distribution. Here we address this question by proposing an alternative matching of the expected values of the clipped Slepian process and the corresponding switched process initiated at the origin. The method has allowed resolving the mathematical correctness of the matching method for a large subclass of the Gaussian processes with monotonic covariance, for which we provide a sufficient condition for the validity of the IIA. Within this class, the IIA produces a valid distribution for the excursion time and is represented in an explicit stochastic form that connects directly to the covariance of the underlying Gaussian process. We compare the excursion level distributions as well as the corresponding persistency exponents obtained through the IIA method with numerically computed exact distributions, and the simulated distribution for several important Gaussian models. We also argue that for stationary Gaussian processes with a non-monotonic covariance, the IIA fails and should not be used.

Various visual foundation models have distinct strengths and weaknesses, both of which can be improved through heterogeneous multi-teacher knowledge distillation without labels, termed "agglomerative models." We build upon this body of work by studying the effect of the teachers' activation statistics, particularly the impact of the loss function on the resulting student model quality. We explore a standard toolkit of statistical normalization techniques to better align the different distributions and assess their effects. Further, we examine the impact on downstream teacher-matching metrics, which motivates the use of Hadamard matrices. With these matrices, we demonstrate useful properties, showing how they can be used for isotropic standardization, where each dimension of a multivariate distribution is standardized using the same scale. We call this technique "PHI Standardization" (PHI-S) and empirically demonstrate that it produces the best student model across the suite of methods studied.

There is a long history, as well as a recent explosion of interest, in statistical and generative modeling approaches based on score functions -- derivatives of the log-likelihood of a distribution. In seminal works, Hyv\"arinen proposed vanilla score matching as a way to learn distributions from data by computing an estimate of the score function of the underlying ground truth, and established connections between this method and established techniques like Contrastive Divergence and Pseudolikelihood estimation. It is by now well-known that vanilla score matching has significant difficulties learning multimodal distributions. Although there are various ways to overcome this difficulty, the following question has remained unanswered -- is there a natural way to sample multimodal distributions using just the vanilla score? Inspired by a long line of related experimental works, we prove that the Langevin diffusion with early stopping, initialized at the empirical distribution, and run on a score function estimated from data successfully generates natural multimodal distributions (mixtures of log-concave distributions).

Detecting test samples drawn sufficiently far away from the training distribution statistically or adversarially is a fundamental requirement for deploying a good classifier in many real-world machine learning applications. However, deep neural networks with the softmax classifier are known to produce highly overconfident posterior distributions even for such abnormal samples. In this paper, we propose a simple yet effective method for detecting any abnormal samples, which is applicable to any pre-trained softmax neural classifier. We obtain the class conditional Gaussian distributions with respect to (low- and upper-level) features of the deep models under Gaussian discriminant analysis, which result in a confidence score based on the Mahalanobis distance. While most prior methods have been evaluated for detecting either out-of-distribution or adversarial samples, but not both, the proposed method achieves the state-of-the-art performances for both cases in our experiments. Moreover, we found that our proposed method is more robust in harsh cases, e.g., when the training dataset has noisy labels or small number of samples. Finally, we show that the proposed method enjoys broader usage by applying it to class-incremental learning: whenever out-of-distribution samples are detected, our classification rule can incorporate new classes well without further training deep models.

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

Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models, when data are supported on an unknown low-dimensional linear subspace. Our result provides sample complexity bounds for distribution estimation using diffusion models. We show that with a properly chosen neural network architecture, the score function can be both accurately approximated and efficiently estimated. Furthermore, the generated distribution based on the estimated score function captures the data geometric structures and converges to a close vicinity of the data distribution. The convergence rate depends on the subspace dimension, indicating that diffusion models can circumvent the curse of data ambient dimensionality.

Few-Shot Class-Incremental Learning (FSCIL) focuses on models learning new concepts from limited data while retaining knowledge of previous classes. Recently, many studies have started to leverage unlabeled samples to assist models in learning from few-shot samples, giving rise to the field of Semi-supervised Few-shot Class-Incremental Learning (Semi-FSCIL). However, these studies often assume that the source of unlabeled data is only confined to novel classes of the current session, which presents a narrow perspective and cannot align well with practical scenarios. To better reflect real-world scenarios, we redefine Semi-FSCIL as Generalized Semi-FSCIL (GSemi-FSCIL) by incorporating both base and all the ever-seen novel classes in the unlabeled set. This change in the composition of unlabeled samples poses a new challenge for existing methods, as they struggle to distinguish between unlabeled samples from base and novel classes. To address this issue, we propose an Ambiguity-guided Learnable Distribution Calibration (ALDC) strategy. ALDC dynamically uses abundant base samples to correct biased feature distributions for few-shot novel classes. Experiments on three benchmark datasets show that our method outperforms existing works, setting new state-of-the-art results.

We consider the problem of weakly supervised object detection, where the training samples are annotated using only image-level labels that indicate the presence or absence of an object category. In order to model the uncertainty in the location of the objects, we employ a dissimilarity coefficient based probabilistic learning objective. The learning objective minimizes the difference between an annotation agnostic prediction distribution and an annotation aware conditional distribution. The main computational challenge is the complex nature of the conditional distribution, which consists of terms over hundreds or thousands of variables. The complexity of the conditional distribution rules out the possibility of explicitly modeling it. Instead, we exploit the fact that deep learning frameworks rely on stochastic optimization. This allows us to use a state of the art discrete generative model that can provide annotation consistent samples from the conditional distribution. Extensive experiments on PASCAL VOC 2007 and 2012 data sets demonstrate the efficacy of our proposed approach.

Real-world large-scale datasets are both noisily labeled and class-imbalanced. The issues seriously hurt the generalization of trained models. It is hence significant to address the simultaneous incorrect labeling and class-imbalance, i.e., the problem of learning with noisy labels on long-tailed data. Previous works develop several methods for the problem. However, they always rely on strong assumptions that are invalid or hard to be checked in practice. In this paper, to handle the problem and address the limitations of prior works, we propose a representation calibration method RCAL. Specifically, RCAL works with the representations extracted by unsupervised contrastive learning. We assume that without incorrect labeling and class imbalance, the representations of instances in each class conform to a multivariate Gaussian distribution, which is much milder and easier to be checked. Based on the assumption, we recover underlying representation distributions from polluted ones resulting from mislabeled and class-imbalanced data. Additional data points are then sampled from the recovered distributions to help generalization. Moreover, during classifier training, representation learning takes advantage of representation robustness brought by contrastive learning, which further improves the classifier performance. We derive theoretical results to discuss the effectiveness of our representation calibration. Experiments on multiple benchmarks justify our claims and confirm the superiority of the proposed method.

Given an algorithmic predictor that is accurate on some source population consisting of strategic human decision subjects, will it remain accurate if the population respond to it? In our setting, an agent or a user corresponds to a sample (X,Y) drawn from a distribution D and will face a model h and its classification result h(X). Agents can modify X to adapt to h, which will incur a distribution shift on (X,Y). Our formulation is motivated by applications where the deployed machine learning models are subjected to human agents, and will ultimately face responsive and interactive data distributions. We formalize the discussions of the transferability of a model by studying how the performance of the model trained on the available source distribution (data) would translate to the performance on its induced domain. We provide both upper bounds for the performance gap due to the induced domain shift, as well as lower bounds for the trade-offs that a classifier has to suffer on either the source training distribution or the induced target distribution. We provide further instantiated analysis for two popular domain adaptation settings, including covariate shift and target shift.

When facing data with imbalanced classes or groups, practitioners follow an intriguing strategy to achieve best results. They throw away examples until the classes or groups are balanced in size, and then perform empirical risk minimization on the reduced training set. This opposes common wisdom in learning theory, where the expected error is supposed to decrease as the dataset grows in size. In this work, we leverage extreme value theory to address this apparent contradiction. Our results show that the tails of the data distribution play an important role in determining the worst-group-accuracy of linear classifiers. When learning on data with heavy tails, throwing away data restores the geometric symmetry of the resulting classifier, and therefore improves its worst-group generalization.

Identifying Out-of-distribution (OOD) data is becoming increasingly critical as the real-world applications of deep learning methods expand. Post-hoc methods modify softmax scores fine-tuned on outlier data or leverage intermediate feature layers to identify distinctive patterns between In-Distribution (ID) and OOD samples. Other methods focus on employing diverse OOD samples to learn discrepancies between ID and OOD. These techniques, however, are typically dependent on the quality of the outlier samples assumed. Density-based methods explicitly model class-conditioned distributions but this requires long training time or retraining the classifier. To tackle these issues, we introduce FlowCon, a new density-based OOD detection technique. Our main innovation lies in efficiently combining the properties of normalizing flow with supervised contrastive learning, ensuring robust representation learning with tractable density estimation. Empirical evaluation shows the enhanced performance of our method across common vision datasets such as CIFAR-10 and CIFAR-100 pretrained on ResNet18 and WideResNet classifiers. We also perform quantitative analysis using likelihood plots and qualitative visualization using UMAP embeddings and demonstrate the robustness of the proposed method under various OOD contexts. Code will be open-sourced post decision.

Conformal prediction (CP) for regression can be challenging, especially when the output distribution is heteroscedastic, multimodal, or skewed. Some of the issues can be addressed by estimating a distribution over the output, but in reality, such approaches can be sensitive to estimation error and yield unstable intervals.~Here, we circumvent the challenges by converting regression to a classification problem and then use CP for classification to obtain CP sets for regression.~To preserve the ordering of the continuous-output space, we design a new loss function and make necessary modifications to the CP classification techniques.~Empirical results on many benchmarks shows that this simple approach gives surprisingly good results on many practical problems.

Major advancements have been made in the field of object detection and segmentation recently. However, when it comes to rare categories, the state-of-the-art methods fail to detect them, resulting in a significant performance gap between rare and frequent categories. In this paper, we identify that Sigmoid or Softmax functions used in deep detectors are a major reason for low performance and are sub-optimal for long-tailed detection and segmentation. To address this, we develop a Gumbel Optimized Loss (GOL), for long-tailed detection and segmentation. It aligns with the Gumbel distribution of rare classes in imbalanced datasets, considering the fact that most classes in long-tailed detection have low expected probability. The proposed GOL significantly outperforms the best state-of-the-art method by 1.1% on AP , and boosts the overall segmentation by 9.0% and detection by 8.0%, particularly improving detection of rare classes by 20.3%, compared to Mask-RCNN, on LVIS dataset. Code available at: https://github.com/kostas1515/GOL

The rapid adoption of text-to-image diffusion models in society underscores an urgent need to address their biases. Without interventions, these biases could propagate a skewed worldview and restrict opportunities for minority groups. In this work, we frame fairness as a distributional alignment problem. Our solution consists of two main technical contributions: (1) a distributional alignment loss that steers specific characteristics of the generated images towards a user-defined target distribution, and (2) adjusted direct finetuning of diffusion model's sampling process (adjusted DFT), which leverages an adjusted gradient to directly optimize losses defined on the generated images. Empirically, our method markedly reduces gender, racial, and their intersectional biases for occupational prompts. Gender bias is significantly reduced even when finetuning just five soft tokens. Crucially, our method supports diverse perspectives of fairness beyond absolute equality, which is demonstrated by controlling age to a 75% young and 25% old distribution while simultaneously debiasing gender and race. Finally, our method is scalable: it can debias multiple concepts at once by simply including these prompts in the finetuning data. We share code and various fair diffusion model adaptors at https://sail-sg.github.io/finetune-fair-diffusion/.

OpenAI's Sora highlights the potential of video generation for developing world models that adhere to fundamental physical laws. However, the ability of video generation models to discover such laws purely from visual data without human priors can be questioned. A world model learning the true law should give predictions robust to nuances and correctly extrapolate on unseen scenarios. In this work, we evaluate across three key scenarios: in-distribution, out-of-distribution, and combinatorial generalization. We developed a 2D simulation testbed for object movement and collisions to generate videos deterministically governed by one or more classical mechanics laws. This provides an unlimited supply of data for large-scale experimentation and enables quantitative evaluation of whether the generated videos adhere to physical laws. We trained diffusion-based video generation models to predict object movements based on initial frames. Our scaling experiments show perfect generalization within the distribution, measurable scaling behavior for combinatorial generalization, but failure in out-of-distribution scenarios. Further experiments reveal two key insights about the generalization mechanisms of these models: (1) the models fail to abstract general physical rules and instead exhibit "case-based" generalization behavior, i.e., mimicking the closest training example; (2) when generalizing to new cases, models are observed to prioritize different factors when referencing training data: color > size > velocity > shape. Our study suggests that scaling alone is insufficient for video generation models to uncover fundamental physical laws, despite its role in Sora's broader success. See our project page at https://phyworld.github.io

Instance segmentation is data-hungry, and as model capacity increases, data scale becomes crucial for improving the accuracy. Most instance segmentation datasets today require costly manual annotation, limiting their data scale. Models trained on such data are prone to overfitting on the training set, especially for those rare categories. While recent works have delved into exploiting generative models to create synthetic datasets for data augmentation, these approaches do not efficiently harness the full potential of generative models. To address these issues, we introduce a more efficient strategy to construct generative datasets for data augmentation, termed DiverGen. Firstly, we provide an explanation of the role of generative data from the perspective of distribution discrepancy. We investigate the impact of different data on the distribution learned by the model. We argue that generative data can expand the data distribution that the model can learn, thus mitigating overfitting. Additionally, we find that the diversity of generative data is crucial for improving model performance and enhance it through various strategies, including category diversity, prompt diversity, and generative model diversity. With these strategies, we can scale the data to millions while maintaining the trend of model performance improvement. On the LVIS dataset, DiverGen significantly outperforms the strong model X-Paste, achieving +1.1 box AP and +1.1 mask AP across all categories, and +1.9 box AP and +2.5 mask AP for rare categories.

Understanding the performance of machine learning (ML) models across diverse data distributions is critically important for reliable applications. Despite recent empirical studies positing a near-perfect linear correlation between in-distribution (ID) and out-of-distribution (OOD) accuracies, we empirically demonstrate that this correlation is more nuanced under subpopulation shifts. Through rigorous experimentation and analysis across a variety of datasets, models, and training epochs, we demonstrate that OOD performance often has a nonlinear correlation with ID performance in subpopulation shifts. Our findings, which contrast previous studies that have posited a linear correlation in model performance during distribution shifts, reveal a "moon shape" correlation (parabolic uptrend curve) between the test performance on the majority subpopulation and the minority subpopulation. This non-trivial nonlinear correlation holds across model architectures, hyperparameters, training durations, and the imbalance between subpopulations. Furthermore, we found that the nonlinearity of this "moon shape" is causally influenced by the degree of spurious correlations in the training data. Our controlled experiments show that stronger spurious correlation in the training data creates more nonlinear performance correlation. We provide complementary experimental and theoretical analyses for this phenomenon, and discuss its implications for ML reliability and fairness. Our work highlights the importance of understanding the nonlinear effects of model improvement on performance in different subpopulations, and has the potential to inform the development of more equitable and responsible machine learning models.

In this paper, we construct a mixture of neural operators (MoNOs) between function spaces whose complexity is distributed over a network of expert neural operators (NOs), with each NO satisfying parameter scaling restrictions. Our main result is a distributed universal approximation theorem guaranteeing that any Lipschitz non-linear operator between L^2([0,1]^d) spaces can be approximated uniformly over the Sobolev unit ball therein, to any given varepsilon>0 accuracy, by an MoNO while satisfying the constraint that: each expert NO has a depth, width, and rank of O(varepsilon^{-1}). Naturally, our result implies that the required number of experts must be large, however, each NO is guaranteed to be small enough to be loadable into the active memory of most computers for reasonable accuracies varepsilon. During our analysis, we also obtain new quantitative expression rates for classical NOs approximating uniformly continuous non-linear operators uniformly on compact subsets of L^2([0,1]^d).

We propose an approach for annotating object classes using free-form text written by undirected and untrained annotators. Free-form labeling is natural for annotators, they intuitively provide very specific and exhaustive labels, and no training stage is necessary. We first collect 729 labels on 15k images using 124 different annotators. Then we automatically enrich the structure of these free-form annotations by discovering a natural vocabulary of 4020 classes within them. This vocabulary represents the natural distribution of objects well and is learned directly from data, instead of being an educated guess done before collecting any labels. Hence, the natural vocabulary emerges from a large mass of free-form annotations. To do so, we (i) map the raw input strings to entities in an ontology of physical objects (which gives them an unambiguous meaning); and (ii) leverage inter-annotator co-occurrences, as well as biases and knowledge specific to individual annotators. Finally, we also automatically extract natural vocabularies of reduced size that have high object coverage while remaining specific. These reduced vocabularies represent the natural distribution of objects much better than commonly used predefined vocabularies. Moreover, they feature more uniform sample distribution over classes.

Out-of-distribution (OOD) detection is crucial for model reliability, as it identifies samples from unknown classes and reduces errors due to unexpected inputs. Vision-Language Models (VLMs) such as CLIP are emerging as powerful tools for OOD detection by integrating multi-modal information. However, the practical application of such systems is challenged by manual prompt engineering, which demands domain expertise and is sensitive to linguistic nuances. In this paper, we introduce Label-driven Automated Prompt Tuning (LAPT), a novel approach to OOD detection that reduces the need for manual prompt engineering. We develop distribution-aware prompts with in-distribution (ID) class names and negative labels mined automatically. Training samples linked to these class labels are collected autonomously via image synthesis and retrieval methods, allowing for prompt learning without manual effort. We utilize a simple cross-entropy loss for prompt optimization, with cross-modal and cross-distribution mixing strategies to reduce image noise and explore the intermediate space between distributions, respectively. The LAPT framework operates autonomously, requiring only ID class names as input and eliminating the need for manual intervention. With extensive experiments, LAPT consistently outperforms manually crafted prompts, setting a new standard for OOD detection. Moreover, LAPT not only enhances the distinction between ID and OOD samples, but also improves the ID classification accuracy and strengthens the generalization robustness to covariate shifts, resulting in outstanding performance in challenging full-spectrum OOD detection tasks. Codes are available at https://github.com/YBZh/LAPT.

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

Solving partial differential equations (PDEs) is a central task in scientific computing. Recently, neural network approximation of PDEs has received increasing attention due to its flexible meshless discretization and its potential for high-dimensional problems. One fundamental numerical difficulty is that random samples in the training set introduce statistical errors into the discretization of loss functional which may become the dominant error in the final approximation, and therefore overshadow the modeling capability of the neural network. In this work, we propose a new minmax formulation to optimize simultaneously the approximate solution, given by a neural network model, and the random samples in the training set, provided by a deep generative model. The key idea is to use a deep generative model to adjust random samples in the training set such that the residual induced by the approximate PDE solution can maintain a smooth profile when it is being minimized. Such an idea is achieved by implicitly embedding the Wasserstein distance between the residual-induced distribution and the uniform distribution into the loss, which is then minimized together with the residual. A nearly uniform residual profile means that its variance is small for any normalized weight function such that the Monte Carlo approximation error of the loss functional is reduced significantly for a certain sample size. The adversarial adaptive sampling (AAS) approach proposed in this work is the first attempt to formulate two essential components, minimizing the residual and seeking the optimal training set, into one minmax objective functional for the neural network approximation of PDEs.

A fundamental question in modern machine learning is why large, over-parameterized models, such as deep neural networks and transformers, tend to generalize well, even when their number of parameters far exceeds the number of training samples. We investigate this phenomenon through the lens of information theory, grounded in universal learning theory. Specifically, we study a Bayesian mixture learner with log-loss and (almost) uniform prior over an expansive hypothesis class. Our key result shows that the learner's regret is not determined by the overall size of the hypothesis class, but rather by the cumulative probability of all models that are close, in Kullback-Leibler divergence distance, to the true data-generating process. We refer to this cumulative probability as the weight of the hypothesis. This leads to a natural notion of model simplicity: simple models are those with large weight and thus require fewer samples to generalize, while complex models have small weight and need more data. This perspective provides a rigorous and intuitive explanation for why over-parameterized models often avoid overfitting: the presence of simple hypotheses allows the posterior to concentrate on them when supported by the data. We further bridge theory and practice by recalling that stochastic gradient descent with Langevin dynamics samples from the correct posterior distribution, enabling our theoretical learner to be approximated using standard machine learning methods combined with ensemble learning. Our analysis yields non-uniform regret bounds and aligns with key practical concepts such as flat minima and model distillation. The results apply broadly across online, batch, and supervised learning settings, offering a unified and principled understanding of the generalization behavior of modern AI systems.

Despite diffusion models' superior capabilities in modeling complex distributions, there are still non-trivial distributional discrepancies between generated and ground-truth images, which has resulted in several notable problems in image generation, including missing object errors in text-to-image generation and low image quality. Existing methods that attempt to address these problems mostly do not tend to address the fundamental cause behind these problems, which is the distributional discrepancies, and hence achieve sub-optimal results. In this paper, we propose a particle filtering framework that can effectively address both problems by explicitly reducing the distributional discrepancies. Specifically, our method relies on a set of external guidance, including a small set of real images and a pre-trained object detector, to gauge the distribution gap, and then design the resampling weight accordingly to correct the gap. Experiments show that our methods can effectively correct missing object errors and improve image quality in various image generation tasks. Notably, our method outperforms the existing strongest baseline by 5% in object occurrence and 1.0 in FID on MS-COCO. Our code is publicly available at https://github.com/UCSB-NLP-Chang/diffusion_resampling.git.

A key challenge of modern machine learning systems is to achieve Out-of-Distribution (OOD) generalization -- generalizing to target data whose distribution differs from that of source data. Despite its significant importance, the fundamental question of ``what are the most effective algorithms for OOD generalization'' remains open even under the standard setting of covariate shift. This paper addresses this fundamental question by proving that, surprisingly, classical Maximum Likelihood Estimation (MLE) purely using source data (without any modification) achieves the minimax optimality for covariate shift under the well-specified setting. That is, no algorithm performs better than MLE in this setting (up to a constant factor), justifying MLE is all you need. Our result holds for a very rich class of parametric models, and does not require any boundedness condition on the density ratio. We illustrate the wide applicability of our framework by instantiating it to three concrete examples -- linear regression, logistic regression, and phase retrieval. This paper further complement the study by proving that, under the misspecified setting, MLE is no longer the optimal choice, whereas Maximum Weighted Likelihood Estimator (MWLE) emerges as minimax optimal in certain scenarios.

In this work, we propose Reciprocal Distribution Alignment (RDA) to address semi-supervised learning (SSL), which is a hyperparameter-free framework that is independent of confidence threshold and works with both the matched (conventionally) and the mismatched class distributions. Distribution mismatch is an often overlooked but more general SSL scenario where the labeled and the unlabeled data do not fall into the identical class distribution. This may lead to the model not exploiting the labeled data reliably and drastically degrade the performance of SSL methods, which could not be rescued by the traditional distribution alignment. In RDA, we enforce a reciprocal alignment on the distributions of the predictions from two classifiers predicting pseudo-labels and complementary labels on the unlabeled data. These two distributions, carrying complementary information, could be utilized to regularize each other without any prior of class distribution. Moreover, we theoretically show that RDA maximizes the input-output mutual information. Our approach achieves promising performance in SSL under a variety of scenarios of mismatched distributions, as well as the conventional matched SSL setting. Our code is available at: https://github.com/NJUyued/RDA4RobustSSL.

Exemplar-free class-incremental learning (EFCIL) presents a significant challenge as the old class samples are absent for new task learning. Due to the severe imbalance between old and new class samples, the learned classifiers can be easily biased toward the new ones. Moreover, continually updating the feature extractor under EFCIL can compromise the discriminative power of old class features, e.g., leading to less compact and more overlapping distributions across classes. Existing methods mainly focus on handling biased classifier learning. In this work, both cases are considered using the proposed method. Specifically, we first introduce a Distribution-Based Global Classifier (DBGC) to avoid bias factors in existing methods, such as data imbalance and sampling. More importantly, the compromised distributions of old classes are simulated via a simple operation, variance enlarging (VE). Incorporating VE based on DBGC results in a novel classification loss for EFCIL. This loss is proven equivalent to an Adaptive Margin Softmax Cross Entropy (AMarX). The proposed method is thus called Adaptive Margin Global Classifier (AMGC). AMGC is simple yet effective. Extensive experiments show that AMGC achieves superior image classification results on its own under a challenging EFCIL setting. Detailed analysis is also provided for further demonstration.

Ensuring the reliability and safety of automated decision-making is crucial. It is well-known that data distribution shifts in machine learning can produce unreliable outcomes. This paper proposes a new approach for measuring the reliability of predictions under distribution shifts. We analyze how the outputs of a trained neural network change using clustering to measure distances between outputs and class centroids. We propose this distance as a metric to evaluate the confidence of predictions under distribution shifts. We assign each prediction to a cluster with centroid representing the mean softmax output for all correct predictions of a given class. We then define a safety threshold for a class as the smallest distance from an incorrect prediction to the given class centroid. We evaluate the approach on the MNIST and CIFAR-10 datasets using a Convolutional Neural Network and a Vision Transformer, respectively. The results show that our approach is consistent across these data sets and network models, and indicate that the proposed metric can offer an efficient way of determining when automated predictions are acceptable and when they should be deferred to human operators given a distribution shift.

Constructing prediction sets with coverage guarantees for unobserved outcomes is a core problem in modern statistics. Methods for predictive inference have been developed for a wide range of settings, but usually only consider test data points one at a time. Here we study the problem of distribution-free predictive inference for a batch of multiple test points, aiming to construct prediction sets for functions -- such as the mean or median -- of any number of unobserved test datapoints. This setting includes constructing simultaneous prediction sets with a high probability of coverage, and selecting datapoints satisfying a specified condition while controlling the number of false claims. For the general task of predictive inference on a function of a batch of test points, we introduce a methodology called batch predictive inference (batch PI), and provide a distribution-free coverage guarantee under exchangeability of the calibration and test data. Batch PI requires the quantiles of a rank ordering function defined on certain subsets of ranks. While computing these quantiles is NP-hard in general, we show that it can be done efficiently in many cases of interest, most notably for batch score functions with a compositional structure -- which includes examples of interest such as the mean -- via a dynamic programming algorithm that we develop. Batch PI has advantages over naive approaches (such as partitioning the calibration data or directly extending conformal prediction) in many settings, as it can deliver informative prediction sets even using small calibration sample sizes. We illustrate that our procedures provide informative inference across the use cases mentioned above, through experiments on both simulated data and a drug-target interaction dataset.

Digitizing pathological images into gigapixel Whole Slide Images (WSIs) has opened new avenues for Computational Pathology (CPath). As positive tissue comprises only a small fraction of gigapixel WSIs, existing Multiple Instance Learning (MIL) methods typically focus on identifying salient instances via attention mechanisms. However, this leads to a bias towards easy-to-classify instances while neglecting challenging ones. Recent studies have shown that hard examples are crucial for accurately modeling discriminative boundaries. Applying such an idea at the instance level, we elaborate a novel MIL framework with masked hard instance mining (MHIM-MIL), which utilizes a Siamese structure with a consistency constraint to explore the hard instances. Using a class-aware instance probability, MHIM-MIL employs a momentum teacher to mask salient instances and implicitly mine hard instances for training the student model. To obtain diverse, non-redundant hard instances, we adopt large-scale random masking while utilizing a global recycle network to mitigate the risk of losing key features. Furthermore, the student updates the teacher using an exponential moving average, which identifies new hard instances for subsequent training iterations and stabilizes optimization. Experimental results on cancer diagnosis, subtyping, survival analysis tasks, and 12 benchmarks demonstrate that MHIM-MIL outperforms the latest methods in both performance and efficiency. The code is available at: https://github.com/DearCaat/MHIM-MIL.

Data collected from the real world typically exhibit long-tailed distributions, where frequent classes contain abundant data while rare ones have only a limited number of samples. While existing supervised learning approaches have been proposed to tackle such data imbalance, the requirement of label supervision would limit their applicability to real-world scenarios in which label annotation might not be available. Without the access to class labels nor the associated class frequencies, we propose Frequency-Aware Self-Supervised Learning (FASSL) in this paper. Targeting at learning from unlabeled data with inherent long-tailed distributions, the goal of FASSL is to produce discriminative feature representations for downstream classification tasks. In FASSL, we first learn frequency-aware prototypes, reflecting the associated long-tailed distribution. Particularly focusing on rare-class samples, the relationships between image data and the derived prototypes are further exploited with the introduced self-supervised learning scheme. Experiments on long-tailed image datasets quantitatively and qualitatively verify the effectiveness of our learning scheme.

One-shot Neural architecture search (One-shot NAS) has been proposed as a time-efficient approach to obtain optimal subnet architectures and weights under different complexity cases by training only once. However, the subnet performance obtained by weight sharing is often inferior to the performance achieved by retraining. In this paper, we investigate the performance gap and attribute it to the use of uniform sampling, which is a common approach in supernet training. Uniform sampling concentrates training resources on subnets with intermediate computational resources, which are sampled with high probability. However, subnets with different complexity regions require different optimal training strategies for optimal performance. To address the problem of uniform sampling, we propose ShiftNAS, a method that can adjust the sampling probability based on the complexity of subnets. We achieve this by evaluating the performance variation of subnets with different complexity and designing an architecture generator that can accurately and efficiently provide subnets with the desired complexity. Both the sampling probability and the architecture generator can be trained end-to-end in a gradient-based manner. With ShiftNAS, we can directly obtain the optimal model architecture and parameters for a given computational complexity. We evaluate our approach on multiple visual network models, including convolutional neural networks (CNNs) and vision transformers (ViTs), and demonstrate that ShiftNAS is model-agnostic. Experimental results on ImageNet show that ShiftNAS can improve the performance of one-shot NAS without additional consumption. Source codes are available at https://github.com/bestfleer/ShiftNAS.

We tackle the problem of novel class discovery, which aims to learn novel classes without supervision based on labeled data from known classes. A key challenge lies in transferring the knowledge in the known-class data to the learning of novel classes. Previous methods mainly focus on building a shared representation space for knowledge transfer and often ignore modeling class relations. To address this, we introduce a class relation representation for the novel classes based on the predicted class distribution of a model trained on known classes. Empirically, we find that such class relation becomes less informative during typical discovery training. To prevent such information loss, we propose a novel knowledge distillation framework, which utilizes our class-relation representation to regularize the learning of novel classes. In addition, to enable a flexible knowledge distillation scheme for each data point in novel classes, we develop a learnable weighting function for the regularization, which adaptively promotes knowledge transfer based on the semantic similarity between the novel and known classes. To validate the effectiveness and generalization of our method, we conduct extensive experiments on multiple benchmarks, including CIFAR100, Stanford Cars, CUB, and FGVC-Aircraft datasets. Our results demonstrate that the proposed method outperforms the previous state-of-the-art methods by a significant margin on almost all benchmarks. Code is available at https://github.com/kleinzcy/Cr-KD-NCD{here}.

This work considers the category distribution heterogeneity in federated learning. This issue is due to biased labeling preferences at multiple clients and is a typical setting of data heterogeneity. To alleviate this issue, most previous works consider either regularizing local models or fine-tuning the global model, while they ignore the adjustment of aggregation weights and simply assign weights based on the dataset size. However, based on our empirical observations and theoretical analysis, we find that the dataset size is not optimal and the discrepancy between local and global category distributions could be a beneficial and complementary indicator for determining aggregation weights. We thus propose a novel aggregation method, Federated Learning with Discrepancy-aware Collaboration (FedDisco), whose aggregation weights not only involve both the dataset size and the discrepancy value, but also contribute to a tighter theoretical upper bound of the optimization error. FedDisco also promotes privacy-preservation, communication and computation efficiency, as well as modularity. Extensive experiments show that our FedDisco outperforms several state-of-the-art methods and can be easily incorporated with many existing methods to further enhance the performance. Our code will be available at https://github.com/MediaBrain-SJTU/FedDisco.

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.

The concept class of low-degree polynomial threshold functions (PTFs) plays a fundamental role in machine learning. In this paper, we study PAC learning of K-sparse degree-d PTFs on R^n, where any such concept depends only on K out of n attributes of the input. Our main contribution is a new algorithm that runs in time ({nd}/{epsilon})^{O(d)} and under the Gaussian marginal distribution, PAC learns the class up to error rate epsilon with O(K^{4d}{epsilon^{2d}} cdot log^{5d} n) samples even when an eta leq O(epsilon^d) fraction of them are corrupted by the nasty noise of Bshouty et al. (2002), possibly the strongest corruption model. Prior to this work, attribute-efficient robust algorithms are established only for the special case of sparse homogeneous halfspaces. Our key ingredients are: 1) a structural result that translates the attribute sparsity to a sparsity pattern of the Chow vector under the basis of Hermite polynomials, and 2) a novel attribute-efficient robust Chow vector estimation algorithm which uses exclusively a restricted Frobenius norm to either certify a good approximation or to validate a sparsity-induced degree-2d polynomial as a filter to detect corrupted samples.

Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of probability theory. Programs may use both higher-order functions and continuous distributions, or even define a probability distribution on functions. But standard probability theory does not handle higher-order functions well: the category of measurable spaces is not cartesian closed. Here we introduce quasi-Borel spaces. We show that these spaces: form a new formalization of probability theory replacing measurable spaces; form a cartesian closed category and so support higher-order functions; form a well-pointed category and so support good proof principles for equational reasoning; and support continuous probability distributions. We demonstrate the use of quasi-Borel spaces for higher-order functions and probability by: showing that a well-known construction of probability theory involving random functions gains a cleaner expression; and generalizing de Finetti's theorem, that is a crucial theorem in probability theory, to quasi-Borel spaces.

A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally tractable. Here, we develop an approach that simultaneously achieves both flexibility and tractability. The essential idea, inspired by non-equilibrium statistical physics, is to systematically and slowly destroy structure in a data distribution through an iterative forward diffusion process. We then learn a reverse diffusion process that restores structure in data, yielding a highly flexible and tractable generative model of the data. This approach allows us to rapidly learn, sample from, and evaluate probabilities in deep generative models with thousands of layers or time steps, as well as to compute conditional and posterior probabilities under the learned model. We additionally release an open source reference implementation of the algorithm.

Addressing imbalanced or long-tailed data is a major challenge in visual recognition tasks due to disparities between training and testing distributions and issues with data noise. We propose the Wrapped Cauchy Distributed Angular Softmax (WCDAS), a novel softmax function that incorporates data-wise Gaussian-based kernels into the angular correlation between feature representations and classifier weights, effectively mitigating noise and sparse sampling concerns. The class-wise distribution of angular representation becomes a sum of these kernels. Our theoretical analysis reveals that the wrapped Cauchy distribution excels the Gaussian distribution in approximating mixed distributions. Additionally, WCDAS uses trainable concentration parameters to dynamically adjust the compactness and margin of each class. Empirical results confirm label-aware behavior in these parameters and demonstrate WCDAS's superiority over other state-of-the-art softmax-based methods in handling long-tailed visual recognition across multiple benchmark datasets. The code is public available.

We prove that under the heat semigroup (P_τ) on the Boolean hypercube, any nonnegative function f: {-1,1}^n to R_+ exhibits a uniform tail bound that is better than that by Markov's inequality. Specifically, for any η> e^3 and τ> 0, align* P_{X \sim μ}\left( P_τf(X) > η\int f dμ\right) \leq c_τ \log \log η{η\log η}, align* where μ is the uniform measure on the Boolean hypercube {-1,1}^n and c_τ is a constant that only depends on τ. This resolves Talagrand's convolution conjecture up to a dimension-free loglog η factor. Its proof relies on properties of the reverse heat process on the Boolean hypercube and a coupling construction based on carefully engineered perturbations of this reverse heat process.

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

Most of the existing Out-Of-Distribution (OOD) detection algorithms depend on single input source: the feature, the logit, or the softmax probability. However, the immense diversity of the OOD examples makes such methods fragile. There are OOD samples that are easy to identify in the feature space while hard to distinguish in the logit space and vice versa. Motivated by this observation, we propose a novel OOD scoring method named Virtual-logit Matching (ViM), which combines the class-agnostic score from feature space and the In-Distribution (ID) class-dependent logits. Specifically, an additional logit representing the virtual OOD class is generated from the residual of the feature against the principal space, and then matched with the original logits by a constant scaling. The probability of this virtual logit after softmax is the indicator of OOD-ness. To facilitate the evaluation of large-scale OOD detection in academia, we create a new OOD dataset for ImageNet-1K, which is human-annotated and is 8.8x the size of existing datasets. We conducted extensive experiments, including CNNs and vision transformers, to demonstrate the effectiveness of the proposed ViM score. In particular, using the BiT-S model, our method gets an average AUROC 90.91% on four difficult OOD benchmarks, which is 4% ahead of the best baseline. Code and dataset are available at https://github.com/haoqiwang/vim.

We study the realizability of simplicial complexes with a given pair of integer sequences, representing the node degree distribution and the facet size distribution, respectively. While the s-uniform variant of the problem is NP-complete when s geq 3, we identify two populations of input sequences, most of which can be solved in polynomial time using a recursive algorithm that we contribute. Combining with a sampler for the simplicial configuration model [J.-G. Young et al., Phys. Rev. E 96, 032312 (2017)], we facilitate the efficient sampling of simplicial ensembles from arbitrary degree and size distributions. We find that, contrary to expectations based on dyadic networks, increasing the nodes' degrees reduces the number of loops in simplicial complexes. Our work unveils a fundamental constraint on the degree-size sequences and sheds light on further analysis of higher-order phenomena based on local structures.

Recently, Qiao, Duan, and Cheng~(2019) proposed a distributed nearest-neighbor classification method, in which a massive dataset is split into smaller groups, each processed with a k-nearest-neighbor classifier, and the final class label is predicted by a majority vote among these groupwise class labels. This paper shows that the distributed algorithm with k=1 over a sufficiently large number of groups attains a minimax optimal error rate up to a multiplicative logarithmic factor under some regularity conditions, for both regression and classification problems. Roughly speaking, distributed 1-nearest-neighbor rules with M groups has a performance comparable to standard Theta(M)-nearest-neighbor rules. In the analysis, alternative rules with a refined aggregation method are proposed and shown to attain exact minimax optimal rates.

Machine learning models frequently experience performance drops under distribution shifts. The underlying cause of such shifts may be multiple simultaneous factors such as changes in data quality, differences in specific covariate distributions, or changes in the relationship between label and features. When a model does fail during deployment, attributing performance change to these factors is critical for the model developer to identify the root cause and take mitigating actions. In this work, we introduce the problem of attributing performance differences between environments to distribution shifts in the underlying data generating mechanisms. We formulate the problem as a cooperative game where the players are distributions. We define the value of a set of distributions to be the change in model performance when only this set of distributions has changed between environments, and derive an importance weighting method for computing the value of an arbitrary set of distributions. The contribution of each distribution to the total performance change is then quantified as its Shapley value. We demonstrate the correctness and utility of our method on synthetic, semi-synthetic, and real-world case studies, showing its effectiveness in attributing performance changes to a wide range of distribution shifts.

Distribution shifts -- where the training distribution differs from the test distribution -- can substantially degrade the accuracy of machine learning (ML) systems deployed in the wild. Despite their ubiquity in the real-world deployments, these distribution shifts are under-represented in the datasets widely used in the ML community today. To address this gap, we present WILDS, a curated benchmark of 10 datasets reflecting a diverse range of distribution shifts that naturally arise in real-world applications, such as shifts across hospitals for tumor identification; across camera traps for wildlife monitoring; and across time and location in satellite imaging and poverty mapping. On each dataset, we show that standard training yields substantially lower out-of-distribution than in-distribution performance. This gap remains even with models trained by existing methods for tackling distribution shifts, underscoring the need for new methods for training models that are more robust to the types of distribution shifts that arise in practice. To facilitate method development, we provide an open-source package that automates dataset loading, contains default model architectures and hyperparameters, and standardizes evaluations. Code and leaderboards are available at https://wilds.stanford.edu.

Recognition problems in long-tailed data, in which the sample size per class is heavily skewed, have gained importance because the distribution of the sample size per class in a dataset is generally exponential unless the sample size is intentionally adjusted. Various methods have been devised to address these problems. Recently, weight balancing, which combines well-known classical regularization techniques with two-stage training, has been proposed. Despite its simplicity, it is known for its high performance compared with existing methods devised in various ways. However, there is a lack of understanding as to why this method is effective for long-tailed data. In this study, we analyze weight balancing by focusing on neural collapse and the cone effect at each training stage and found that it can be decomposed into an increase in Fisher's discriminant ratio of the feature extractor caused by weight decay and cross entropy loss and implicit logit adjustment caused by weight decay and class-balanced loss. Our analysis enables the training method to be further simplified by reducing the number of training stages to one while increasing accuracy.

A large-scale deep model pre-trained on massive labeled or unlabeled data transfers well to downstream tasks. Linear evaluation freezes parameters in the pre-trained model and trains a linear classifier separately, which is efficient and attractive for transfer. However, little work has investigated the classifier in linear evaluation except for the default logistic regression. Inspired by the statistical efficiency of naive Bayes, the paper revisits the classical topic on discriminative vs. generative classifiers. Theoretically, the paper considers the surrogate loss instead of the zero-one loss in analyses and generalizes the classical results from binary cases to multiclass ones. We show that, under mild assumptions, multiclass naive Bayes requires O(log n) samples to approach its asymptotic error while the corresponding multiclass logistic regression requires O(n) samples, where n is the feature dimension. To establish it, we present a multiclass H-consistency bound framework and an explicit bound for logistic loss, which are of independent interests. Simulation results on a mixture of Gaussian validate our theoretical findings. Experiments on various pre-trained deep vision models show that naive Bayes consistently converges faster as the number of data increases. Besides, naive Bayes shows promise in few-shot cases and we observe the "two regimes" phenomenon in pre-trained supervised models. Our code is available at https://github.com/ML-GSAI/Revisiting-Dis-vs-Gen-Classifiers.

Categorical variables are a natural choice for representing discrete structure in the world. However, stochastic neural networks rarely use categorical latent variables due to the inability to backpropagate through samples. In this work, we present an efficient gradient estimator that replaces the non-differentiable sample from a categorical distribution with a differentiable sample from a novel Gumbel-Softmax distribution. This distribution has the essential property that it can be smoothly annealed into a categorical distribution. We show that our Gumbel-Softmax estimator outperforms state-of-the-art gradient estimators on structured output prediction and unsupervised generative modeling tasks with categorical latent variables, and enables large speedups on semi-supervised classification.

In this paper we argue for the fundamental importance of the value distribution: the distribution of the random return received by a reinforcement learning agent. This is in contrast to the common approach to reinforcement learning which models the expectation of this return, or value. Although there is an established body of literature studying the value distribution, thus far it has always been used for a specific purpose such as implementing risk-aware behaviour. We begin with theoretical results in both the policy evaluation and control settings, exposing a significant distributional instability in the latter. We then use the distributional perspective to design a new algorithm which applies Bellman's equation to the learning of approximate value distributions. We evaluate our algorithm using the suite of games from the Arcade Learning Environment. We obtain both state-of-the-art results and anecdotal evidence demonstrating the importance of the value distribution in approximate reinforcement learning. Finally, we combine theoretical and empirical evidence to highlight the ways in which the value distribution impacts learning in the approximate setting.

We study the problem of estimating the distribution of the return of a policy using an offline dataset that is not generated from the policy, i.e., distributional offline policy evaluation (OPE). We propose an algorithm called Fitted Likelihood Estimation (FLE), which conducts a sequence of Maximum Likelihood Estimation (MLE) and has the flexibility of integrating any state-of-the-art probabilistic generative models as long as it can be trained via MLE. FLE can be used for both finite-horizon and infinite-horizon discounted settings where rewards can be multi-dimensional vectors. Our theoretical results show that for both finite-horizon and infinite-horizon discounted settings, FLE can learn distributions that are close to the ground truth under total variation distance and Wasserstein distance, respectively. Our theoretical results hold under the conditions that the offline data covers the test policy's traces and that the supervised learning MLE procedures succeed. Experimentally, we demonstrate the performance of FLE with two generative models, Gaussian mixture models and diffusion models. For the multi-dimensional reward setting, FLE with diffusion models is capable of estimating the complicated distribution of the return of a test policy.

The study of universal approximation properties (UAP) for neural networks (NN) has a long history. When the network width is unlimited, only a single hidden layer is sufficient for UAP. In contrast, when the depth is unlimited, the width for UAP needs to be not less than the critical width w^*_{min}=max(d_x,d_y), where d_x and d_y are the dimensions of the input and output, respectively. Recently, cai2022achieve shows that a leaky-ReLU NN with this critical width can achieve UAP for L^p functions on a compact domain K, i.e., the UAP for L^p(K,R^{d_y}). This paper examines a uniform UAP for the function class C(K,R^{d_y}) and gives the exact minimum width of the leaky-ReLU NN as w_{min}=max(d_x+1,d_y)+1_{d_y=d_x+1}, which involves the effects of the output dimensions. To obtain this result, we propose a novel lift-flow-discretization approach that shows that the uniform UAP has a deep connection with topological theory.

Generating functions, which are widely used in combinatorics and probability theory, encode function values into the coefficients of a polynomial. In this paper, we explore their use as a tractable probabilistic model, and propose probabilistic generating circuits (PGCs) for their efficient representation. PGCs are strictly more expressive efficient than many existing tractable probabilistic models, including determinantal point processes (DPPs), probabilistic circuits (PCs) such as sum-product networks, and tractable graphical models. We contend that PGCs are not just a theoretical framework that unifies vastly different existing models, but also show great potential in modeling realistic data. We exhibit a simple class of PGCs that are not trivially subsumed by simple combinations of PCs and DPPs, and obtain competitive performance on a suite of density estimation benchmarks. We also highlight PGCs' connection to the theory of strongly Rayleigh distributions.

Diffusion models for continuous data gained widespread adoption owing to their high quality generation and control mechanisms. However, controllable diffusion on discrete data faces challenges given that continuous guidance methods do not directly apply to discrete diffusion. Here, we provide a straightforward derivation of classifier-free and classifier-based guidance for discrete diffusion, as well as a new class of diffusion models that leverage uniform noise and that are more guidable because they can continuously edit their outputs. We improve the quality of these models with a novel continuous-time variational lower bound that yields state-of-the-art performance, especially in settings involving guidance or fast generation. Empirically, we demonstrate that our guidance mechanisms combined with uniform noise diffusion improve controllable generation relative to autoregressive and diffusion baselines on several discrete data domains, including genomic sequences, small molecule design, and discretized image generation.