Daily Papers

Learning the tail behavior of a distribution is a notoriously difficult problem. By definition, the number of samples from the tail is small, and deep generative models, such as normalizing flows, tend to concentrate on learning the body of the distribution. In this paper, we focus on improving the ability of normalizing flows to correctly capture the tail behavior and, thus, form more accurate models. We prove that the marginal tailedness of an autoregressive flow can be controlled via the tailedness of the marginals of its base distribution. This theoretical insight leads us to a novel type of flows based on flexible base distributions and data-driven linear layers. An empirical analysis shows that the proposed method improves on the accuracy -- especially on the tails of the distribution -- and is able to generate heavy-tailed data. We demonstrate its application on a weather and climate example, in which capturing the tail behavior is essential.

We introduce a general, flexible, parametric survival modelling framework which encompasses key shapes of hazard function (constant, increasing, decreasing, up-then-down, down-then-up), various common survival distributions (log-logistic, Burr type XII, Weibull, Gompertz), and includes defective distributions (i.e., cure models). This generality is achieved using four basic distributional parameters: two scale-type parameters and two shape parameters. Generalising to covariate dependence, the scale-type regression components correspond to accelerated failure time (AFT) and proportional hazards (PH) models. Therefore, this general formulation unifies the most popular survival models which allows us to consider the practical value of possible modelling choices for survival data. Furthermore, in line with our proposed flexible baseline distribution, we advocate the use of multi-parameter regression in which more than one distributional parameter depends on covariates - rather than the usual convention of having a single covariate-dependent (scale) parameter. While many choices are available, we suggest introducing covariates through just one or other of the two scale parameters, which covers AFT and PH models, in combination with a `power' shape parameter, which allows for more complex non-AFT/non-PH effects, while the other shape parameter remains covariate-independent, and handles automatic selection of the baseline distribution. We explore inferential issues in simulations, both with and without a covariate, with particular focus on evidence concerning the need, or otherwise, to include both AFT and PH parameters. We illustrate the efficacy of our modelling framework by investigating differences between treatment groups using data from a lung cancer study and a melanoma study. Censoring is accommodated throughout.

In machine learning, generalization against distribution shifts -- where deployment conditions diverge from the training scenarios -- is crucial, particularly in fields like climate modeling, biomedicine, and autonomous driving. The emergence of foundation models, distinguished by their extensive pretraining and task versatility, has led to an increased interest in their adaptability to distribution shifts. GPT-4V(ision) acts as the most advanced publicly accessible multimodal foundation model, with extensive applications across various domains, including anomaly detection, video understanding, image generation, and medical diagnosis. However, its robustness against data distributions remains largely underexplored. Addressing this gap, this study rigorously evaluates GPT-4V's adaptability and generalization capabilities in dynamic environments, benchmarking against prominent models like CLIP and LLaVA. We delve into GPT-4V's zero-shot generalization across 13 diverse datasets spanning natural, medical, and molecular domains. We further investigate its adaptability to controlled data perturbations and examine the efficacy of in-context learning as a tool to enhance its adaptation. Our findings delineate GPT-4V's capability boundaries in distribution shifts, shedding light on its strengths and limitations across various scenarios. Importantly, this investigation contributes to our understanding of how AI foundation models generalize to distribution shifts, offering pivotal insights into their adaptability and robustness. Code is publicly available at https://github.com/jameszhou-gl/gpt-4v-distribution-shift.

Split conformal prediction has recently sparked great interest due to its ability to provide formally guaranteed uncertainty sets or intervals for predictions made by black-box neural models, ensuring a predefined probability of containing the actual ground truth. While the original formulation assumes data exchangeability, some extensions handle non-exchangeable data, which is often the case in many real-world scenarios. In parallel, some progress has been made in conformal methods that provide statistical guarantees for a broader range of objectives, such as bounding the best F_1-score or minimizing the false negative rate in expectation. In this paper, we leverage and extend these two lines of work by proposing non-exchangeable conformal risk control, which allows controlling the expected value of any monotone loss function when the data is not exchangeable. Our framework is flexible, makes very few assumptions, and allows weighting the data based on its relevance for a given test example; a careful choice of weights may result on tighter bounds, making our framework useful in the presence of change points, time series, or other forms of distribution drift. Experiments with both synthetic and real world data show the usefulness of our method.

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.

Large-scale commercial platforms usually involve numerous business domains for diverse business strategies and expect their recommendation systems to provide click-through rate (CTR) predictions for multiple domains simultaneously. Existing promising and widely-used multi-domain models discover domain relationships by explicitly constructing domain-specific networks, but the computation and memory boost significantly with the increase of domains. To reduce computational complexity, manually grouping domains with particular business strategies is common in industrial applications. However, this pre-defined data partitioning way heavily relies on prior knowledge, and it may neglect the underlying data distribution of each domain, hence limiting the model's representation capability. Regarding the above issues, we propose an elegant and flexible multi-distribution modeling paradigm, named Adaptive Distribution Hierarchical Model (AdaptDHM), which is an end-to-end optimization hierarchical structure consisting of a clustering process and classification process. Specifically, we design a distribution adaptation module with a customized dynamic routing mechanism. Instead of introducing prior knowledge for pre-defined data allocation, this routing algorithm adaptively provides a distribution coefficient for each sample to determine which cluster it belongs to. Each cluster corresponds to a particular distribution so that the model can sufficiently capture the commonalities and distinctions between these distinct clusters. Extensive experiments on both public and large-scale Alibaba industrial datasets verify the effectiveness and efficiency of AdaptDHM: Our model achieves impressive prediction accuracy and its time cost during the training stage is more than 50% less than that of other models.

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.

Masked diffusion models (MDMs) have recently emerged as a promising alternative to autoregressive models over discrete domains. MDMs generate sequences in an any-order, parallel fashion, enabling fast inference and strong performance on non-causal tasks. However, a crucial limitation is that they do not support token insertions and are thus limited to fixed-length generations. To this end, we introduce Flexible Masked Diffusion Models (FlexMDMs), a discrete diffusion paradigm that simultaneously can model sequences of flexible length while provably retaining MDMs' flexibility of any-order inference. Grounded in an extension of the stochastic interpolant framework, FlexMDMs generate sequences by inserting mask tokens and unmasking them. Empirically, we show that FlexMDMs match MDMs in perplexity while modeling length statistics with much higher fidelity. On a synthetic maze planning task, they achieve approx 60 % higher success rate than MDM baselines. Finally, we show pretrained MDMs can easily be retrofitted into FlexMDMs: on 16 H100s, it takes only three days to fine-tune LLaDA-8B into a FlexMDM, achieving superior performance on math (GSM8K, 58% to 67%) and code infilling performance (52% to 65%).

While previous distribution shift detection approaches can identify if a shift has occurred, these approaches cannot localize which specific features have caused a distribution shift -- a critical step in diagnosing or fixing any underlying issue. For example, in military sensor networks, users will want to detect when one or more of the sensors has been compromised, and critically, they will want to know which specific sensors might be compromised. Thus, we first define a formalization of this problem as multiple conditional distribution hypothesis tests and propose both non-parametric and parametric statistical tests. For both efficiency and flexibility, we then propose to use a test statistic based on the density model score function (i.e. gradient with respect to the input) -- which can easily compute test statistics for all dimensions in a single forward and backward pass. Any density model could be used for computing the necessary statistics including deep density models such as normalizing flows or autoregressive models. We additionally develop methods for identifying when and where a shift occurs in multivariate time-series data and show results for multiple scenarios using realistic attack models on both simulated and real world data.

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.

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.

This work studies discrete diffusion probabilistic models with applications to natural language generation. We derive an alternative yet equivalent formulation of the sampling from discrete diffusion processes and leverage this insight to develop a family of reparameterized discrete diffusion models. The derived generic framework is highly flexible, offers a fresh perspective of the generation process in discrete diffusion models, and features more effective training and decoding techniques. We conduct extensive experiments to evaluate the text generation capability of our model, demonstrating significant improvements over existing diffusion models.

The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference, focusing on mean-field or other simple structured approximations. This restriction has a significant impact on the quality of inferences made using variational methods. We introduce a new approach for specifying flexible, arbitrarily complex and scalable approximate posterior distributions. Our approximations are distributions constructed through a normalizing flow, whereby a simple initial density is transformed into a more complex one by applying a sequence of invertible transformations until a desired level of complexity is attained. We use this view of normalizing flows to develop categories of finite and infinitesimal flows and provide a unified view of approaches for constructing rich posterior approximations. We demonstrate that the theoretical advantages of having posteriors that better match the true posterior, combined with the scalability of amortized variational approaches, provides a clear improvement in performance and applicability of variational inference.

We propose a Distributional Approach for addressing Controlled Text Generation from pre-trained Language Models (LMs). This approach permits to specify, in a single formal framework, both "pointwise" and "distributional" constraints over the target LM -- to our knowledge, the first model with such generality -- while minimizing KL divergence from the initial LM distribution. The optimal target distribution is then uniquely determined as an explicit EBM (Energy-Based Model) representation. From that optimal representation we then train a target controlled Autoregressive LM through an adaptive distributional variant of Policy Gradient. We conduct a first set of experiments over pointwise constraints showing the advantages of our approach over a set of baselines, in terms of obtaining a controlled LM balancing constraint satisfaction with divergence from the initial LM. We then perform experiments over distributional constraints, a unique feature of our approach, demonstrating its potential as a remedy to the problem of Bias in Language Models. Through an ablation study, we show the effectiveness of our adaptive technique for obtaining faster convergence. (Code available at https://github.com/naver/gdc)

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.

Many real-world problems require reasoning across multiple scales, demanding models which operate not on single data points, but on entire distributions. We introduce generative distribution embeddings (GDE), a framework that lifts autoencoders to the space of distributions. In GDEs, an encoder acts on sets of samples, and the decoder is replaced by a generator which aims to match the input distribution. This framework enables learning representations of distributions by coupling conditional generative models with encoder networks which satisfy a criterion we call distributional invariance. We show that GDEs learn predictive sufficient statistics embedded in the Wasserstein space, such that latent GDE distances approximately recover the W_2 distance, and latent interpolation approximately recovers optimal transport trajectories for Gaussian and Gaussian mixture distributions. We systematically benchmark GDEs against existing approaches on synthetic datasets, demonstrating consistently stronger performance. We then apply GDEs to six key problems in computational biology: learning representations of cell populations from lineage-tracing data (150K cells), predicting perturbation effects on single-cell transcriptomes (1M cells), predicting perturbation effects on cellular phenotypes (20M single-cell images), modeling tissue-specific DNA methylation patterns (253M sequences), designing synthetic yeast promoters (34M sequences), and spatiotemporal modeling of viral protein sequences (1M sequences).

Molecules are frequently represented as graphs, but the underlying 3D molecular geometry (the locations of the atoms) ultimately determines most molecular properties. However, most molecules are not static and at room temperature adopt a wide variety of geometries or conformations. The resulting distribution on geometries p(x) is known as the Boltzmann distribution, and many molecular properties are expectations computed under this distribution. Generating accurate samples from the Boltzmann distribution is therefore essential for computing these expectations accurately. Traditional sampling-based methods are computationally expensive, and most recent machine learning-based methods have focused on identifying modes in this distribution rather than generating true samples. Generating such samples requires capturing conformational variability, and it has been widely recognized that the majority of conformational variability in molecules arises from rotatable bonds. In this work, we present VonMisesNet, a new graph neural network that captures conformational variability via a variational approximation of rotatable bond torsion angles as a mixture of von Mises distributions. We demonstrate that VonMisesNet can generate conformations for arbitrary molecules in a way that is both physically accurate with respect to the Boltzmann distribution and orders of magnitude faster than existing sampling methods.

Language models (LM) are capable of remarkably complex linguistic tasks; however, numerical reasoning is an area in which they frequently struggle. An important but rarely evaluated form of reasoning is understanding probability distributions. In this paper, we focus on evaluating the probabilistic reasoning capabilities of LMs using idealized and real-world statistical distributions. We perform a systematic evaluation of state-of-the-art LMs on three tasks: estimating percentiles, drawing samples, and calculating probabilities. We evaluate three ways to provide context to LMs 1) anchoring examples from within a distribution or family of distributions, 2) real-world context, 3) summary statistics on which to base a Normal approximation. Models can make inferences about distributions, and can be further aided by the incorporation of real-world context, example shots and simplified assumptions, even if these assumptions are incorrect or misspecified. To conduct this work, we developed a comprehensive benchmark distribution dataset with associated question-answer pairs that we will release publicly.

Scaling laws offer valuable insights into the design of time series foundation models (TSFMs). However, previous research has largely focused on the scaling laws of TSFMs for in-distribution (ID) data, leaving their out-of-distribution (OOD) scaling behavior and the influence of model architectures less explored. In this work, we examine two common TSFM architectures, encoder-only and decoder-only Transformers, and investigate their scaling behavior on both ID and OOD data. These models are trained and evaluated across varying parameter counts, compute budgets, and dataset sizes. Our experiments reveal that the log-likelihood loss of TSFMs exhibits similar scaling behavior in both OOD and ID settings. We further compare the scaling properties across different architectures, incorporating two state-of-the-art TSFMs as case studies, showing that model architecture plays a significant role in scaling. The encoder-only Transformers demonstrate better scalability than the decoder-only Transformers, while the architectural enhancements in the two advanced TSFMs primarily improve ID performance but reduce OOD scalability. While scaling up TSFMs is expected to drive performance breakthroughs, the lack of a comprehensive understanding of TSFM scaling laws has hindered the development of a robust framework to guide model scaling. We fill this gap in this work by synthesizing our findings and providing practical guidelines for designing and scaling larger TSFMs with enhanced model capabilities.

We propose a new approach for propagating stable probability distributions through neural networks. Our method is based on local linearization, which we show to be an optimal approximation in terms of total variation distance for the ReLU non-linearity. This allows propagating Gaussian and Cauchy input uncertainties through neural networks to quantify their output uncertainties. To demonstrate the utility of propagating distributions, we apply the proposed method to predicting calibrated confidence intervals and selective prediction on out-of-distribution data. The results demonstrate a broad applicability of propagating distributions and show the advantages of our method over other approaches such as moment matching.

In this paper, we present a novel approach to accelerate the Bayesian inference process, focusing specifically on the nested sampling algorithms. Bayesian inference plays a crucial role in cosmological parameter estimation, providing a robust framework for extracting theoretical insights from observational data. However, its computational demands can be substantial, primarily due to the need for numerous likelihood function evaluations. Our proposed method utilizes the power of deep learning, employing feedforward neural networks to approximate the likelihood function dynamically during the Bayesian inference process. Unlike traditional approaches, our method trains neural networks on-the-fly using the current set of live points as training data, without the need for pre-training. This flexibility enables adaptation to various theoretical models and datasets. We perform simple hyperparameter optimization using genetic algorithms to suggest initial neural network architectures for learning each likelihood function. Once sufficient accuracy is achieved, the neural network replaces the original likelihood function. The implementation integrates with nested sampling algorithms and has been thoroughly evaluated using both simple cosmological dark energy models and diverse observational datasets. Additionally, we explore the potential of genetic algorithms for generating initial live points within nested sampling inference, opening up new avenues for enhancing the efficiency and effectiveness of Bayesian inference methods.

Generative models inspired by dynamical transport of measure -- such as flows and diffusions -- construct a continuous-time map between two probability densities. Conventionally, one of these is the target density, only accessible through samples, while the other is taken as a simple base density that is data-agnostic. In this work, using the framework of stochastic interpolants, we formalize how to couple the base and the target densities. This enables us to incorporate information about class labels or continuous embeddings to construct dynamical transport maps that serve as conditional generative models. We show that these transport maps can be learned by solving a simple square loss regression problem analogous to the standard independent setting. We demonstrate the usefulness of constructing dependent couplings in practice through experiments in super-resolution and in-painting.

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.

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

We study 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.

Adapting a pre-trained foundation model on downstream tasks should ensure robustness against distribution shifts without the need to retrain the whole model. Although existing weight interpolation methods are simple yet effective, we argue their static nature limits downstream performance while achieving efficiency. In this work, we propose DaWin, a training-free dynamic weight interpolation method that leverages the entropy of individual models over each unlabeled test sample to assess model expertise, and compute per-sample interpolation coefficients dynamically. Unlike previous works that typically rely on additional training to learn such coefficients, our approach requires no training. Then, we propose a mixture modeling approach that greatly reduces inference overhead raised by dynamic interpolation. We validate DaWin on the large-scale visual recognition benchmarks, spanning 14 tasks across robust fine-tuning -- ImageNet and derived five distribution shift benchmarks -- and multi-task learning with eight classification tasks. Results demonstrate that DaWin achieves significant performance gain in considered settings, with minimal computational overhead. We further discuss DaWin's analytic behavior to explain its empirical success.

As black-box models increasingly power high-stakes applications, a variety of data-driven explanation methods have been introduced. Meanwhile, machine learning models are constantly challenged by distributional shifts. A question naturally arises: Are data-driven explanations robust against out-of-distribution data? Our empirical results show that even though predict correctly, the model might still yield unreliable explanations under distributional shifts. How to develop robust explanations against out-of-distribution data? To address this problem, we propose an end-to-end model-agnostic learning framework Distributionally Robust Explanations (DRE). The key idea is, inspired by self-supervised learning, to fully utilizes the inter-distribution information to provide supervisory signals for the learning of explanations without human annotation. Can robust explanations benefit the model's generalization capability? We conduct extensive experiments on a wide range of tasks and data types, including classification and regression on image and scientific tabular data. Our results demonstrate that the proposed method significantly improves the model's performance in terms of explanation and prediction robustness against distributional shifts.

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

Despite their remarkable performance, modern Diffusion Transformers are hindered by substantial resource requirements during inference, stemming from the fixed and large amount of compute needed for each denoising step. In this work, we revisit the conventional static paradigm that allocates a fixed compute budget per denoising iteration and propose a dynamic strategy instead. Our simple and sample-efficient framework enables pre-trained DiT models to be converted into flexible ones -- dubbed FlexiDiT -- allowing them to process inputs at varying compute budgets. We demonstrate how a single flexible model can generate images without any drop in quality, while reducing the required FLOPs by more than 40\% compared to their static counterparts, for both class-conditioned and text-conditioned image generation. Our method is general and agnostic to input and conditioning modalities. We show how our approach can be readily extended for video generation, where FlexiDiT models generate samples with up to 75\% less compute without compromising performance.

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.

Masked language models (MLM) do not explicitly define a distribution over language, i.e., they are not language models per se. However, recent work has implicitly treated them as such for the purposes of generation and scoring. This paper studies methods for deriving explicit joint distributions from MLMs, focusing on distributions over two tokens, which makes it possible to calculate exact distributional properties. We find that an approach based on identifying joints whose conditionals are closest to those of the MLM works well and outperforms existing Markov random field-based approaches. We further find that this derived model's conditionals can even occasionally outperform the original MLM's conditionals.

Popular approaches for quantifying predictive uncertainty in deep neural networks often involve distributions over weights or multiple models, for instance via Markov Chain sampling, ensembling, or Monte Carlo dropout. These techniques usually incur overhead by having to train multiple model instances or do not produce very diverse predictions. This comprehensive and extensive survey aims to familiarize the reader with an alternative class of models based on the concept of Evidential Deep Learning: For unfamiliar data, they aim to admit "what they don't know", and fall back onto a prior belief. Furthermore, they allow uncertainty estimation in a single model and forward pass by parameterizing distributions over distributions. This survey recapitulates existing works, focusing on the implementation in a classification setting, before surveying the application of the same paradigm to regression. We also reflect on the strengths and weaknesses compared to other existing methods and provide the most fundamental derivations using a unified notation to aid future research.

While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However, existing methods are often computationally expensive, or demand costly retraining when priors change, limiting their utility, particularly in sequential inference problems such as real-time sensor fusion. To address these challenges, we introduce the Distribution Transformer -- a novel architecture that can learn arbitrary distribution-to-distribution mappings. Our method can be trained to map a prior to the corresponding posterior, conditioned on some dataset -- thus performing approximate Bayesian inference. Our novel architecture represents a prior distribution as a (universally-approximating) Gaussian Mixture Model (GMM), and transforms it into a GMM representation of the posterior. The components of the GMM attend to each other via self-attention, and to the datapoints via cross-attention. We demonstrate that Distribution Transformers both maintain flexibility to vary the prior, and significantly reduces computation times-from minutes to milliseconds-while achieving log-likelihood performance on par with or superior to existing approximate inference methods across tasks such as sequential inference, quantum system parameter inference, and Gaussian Process predictive posterior inference with hyperpriors.

With the rapid advancement of 2D generative models, preserving subject identity while enabling diverse editing has emerged as a critical research focus. Existing methods typically face inherent trade-offs between identity preservation and personalized manipulation. We introduce FlexIP, a novel framework that decouples these objectives through two dedicated components: a Personalization Adapter for stylistic manipulation and a Preservation Adapter for identity maintenance. By explicitly injecting both control mechanisms into the generative model, our framework enables flexible parameterized control during inference through dynamic tuning of the weight adapter. Experimental results demonstrate that our approach breaks through the performance limitations of conventional methods, achieving superior identity preservation while supporting more diverse personalized generation capabilities (Project Page: https://flexip-tech.github.io/flexip/).

The existence of a plethora of language models makes the problem of selecting the best one for a custom task challenging. Most state-of-the-art methods leverage transformer-based models (e.g., BERT) or their variants. Training such models and exploring their hyperparameter space, however, is computationally expensive. Prior work proposes several neural architecture search (NAS) methods that employ performance predictors (e.g., surrogate models) to address this issue; however, analysis has been limited to homogeneous models that use fixed dimensionality throughout the network. This leads to sub-optimal architectures. To address this limitation, we propose a suite of heterogeneous and flexible models, namely FlexiBERT, that have varied encoder layers with a diverse set of possible operations and different hidden dimensions. For better-posed surrogate modeling in this expanded design space, we propose a new graph-similarity-based embedding scheme. We also propose a novel NAS policy, called BOSHNAS, that leverages this new scheme, Bayesian modeling, and second-order optimization, to quickly train and use a neural surrogate model to converge to the optimal architecture. A comprehensive set of experiments shows that the proposed policy, when applied to the FlexiBERT design space, pushes the performance frontier upwards compared to traditional models. FlexiBERT-Mini, one of our proposed models, has 3% fewer parameters than BERT-Mini and achieves 8.9% higher GLUE score. A FlexiBERT model with equivalent performance as the best homogeneous model achieves 2.6x smaller size. FlexiBERT-Large, another proposed model, achieves state-of-the-art results, outperforming the baseline models by at least 5.7% on the GLUE benchmark.

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.

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.

Reliable uncertainty quantification remains a central challenge in predictive modeling. While Bayesian methods are theoretically appealing, their predictive intervals can exhibit poor frequentist calibration, particularly with small sample sizes or model misspecification. We introduce a practical and broadly applicable Bayesian conformal approach based on the influence-function Bayesian bootstrap (BB) with data-driven tuning of the Dirichlet concentration parameter, α. By efficiently approximating the Bayesian bootstrap predictive distribution via influence functions and calibrating α to optimize empirical coverage or average log-probability, our method constructs prediction intervals and distributions that are both well-calibrated and sharp. Across a range of regression models and data settings, this Bayesian conformal framework consistently yields improved empirical coverage and log-score compared to standard Bayesian posteriors. Our procedure is fast, easy to implement, and offers a flexible approach for distributional calibration in predictive modeling.

We propose a method for adapting neural networks to distribution shifts at test-time. In contrast to training-time robustness mechanisms that attempt to anticipate and counter the shift, we create a closed-loop system and make use of a test-time feedback signal to adapt a network on the fly. We show that this loop can be effectively implemented using a learning-based function, which realizes an amortized optimizer for the network. This leads to an adaptation method, named Rapid Network Adaptation (RNA), that is notably more flexible and orders of magnitude faster than the baselines. Through a broad set of experiments using various adaptation signals and target tasks, we study the efficiency and flexibility of this method. We perform the evaluations using various datasets (Taskonomy, Replica, ScanNet, Hypersim, COCO, ImageNet), tasks (depth, optical flow, semantic segmentation, classification), and distribution shifts (Cross-datasets, 2D and 3D Common Corruptions) with promising results. We end with a discussion on general formulations for handling distribution shifts and our observations from comparing with similar approaches from other domains.

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.

Deep learning has achieved tremendous success with independent and identically distributed (i.i.d.) data. However, the performance of neural networks often degenerates drastically when encountering out-of-distribution (OoD) data, i.e., when training and test data are sampled from different distributions. While a plethora of algorithms have been proposed for OoD generalization, our understanding of the data used to train and evaluate these algorithms remains stagnant. In this work, we first identify and measure two distinct kinds of distribution shifts that are ubiquitous in various datasets. Next, through extensive experiments, we compare OoD generalization algorithms across two groups of benchmarks, each dominated by one of the distribution shifts, revealing their strengths on one shift as well as limitations on the other shift. Overall, we position existing datasets and algorithms from different research areas seemingly unconnected into the same coherent picture. It may serve as a foothold that can be resorted to by future OoD generalization research. Our code is available at https://github.com/ynysjtu/ood_bench.

We present Scalable Interpolant Transformers (SiT), a family of generative models built on the backbone of Diffusion Transformers (DiT). The interpolant framework, which allows for connecting two distributions in a more flexible way than standard diffusion models, makes possible a modular study of various design choices impacting generative models built on dynamical transport: using discrete vs. continuous time learning, deciding the objective for the model to learn, choosing the interpolant connecting the distributions, and deploying a deterministic or stochastic sampler. By carefully introducing the above ingredients, SiT surpasses DiT uniformly across model sizes on the conditional ImageNet 256x256 benchmark using the exact same backbone, number of parameters, and GFLOPs. By exploring various diffusion coefficients, which can be tuned separately from learning, SiT achieves an FID-50K score of 2.06.

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.

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.

Current model quantization methods have shown their promising capability in reducing storage space and computation complexity. However, due to the diversity of quantization forms supported by different hardware, one limitation of existing solutions is that usually require repeated optimization for different scenarios. How to construct a model with flexible quantization forms has been less studied. In this paper, we explore a one-shot network quantization regime, named Elastic Quantization Neural Networks (EQ-Net), which aims to train a robust weight-sharing quantization supernet. First of all, we propose an elastic quantization space (including elastic bit-width, granularity, and symmetry) to adapt to various mainstream quantitative forms. Secondly, we propose the Weight Distribution Regularization Loss (WDR-Loss) and Group Progressive Guidance Loss (GPG-Loss) to bridge the inconsistency of the distribution for weights and output logits in the elastic quantization space gap. Lastly, we incorporate genetic algorithms and the proposed Conditional Quantization-Aware Accuracy Predictor (CQAP) as an estimator to quickly search mixed-precision quantized neural networks in supernet. Extensive experiments demonstrate that our EQ-Net is close to or even better than its static counterparts as well as state-of-the-art robust bit-width methods. Code can be available at https://github.com/xuke225/EQ-Net.git{https://github.com/xuke225/EQ-Net}.

Calibrated uncertainty estimates in machine learning are crucial to many fields such as autonomous vehicles, medicine, and weather and climate forecasting. While there is extensive literature on uncertainty calibration for classification, the classification findings do not always translate to regression. As a result, modern models for predicting uncertainty in regression settings typically produce uncalibrated and overconfident estimates. To address these gaps, we present a calibration method for regression settings that does not assume a particular uncertainty distribution over the error: Calibrating Regression Uncertainty Distributions Empirically (CRUDE). CRUDE makes the weaker assumption that error distributions have a constant arbitrary shape across the output space, shifted by predicted mean and scaled by predicted standard deviation. We detail a theoretical connection between CRUDE and conformal inference. Across an extensive set of regression tasks, CRUDE demonstrates consistently sharper, better calibrated, and more accurate uncertainty estimates than state-of-the-art techniques.

Applying diffusion models in reinforcement learning for long-term planning has gained much attention recently. Several diffusion-based methods have successfully leveraged the modeling capabilities of diffusion for arbitrary distributions. These methods generate subsequent trajectories for planning and have demonstrated significant improvement. However, these methods are limited by their plain base distributions and their overlooking of the diversity of samples, in which different states have different returns. They simply leverage diffusion to learn the distribution of offline dataset, generate the trajectories whose states share the same distribution with the offline dataset. As a result, the probability of these models reaching the high-return states is largely dependent on the dataset distribution. Even equipped with the guidance model, the performance is still suppressed. To address these limitations, in this paper, we propose a novel method called CDiffuser, which devises a return contrast mechanism to pull the states in generated trajectories towards high-return states while pushing them away from low-return states to improve the base distribution. Experiments on 14 commonly used D4RL benchmarks demonstrate the effectiveness of our proposed method.

Large language models (LLMs) have enabled the development of numerous specialized, task-specific variants. However, the maintenance and deployment of these individual models present substantial challenges in terms of resource utilization and operational efficiency. In this work, we propose the Mixture of Distributions (MoD) framework, a novel approach for merging LLMs that operates directly on their output probability distributions, rather than on model weights. Unlike traditional weight-averaging methods, MoD effectively preserves the specialized capabilities of individual models while enabling efficient knowledge sharing across tasks. Through extensive experimentation on mathematical reasoning benchmarks using Qwen2.5 models, we demonstrate that MoD significantly outperforms existing model merging techniques across multiple benchmarks. All code, data, and experimental materials are published at https://github.com/knovel-eng/mod.

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 rapid development of Large Language Models (LLMs) has substantially expanded the range of tasks they can address. In the field of Natural Language Processing (NLP), researchers have shifted their focus from conventional NLP tasks (e.g., sequence tagging and parsing) towards tasks that revolve around aligning with human needs (e.g., brainstorming and email writing). This shift in task distribution imposes new requirements on evaluating these aligned models regarding generality (i.e., assessing performance across diverse scenarios), flexibility (i.e., examining under different protocols), and interpretability (i.e., scrutinizing models with explanations). In this paper, we propose a generative judge with 13B parameters, Auto-J, designed to address these challenges. Our model is trained on user queries and LLM-generated responses under massive real-world scenarios and accommodates diverse evaluation protocols (e.g., pairwise response comparison and single-response evaluation) with well-structured natural language critiques. To demonstrate the efficacy of our approach, we construct a new testbed covering 58 different scenarios. Experimentally, Auto-J outperforms a series of strong competitors, including both open-source and closed-source models, by a large margin. We also provide detailed analysis and case studies to further reveal the potential of our method and make a variety of resources public at https://github.com/GAIR-NLP/auto-j.

Ocean scientists have been collecting visual data to study marine organisms for decades. These images and videos are extremely valuable both for basic science and environmental monitoring tasks. There are tools for automatically processing these data, but none that are capable of handling the extreme variability in sample populations, image quality, and habitat characteristics that are common in visual sampling of the ocean. Such distribution shifts can occur over very short physical distances and in narrow time windows. Creating models that are able to recognize when an image or video sequence contains a new organism, an unusual collection of animals, or is otherwise out-of-sample is critical to fully leverage visual data in the ocean. The FathomNet2023 competition dataset presents a realistic scenario where the set of animals in the target data differs from the training data. The challenge is both to identify the organisms in a target image and assess whether it is out-of-sample.

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

Understanding how machine learning models respond to distributional shifts is a key research challenge. Mazes serve as an excellent testbed due to varied generation algorithms offering a nuanced platform to simulate both subtle and pronounced distributional shifts. To enable systematic investigations of model behavior on out-of-distribution data, we present maze-dataset, a comprehensive library for generating, processing, and visualizing datasets consisting of maze-solving tasks. With this library, researchers can easily create datasets, having extensive control over the generation algorithm used, the parameters fed to the algorithm of choice, and the filters that generated mazes must satisfy. Furthermore, it supports multiple output formats, including rasterized and text-based, catering to convolutional neural networks and autoregressive transformer models. These formats, along with tools for visualizing and converting between them, ensure versatility and adaptability in research applications.

Intermittent demand forecasting poses unique challenges due to sparse observations, cold-start items, and obsolescence. Classical models such as Croston, SBA, and the Teunter-Syntetos-Babai (TSB) method provide simple heuristics but lack a principled generative foundation. Deep learning models address these limitations but often require large datasets and sacrifice interpretability. We introduce TSB-HB, a hierarchical Bayesian extension of TSB. Demand occurrence is modeled with a Beta-Binomial distribution, while nonzero demand sizes follow a Log-Normal distribution. Crucially, hierarchical priors enable partial pooling across items, stabilizing estimates for sparse or cold-start series while preserving heterogeneity. This framework yields a fully generative and interpretable model that generalizes classical exponential smoothing. On the UCI Online Retail dataset, TSB-HB achieves lower RMSE and RMSSE than Croston, SBA, TSB, ADIDA, IMAPA, ARIMA and Theta, and on a subset of the M5 dataset it outperforms all classical baselines we evaluate. The model provides calibrated probabilistic forecasts and improved accuracy on intermittent and lumpy items by combining a generative formulation with hierarchical shrinkage, while remaining interpretable and scalable.

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.

Is bigger always better for time series foundation models? With the question in mind, we explore an alternative to training a single, large monolithic model: building a portfolio of smaller, pretrained forecasting models. By applying ensembling or model selection over these portfolios, we achieve competitive performance on large-scale benchmarks using much fewer parameters. We explore strategies for designing such portfolios and find that collections of specialist models consistently outperform portfolios of independently trained generalists. Remarkably, we demonstrate that post-training a base model is a compute-effective approach for creating sufficiently diverse specialists, and provide evidences that ensembling and model selection are more compute-efficient than test-time fine-tuning.

A growing trend for value-based reinforcement learning (RL) algorithms is to capture more information than scalar value functions in the value network. One of the most well-known methods in this branch is distributional RL, which models return distribution instead of scalar value. In another line of work, hybrid reward architectures (HRA) in RL have studied to model source-specific value functions for each source of reward, which is also shown to be beneficial in performance. To fully inherit the benefits of distributional RL and hybrid reward architectures, we introduce Multi-Dimensional Distributional DQN (MD3QN), which extends distributional RL to model the joint return distribution from multiple reward sources. As a by-product of joint distribution modeling, MD3QN can capture not only the randomness in returns for each source of reward, but also the rich reward correlation between the randomness of different sources. We prove the convergence for the joint distributional Bellman operator and build our empirical algorithm by minimizing the Maximum Mean Discrepancy between joint return distribution and its Bellman target. In experiments, our method accurately models the joint return distribution in environments with richly correlated reward functions, and outperforms previous RL methods utilizing multi-dimensional reward functions in the control setting.

Few shot classification aims to learn to recognize novel categories using only limited samples per category. Most current few shot methods use a base dataset rich in labeled examples to train an encoder that is used for obtaining representations of support instances for novel classes. Since the test instances are from a distribution different to the base distribution, their feature representations are of poor quality, degrading performance. In this paper we propose to make use of the well-trained feature representations of the base dataset that are closest to each support instance to improve its representation during meta-test time. To this end, we propose BaseTransformers, that attends to the most relevant regions of the base dataset feature space and improves support instance representations. Experiments on three benchmark data sets show that our method works well for several backbones and achieves state-of-the-art results in the inductive one shot setting. Code is available at github.com/mayug/BaseTransformers

Bayesian inference provides principled uncertainty quantification but is often limited by challenges of prior elicitation, likelihood misspecification, and computational burden. The martingale posterior (MGP, Fong et al., 2023) offers an alternative, replacing prior-likelihood elicitation with a predictive rule - namely, a sequence of one-step-ahead predictive distributions - for forward data generation. The utility of MGPs depends on the choice of predictive rule, yet the literature has offered few compelling examples. Foundation transformers are well-suited here, as their autoregressive generation mirrors this forward simulation and their general-purpose design enables rich predictive modeling. We introduce TabMGP, an MGP built on TabPFN, a transformer foundation model that is currently state-of-the-art for tabular data. TabMGP produces credible sets with near-nominal coverage and often outperforms both existing MGP constructions and standard Bayes.

A distribution shift can have fundamental consequences such as signaling a change in the operating environment or significantly reducing the accuracy of downstream models. Thus, understanding distribution shifts is critical for examining and hopefully mitigating the effect of such a shift. Most prior work focuses on merely detecting if a shift has occurred and assumes any detected shift can be understood and handled appropriately by a human operator. We hope to aid in these manual mitigation tasks by explaining the distribution shift using interpretable transportation maps from the original distribution to the shifted one. We derive our interpretable mappings from a relaxation of optimal transport, where the candidate mappings are restricted to a set of interpretable mappings. We then inspect multiple quintessential use-cases of distribution shift in real-world tabular, text, and image datasets to showcase how our explanatory mappings provide a better balance between detail and interpretability than baseline explanations by both visual inspection and our PercentExplained metric.

Pre-trained foundation models (FMs) have shown exceptional performance in univariate time series forecasting tasks. However, several practical challenges persist, including managing intricate dependencies among features and quantifying uncertainty in predictions. This study aims to tackle these critical limitations by introducing adapters; feature-space transformations that facilitate the effective use of pre-trained univariate time series FMs for multivariate tasks. Adapters operate by projecting multivariate inputs into a suitable latent space and applying the FM independently to each dimension. Inspired by the literature on representation learning and partially stochastic Bayesian neural networks, we present a range of adapters and optimization/inference strategies. Experiments conducted on both synthetic and real-world datasets confirm the efficacy of adapters, demonstrating substantial enhancements in forecasting accuracy and uncertainty quantification compared to baseline methods. Our framework, AdaPTS, positions adapters as a modular, scalable, and effective solution for leveraging time series FMs in multivariate contexts, thereby promoting their wider adoption in real-world applications. We release the code at https://github.com/abenechehab/AdaPTS.

Quantile regression is a fundamental problem in statistical learning motivated by a need to quantify uncertainty in predictions, or to model a diverse population without being overly reductive. For instance, epidemiological forecasts, cost estimates, and revenue predictions all benefit from being able to quantify the range of possible values accurately. As such, many models have been developed for this problem over many years of research in statistics, machine learning, and related fields. Rather than proposing yet another (new) algorithm for quantile regression we adopt a meta viewpoint: we investigate methods for aggregating any number of conditional quantile models, in order to improve accuracy and robustness. We consider weighted ensembles where weights may vary over not only individual models, but also over quantile levels, and feature values. All of the models we consider in this paper can be fit using modern deep learning toolkits, and hence are widely accessible (from an implementation point of view) and scalable. To improve the accuracy of the predicted quantiles (or equivalently, prediction intervals), we develop tools for ensuring that quantiles remain monotonically ordered, and apply conformal calibration methods. These can be used without any modification of the original library of base models. We also review some basic theory surrounding quantile aggregation and related scoring rules, and contribute a few new results to this literature (for example, the fact that post sorting or post isotonic regression can only improve the weighted interval score). Finally, we provide an extensive suite of empirical comparisons across 34 data sets from two different benchmark repositories.

Transformer models are deployed in a wide range of settings, from multi-accelerator clusters to standalone mobile phones. The diverse inference constraints in these scenarios necessitate practitioners to train foundation models such as PaLM 2, Llama, & ViTs as a series of models of varying sizes. Due to significant training costs, only a select few model sizes are trained and supported, limiting more fine-grained control over relevant tradeoffs, including latency, cost, and accuracy. This work introduces MatFormer, a nested Transformer architecture designed to offer elasticity in a variety of deployment constraints. Each Feed Forward Network (FFN) block of a MatFormer model is jointly optimized with a few nested smaller FFN blocks. This training procedure allows for the Mix'n'Match of model granularities across layers -- i.e., a trained universal MatFormer model enables extraction of hundreds of accurate smaller models, which were never explicitly optimized. We empirically demonstrate MatFormer's effectiveness across different model classes (decoders & encoders), modalities (language & vision), and scales (up to 2.6B parameters). We find that a 2.6B decoder-only MatFormer language model (MatLM) allows us to extract smaller models spanning from 1.5B to 2.6B, each exhibiting comparable validation loss and one-shot downstream evaluations to their independently trained counterparts. Furthermore, we observe that smaller encoders extracted from a universal MatFormer-based ViT (MatViT) encoder preserve the metric-space structure for adaptive large-scale retrieval. Finally, we showcase that speculative decoding with the accurate and consistent submodels extracted from MatFormer can further reduce inference latency.

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.

Training modern LLMs is extremely resource intensive, and customizing them for various deployment scenarios characterized by limited compute and memory resources through repeated training is impractical. In this paper, we introduce Flextron, a network architecture and post-training model optimization framework supporting flexible model deployment. The Flextron architecture utilizes a nested elastic structure to rapidly adapt to specific user-defined latency and accuracy targets during inference with no additional fine-tuning required. It is also input-adaptive, and can automatically route tokens through its sub-networks for improved performance and efficiency. We present a sample-efficient training method and associated routing algorithms for systematically transforming an existing trained LLM into a Flextron model. We evaluate Flextron on the GPT-3 and LLama-2 family of LLMs, and demonstrate superior performance over multiple end-to-end trained variants and other state-of-the-art elastic networks, all with a single pretraining run that consumes a mere 7.63% tokens compared to original pretraining.

Long-tailed classification is challenging due to its heavy imbalance in class probabilities. While existing methods often focus on overall accuracy or accuracy for tail classes, they overlook a critical aspect: certain types of errors can carry greater risks than others in real-world long-tailed problems. For example, misclassifying patients (a tail class) as healthy individuals (a head class) entails far more serious consequences than the reverse scenario. To address this critical issue, we introduce Making Reliable and Flexible Decisions in Long-tailed Classification (RF-DLC), a novel framework aimed at reliable predictions in long-tailed problems. Leveraging Bayesian Decision Theory, we introduce an integrated gain to seamlessly combine long-tailed data distributions and the decision-making procedure. We further propose an efficient variational optimization strategy for the decision risk objective. Our method adapts readily to diverse utility matrices, which can be designed for specific tasks, ensuring its flexibility for different problem settings. In empirical evaluation, we design a new metric, False Head Rate, to quantify tail-sensitivity risk, along with comprehensive experiments on multiple real-world tasks, including large-scale image classification and uncertainty quantification, to demonstrate the reliability and flexibility of our method.

Survival analysis, or time-to-event modelling, is a classical statistical problem that has garnered a lot of interest for its practical use in epidemiology, demographics or actuarial sciences. Recent advances on the subject from the point of view of machine learning have been concerned with precise per-individual predictions instead of population studies, driven by the rise of individualized medicine. We introduce here a conditional normalizing flow based estimate of the time-to-event density as a way to model highly flexible and individualized conditional survival distributions. We use a novel hierarchical formulation of normalizing flows to enable efficient fitting of flexible conditional distributions without overfitting and show how the normalizing flow formulation can be efficiently adapted to the censored setting. We experimentally validate the proposed approach on a synthetic dataset as well as four open medical datasets and an example of a common financial problem.

Foundation models, specifically Large Language Models (LLMs), have lately gained wide-spread attention and adoption. Reinforcement Learning with Human Feedback (RLHF) involves training a reward model to capture desired behaviors, which is then used to align LLM's. These reward models are additionally used at inference-time to estimate LLM responses' adherence to those desired behaviors. However, there is little work measuring how robust these reward models are to distribution shifts. In this work, we evaluate how reward model performance - measured via accuracy and calibration (i.e. alignment between accuracy and confidence) - is affected by distribution shift. We show novel calibration patterns and accuracy drops due to OOD prompts and responses, and that the reward model is more sensitive to shifts in responses than prompts. Additionally, we adapt an OOD detection technique commonly used in classification to the reward model setting to detect these distribution shifts in prompts and responses.

Training multiple tasks jointly in one deep network yields reduced latency during inference and better performance over the single-task counterpart by sharing certain layers of a network. However, over-sharing a network could erroneously enforce over-generalization, causing negative knowledge transfer across tasks. Prior works rely on human intuition or pre-computed task relatedness scores for ad hoc branching structures. They provide sub-optimal end results and often require huge efforts for the trial-and-error process. In this work, we present an automated multi-task learning algorithm that learns where to share or branch within a network, designing an effective network topology that is directly optimized for multiple objectives across tasks. Specifically, we propose a novel tree-structured design space that casts a tree branching operation as a gumbel-softmax sampling procedure. This enables differentiable network splitting that is end-to-end trainable. We validate the proposed method on controlled synthetic data, CelebA, and Taskonomy.

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

Recently, test-time adaptation (TTA) has been proposed as a promising solution for addressing distribution shifts. It allows a base model to adapt to an unforeseen distribution during inference by leveraging the information from the batch of (unlabeled) test data. However, we uncover a novel security vulnerability of TTA based on the insight that predictions on benign samples can be impacted by malicious samples in the same batch. To exploit this vulnerability, we propose Distribution Invading Attack (DIA), which injects a small fraction of malicious data into the test batch. DIA causes models using TTA to misclassify benign and unperturbed test data, providing an entirely new capability for adversaries that is infeasible in canonical machine learning pipelines. Through comprehensive evaluations, we demonstrate the high effectiveness of our attack on multiple benchmarks across six TTA methods. In response, we investigate two countermeasures to robustify the existing insecure TTA implementations, following the principle of "security by design". Together, we hope our findings can make the community aware of the utility-security tradeoffs in deploying TTA and provide valuable insights for developing robust TTA approaches.

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 paper, we study the infinite-depth limit of finite-width residual neural networks with random Gaussian weights. With proper scaling, we show that by fixing the width and taking the depth to infinity, the pre-activations converge in distribution to a zero-drift diffusion process. Unlike the infinite-width limit where the pre-activation converge weakly to a Gaussian random variable, we show that the infinite-depth limit yields different distributions depending on the choice of the activation function. We document two cases where these distributions have closed-form (different) expressions. We further show an intriguing change of regime phenomenon of the post-activation norms when the width increases from 3 to 4. Lastly, we study the sequential limit infinite-depth-then-infinite-width and compare it with the more commonly studied infinite-width-then-infinite-depth limit.

Distribution inference, sometimes called property inference, infers statistical properties about a training set from access to a model trained on that data. Distribution inference attacks can pose serious risks when models are trained on private data, but are difficult to distinguish from the intrinsic purpose of statistical machine learning -- namely, to produce models that capture statistical properties about a distribution. Motivated by Yeom et al.'s membership inference framework, we propose a formal definition of distribution inference attacks that is general enough to describe a broad class of attacks distinguishing between possible training distributions. We show how our definition captures previous ratio-based property inference attacks as well as new kinds of attack including revealing the average node degree or clustering coefficient of a training graph. To understand distribution inference risks, we introduce a metric that quantifies observed leakage by relating it to the leakage that would occur if samples from the training distribution were provided directly to the adversary. We report on a series of experiments across a range of different distributions using both novel black-box attacks and improved versions of the state-of-the-art white-box attacks. Our results show that inexpensive attacks are often as effective as expensive meta-classifier attacks, and that there are surprising asymmetries in the effectiveness of attacks. Code is available at https://github.com/iamgroot42/FormEstDistRisks

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

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

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

We introduce Probabilistic Dependent Type Systems (PDTS) via a functional language based on a subsystem of intuitionistic type theory including dependent sums and products, which is expanded to include stochastic functions. We provide a sampling-based semantics for the language based on non-deterministic beta reduction. Further, we derive a probabilistic logic from the PDTS introduced as a direct result of the Curry-Howard isomorphism. The probabilistic logic derived is shown to provide a universal representation for finite discrete distributions.

Allocating more computation during inference time (test-time scaling) improves language model performance, especially for reasoning tasks. However, popular methods like Best-of-N sampling often show diminishing returns as N increases. To address this inefficiency, we introduce a general test-time calibration framework that adaptively modifies the model toward high-reward reasoning paths, with theoretical guarantees of improving the lower bound of expected reward under finite sampling, all without large language model (LLM) retraining. Within this framework, we propose CarBoN (Calibrated Best-of-N), a two-phase method that first explores the solution space and then learns a calibration of the logits via an input-specific temperature T and additive shift vector delta, guiding generation toward more reliable reasoning. Experiments on MATH-500 and AIME-2024 show that CarBoN improves efficiency, with up to 4times fewer rollouts to reach the same accuracy, while often achieving higher accuracy under fixed budgets. We also analyze the complementary roles of T and delta in balancing output diversity and correctness, and demonstrate that the framework also generalizes to step-level sampling strategies such as beam search. For more information, please refer to our project page at huggingface.co/spaces/TrustSafeAI/Test-Time-Calibration.

Language models (LMs) are increasingly used as simulacra for people, yet their ability to match the distribution of views of a specific demographic group and be distributionally aligned remains uncertain. This notion of distributional alignment is complex, as there is significant variation in the types of attributes that are simulated. Prior works have underexplored the role of three critical variables -- the question domain, steering method, and distribution expression method -- which motivates our contribution of a benchmark explicitly addressing these dimensions. We construct a dataset expanding beyond political values, create human baselines for this task, and evaluate the extent to which an LM can align with a particular group's opinion distribution to inform design choices of such simulation systems. Our analysis reveals open problems regarding if, and how, LMs can be used to simulate humans, and that LLMs can more accurately describe the opinion distribution than simulate such distributions.

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.

Low-bit quantization is challenging to maintain high performance with limited model capacity (e.g., 4-bit for both weights and activations). Naturally, the distribution of both weights and activations in deep neural network are Gaussian-like. Nevertheless, due to the limited bitwidth of low-bit model, uniform-like distributed weights and activations have been proved to be more friendly to quantization while preserving accuracy~Han2015Learning. Motivated by this, we propose Scale-Clip, a Distribution Reshaping technique that can reshape weights or activations into a uniform-like distribution in a dynamic manner. Furthermore, to increase the model capability for a low-bit model, a novel Group-based Quantization algorithm is proposed to split the filters into several groups. Different groups can learn different quantization parameters, which can be elegantly merged in to batch normalization layer without extra computational cost in the inference stage. Finally, we integrate Scale-Clip technique with Group-based Quantization algorithm and propose the Group-based Distribution Reshaping Quantization (GDQR) framework to further improve the quantization performance. Experiments on various networks (e.g. VGGNet and ResNet) and vision tasks (e.g. classification, detection and segmentation) demonstrate that our framework achieves good performance.

Post-training of Large Language Models often involves a pipeline of Supervised Finetuning (SFT) followed by Preference Finetuning (PFT) using methods like Direct Preference Optimization. Both stages require annotated data that are very different in structure and costs. We study how to optimally allocate a fixed training data budget between the two stages, through extensive experiments spanning four diverse tasks, multiple model sizes and various data annotation costs. Our findings reveal that just SFT on the base model dominates performance in low-data regimes (<1,000 annotated examples). With larger data-budgets, we observe that a combination of SFT and PFT, often with increasing portions allocated towards preference data yields optimal performance. However, completely eliminating SFT and running PFT directly on the base model yields suboptimal performance, described as the cold start problem on tasks like mathematics. We observe that this is due to the distribution shift arising from using DPO directly on the base model to elicit step-by-step reasoning. This limitation can be effectively addressed by allocating even a small portion (<10%) of the budget to SFT first, resulting in performance improvements of 15-20% on analytical benchmarks like GSM8k. These results provide actionable insights for researchers and practitioners optimizing model development under budget constraints, where high-quality data curation often represents a significant portion of the total costs of model development.

This work challenges the residual prediction paradigm in visual autoregressive modeling and presents FlexVAR, a new Flexible Visual AutoRegressive image generation paradigm. FlexVAR facilitates autoregressive learning with ground-truth prediction, enabling each step to independently produce plausible images. This simple, intuitive approach swiftly learns visual distributions and makes the generation process more flexible and adaptable. Trained solely on low-resolution images (leq 256px), FlexVAR can: (1) Generate images of various resolutions and aspect ratios, even exceeding the resolution of the training images. (2) Support various image-to-image tasks, including image refinement, in/out-painting, and image expansion. (3) Adapt to various autoregressive steps, allowing for faster inference with fewer steps or enhancing image quality with more steps. Our 1.0B model outperforms its VAR counterpart on the ImageNet 256times256 benchmark. Moreover, when zero-shot transfer the image generation process with 13 steps, the performance further improves to 2.08 FID, outperforming state-of-the-art autoregressive models AiM/VAR by 0.25/0.28 FID and popular diffusion models LDM/DiT by 1.52/0.19 FID, respectively. When transferring our 1.0B model to the ImageNet 512times512 benchmark in a zero-shot manner, FlexVAR achieves competitive results compared to the VAR 2.3B model, which is a fully supervised model trained at 512times512 resolution.

Bayesian deep learning counts on the quality of posterior distribution estimation. However, the posterior of deep neural networks is highly multi-modal in nature, with local modes exhibiting varying generalization performance. Given a practical budget, targeting at the original posterior can lead to suboptimal performance, as some samples may become trapped in "bad" modes and suffer from overfitting. Leveraging the observation that "good" modes with low generalization error often reside in flat basins of the energy landscape, we propose to bias sampling on the posterior toward these flat regions. Specifically, we introduce an auxiliary guiding variable, the stationary distribution of which resembles a smoothed posterior free from sharp modes, to lead the MCMC sampler to flat basins. By integrating this guiding variable with the model parameter, we create a simple joint distribution that enables efficient sampling with minimal computational overhead. We prove the convergence of our method and further show that it converges faster than several existing flatness-aware methods in the strongly convex setting. Empirical results demonstrate that our method can successfully sample from flat basins of the posterior, and outperforms all compared baselines on multiple benchmarks including classification, calibration, and out-of-distribution detection.

This paper studies distributional model risk in marginal problems, where each marginal measure is assumed to lie in a Wasserstein ball centered at a fixed reference measure with a given radius. Theoretically, we establish several fundamental results including strong duality, finiteness of the proposed Wasserstein distributional model risk, and the existence of an optimizer at each radius. In addition, we show continuity of the Wasserstein distributional model risk as a function of the radius. Using strong duality, we extend the well-known Makarov bounds for the distribution function of the sum of two random variables with given marginals to Wasserstein distributionally robust Markarov bounds. Practically, we illustrate our results on four distinct applications when the sample information comes from multiple data sources and only some marginal reference measures are identified. They are: partial identification of treatment effects; externally valid treatment choice via robust welfare functions; Wasserstein distributionally robust estimation under data combination; and evaluation of the worst aggregate risk measures.

Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate dimension reduction, typically achieved via basis expansions. Currently, these bases are chosen a priori without the information for the task at hand and thus may not be effective for the designated task. We instead propose to adaptively learn these bases in an end-to-end fashion. We introduce neural networks that employ a new Basis Layer whose hidden units are each basis functions themselves implemented as a micro neural network. Our architecture learns to apply parsimonious dimension reduction to functional inputs that focuses only on information relevant to the target rather than irrelevant variation in the input function. Across numerous classification/regression tasks with functional data, our method empirically outperforms other types of neural networks, and we prove that our approach is statistically consistent with low generalization error. Code is available at: https://github.com/jwyyy/AdaFNN.

Current machine learning systems are brittle in the face of distribution shifts (DS), where the target distribution that the system is tested on differs from the source distribution used to train the system. This problem of robustness to DS has been studied extensively in the field of domain adaptation. For deep neural networks, a popular framework for unsupervised domain adaptation (UDA) is domain matching, in which algorithms try to align the marginal distributions in the feature or output space. The current theoretical understanding of these methods, however, is limited and existing theoretical results are not precise enough to characterize their performance in practice. In this paper, we derive new bounds based on optimal transport that analyze the UDA problem. Our new bounds include a term which we dub as entanglement, consisting of an expectation of Wasserstein distance between conditionals with respect to changing data distributions. Analysis of the entanglement term provides a novel perspective on the unoptimizable aspects of UDA. In various experiments with multiple models across several DS scenarios, we show that this term can be used to explain the varying performance of UDA algorithms.

The distribution of subpopulations is an important property hidden within a dataset. Uncovering and analyzing the subpopulation distribution within datasets provides a comprehensive understanding of the datasets, standing as a powerful tool beneficial to various downstream tasks, including Dataset Subpopulation Organization, Subpopulation Shift, and Slice Discovery. Despite its importance, there has been no work that systematically explores the subpopulation distribution of datasets to our knowledge. To address the limitation and solve all the mentioned tasks in a unified way, we introduce a novel concept of subpopulation structures to represent, analyze, and utilize subpopulation distributions within datasets. To characterize the structures in an interpretable manner, we propose the Subpopulation Structure Discovery with Large Language Models (SSD-LLM) framework, which employs world knowledge and instruction-following capabilities of Large Language Models (LLMs) to linguistically analyze informative image captions and summarize the structures. Furthermore, we propose complete workflows to address downstream tasks, named Task-specific Tuning, showcasing the application of the discovered structure to a spectrum of subpopulation-related tasks, including dataset subpopulation organization, subpopulation shift, and slice discovery. Furthermore, we propose complete workflows to address downstream tasks, named Task-specific Tuning, showcasing the application of the discovered structure to a spectrum of subpopulation-related tasks, including dataset subpopulation organization, subpopulation shift, and slice discovery.

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

Federated learning (FL) is a distributed machine learning framework where the global model of a central server is trained via multiple collaborative steps by participating clients without sharing their data. While being a flexible framework, where the distribution of local data, participation rate, and computing power of each client can greatly vary, such flexibility gives rise to many new challenges, especially in the hyperparameter tuning on the client side. We propose Delta-SGD, a simple step size rule for SGD that enables each client to use its own step size by adapting to the local smoothness of the function each client is optimizing. We provide theoretical and empirical results where the benefit of the client adaptivity is shown in various FL scenarios.

Categorical distributions are ubiquitous in machine learning, e.g., in classification, language models, and recommendation systems. However, when the number of possible outcomes is very large, using categorical distributions becomes computationally expensive, as the complexity scales linearly with the number of outcomes. To address this problem, we propose augment and reduce (A&R), a method to alleviate the computational complexity. A&R uses two ideas: latent variable augmentation and stochastic variational inference. It maximizes a lower bound on the marginal likelihood of the data. Unlike existing methods which are specific to softmax, A&R is more general and is amenable to other categorical models, such as multinomial probit. On several large-scale classification problems, we show that A&R provides a tighter bound on the marginal likelihood and has better predictive performance than existing approaches.

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.

The presence of distribution shifts poses a significant challenge for deploying modern machine learning models in real-world applications. This work focuses on the target shift problem in a regression setting (Zhang et al., 2013; Nguyen et al., 2016). More specifically, the target variable y (also known as the response variable), which is continuous, has different marginal distributions in the training source and testing domain, while the conditional distribution of features x given y remains the same. While most literature focuses on classification tasks with finite target space, the regression problem has an infinite dimensional target space, which makes many of the existing methods inapplicable. In this work, we show that the continuous target shift problem can be addressed by estimating the importance weight function from an ill-posed integral equation. We propose a nonparametric regularized approach named ReTaSA to solve the ill-posed integral equation and provide theoretical justification for the estimated importance weight function. The effectiveness of the proposed method has been demonstrated with extensive numerical studies on synthetic and real-world datasets.

Missing values, irregularly collected samples, and multi-resolution signals commonly occur in multivariate time series data, making predictive tasks difficult. These challenges are especially prevalent in the healthcare domain, where patients' vital signs and electronic records are collected at different frequencies and have occasionally missing information due to the imperfections in equipment or patient circumstances. Researchers have handled each of these issues differently, often handling missing data through mean value imputation and then using sequence models over the multivariate signals while ignoring the different resolution of signals. We propose a unified model named Multi-resolution Flexible Irregular Time series Network (Multi-FIT). The building block for Multi-FIT is the FIT network. The FIT network creates an informative dense representation at each time step using signal information such as last observed value, time difference since the last observed time stamp and overall mean for the signal. Vertical FIT (FIT-V) is a variant of FIT which also models the relationship between different temporal signals while creating the informative dense representations for the signal. The multi-FIT model uses multiple FIT networks for sets of signals with different resolutions, further facilitating the construction of flexible representations. Our model has three main contributions: a.) it does not impute values but rather creates informative representations to provide flexibility to the model for creating task-specific representations b.) it models the relationship between different signals in the form of support signals c.) it models different resolutions in parallel before merging them for the final prediction task. The FIT, FIT-V and Multi-FIT networks improve upon the state-of-the-art models for three predictive tasks, including the forecasting of patient survival.

Traditional Federated Learning (FL) faces significant challenges in terms of efficiency and accuracy, particularly in heterogeneous environments where clients employ diverse model architectures and have varying computational resources. Such heterogeneity complicates the aggregation process, leading to performance bottlenecks and reduced model generalizability. To address these issues, we propose FedADP, a federated learning framework designed to adapt to client heterogeneity by dynamically adjusting model architectures during aggregation. FedADP enables effective collaboration among clients with differing capabilities, maximizing resource utilization and ensuring model quality. Our experimental results demonstrate that FedADP significantly outperforms existing methods, such as FlexiFed, achieving an accuracy improvement of up to 23.30%, thereby enhancing model adaptability and training efficiency in heterogeneous real-world settings.

Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies to compute forces and higher-order derivatives. Furthermore, such densities are often defined on non-trivial topologies. A recent example are Boltzmann Generators for generating 3D-structures of peptides and small proteins. These generative models leverage the space of internal coordinates (dihedrals, angles, and bonds), which is a product of hypertori and compact intervals. In this work, we introduce a class of smooth mixture transformations working on both compact intervals and hypertori. Mixture transformations employ root-finding methods to invert them in practice, which has so far prevented bi-directional flow training. To this end, we show that parameter gradients and forces of such inverses can be computed from forward evaluations via the inverse function theorem. We demonstrate two advantages of such smooth flows: they allow training by force matching to simulation data and can be used as potentials in molecular dynamics simulations.

In learned image compression, probabilistic models play an essential role in characterizing the distribution of latent variables. The Gaussian model with mean and scale parameters has been widely used for its simplicity and effectiveness. Probabilistic models with more parameters, such as the Gaussian mixture models, can fit the distribution of latent variables more precisely, but the corresponding complexity will also be higher. To balance between compression performance and complexity, we extend the Gaussian model to the generalized Gaussian model for more flexible latent distribution modeling, introducing only one additional shape parameter, beta, than the Gaussian model. To enhance the performance of the generalized Gaussian model by alleviating the train-test mismatch, we propose improved training methods, including beta-dependent lower bounds for scale parameters and gradient rectification. Our proposed generalized Gaussian model, coupled with the improved training methods, is demonstrated to outperform the Gaussian and Gaussian mixture models on a variety of learned image compression methods.

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

Given a set of K probability densities, we consider the multimarginal generative modeling problem of learning a joint distribution that recovers these densities as marginals. The structure of this joint distribution should identify multi-way correspondences among the prescribed marginals. We formalize an approach to this task within a generalization of the stochastic interpolant framework, leading to efficient learning algorithms built upon dynamical transport of measure. Our generative models are defined by velocity and score fields that can be characterized as the minimizers of simple quadratic objectives, and they are defined on a simplex that generalizes the time variable in the usual dynamical transport framework. The resulting transport on the simplex is influenced by all marginals, and we show that multi-way correspondences can be extracted. The identification of such correspondences has applications to style transfer, algorithmic fairness, and data decorruption. In addition, the multimarginal perspective enables an efficient algorithm for reducing the dynamical transport cost in the ordinary two-marginal setting. We demonstrate these capacities with several numerical examples.

Structured outputs are essential for large language models (LLMs) in critical applications like agents and information extraction. Despite their capabilities, LLMs often generate outputs that deviate from predefined schemas, significantly hampering reliable application development. We present SLOT (Structured LLM Output Transformer), a model-agnostic approach that transforms unstructured LLM outputs into precise structured formats. While existing solutions predominantly rely on constrained decoding techniques or are tightly coupled with specific models, SLOT employs a fine-tuned lightweight language model as a post-processing layer, achieving flexibility across various LLMs and schema specifications. We introduce a systematic pipeline for data curation and synthesis alongside a formal evaluation methodology that quantifies both schema accuracy and content fidelity. Our results demonstrate that fine-tuned Mistral-7B model with constrained decoding achieves near perfect schema accuracy (99.5%) and content similarity (94.0%), outperforming Claude-3.5-Sonnet by substantial margins (+25 and +20 percentage points, respectively). Notably, even compact models like Llama-3.2-1B can match or exceed the structured output capabilities of much larger proprietary models when equipped with SLOT, enabling reliable structured generation in resource-constrained environments.

Post-training quantization (PTQ) has been gaining popularity for the deployment of deep neural networks on resource-limited devices since unlike quantization-aware training, neither a full training dataset nor end-to-end training is required at all. As PTQ schemes based on reconstructing each layer or block output turn out to be effective to enhance quantized model performance, recent works have developed algorithms to devise and learn a new weight-rounding scheme so as to better reconstruct each layer or block output. In this work, we propose a simple yet effective new weight-rounding mechanism for PTQ, coined FlexRound, based on element-wise division instead of typical element-wise addition such that FlexRound enables jointly learning a common quantization grid size as well as a different scale for each pre-trained weight. Thanks to the reciprocal rule of derivatives induced by element-wise division, FlexRound is inherently able to exploit pre-trained weights when updating their corresponding scales, and thus, flexibly quantize pre-trained weights depending on their magnitudes. We empirically validate the efficacy of FlexRound on a wide range of models and tasks. To the best of our knowledge, our work is the first to carry out comprehensive experiments on not only image classification and natural language understanding but also natural language generation, assuming a per-tensor uniform PTQ setting. Moreover, we demonstrate, for the first time, that large language models can be efficiently quantized, with only a negligible impact on performance compared to half-precision baselines, achieved by reconstructing the output in a block-by-block manner.

As an efficient alternative to conventional full finetuning, parameter-efficient finetuning (PEFT) is becoming the prevailing method to adapt pretrained language models. In PEFT, a lightweight module is learned on each dataset while the underlying pretrained language model remains unchanged, resulting in multiple compact modules representing diverse skills when applied to various domains and tasks. In this paper, we propose to compose these parameter-efficient modules through linear arithmetic operations in the weight space, thereby integrating different module capabilities. Specifically, we first define addition and negation operators for the module, and then further compose these two basic operators to perform flexible arithmetic. Our approach requires no additional training and enables highly flexible module composition. We apply different arithmetic operations to compose the parameter-efficient modules for (1) distribution generalization, (2) multi-tasking, (3) unlearning, and (4) domain transfer. Additionally, we extend our approach to detoxify Alpaca-LoRA, the latest instruction-tuned large language model based on LLaMA. Empirical results demonstrate that our approach produces new and effective parameter-efficient modules that significantly outperform existing ones across all settings.

In contrast to classical reinforcement learning, distributional reinforcement learning algorithms aim to learn the distribution of returns rather than their expected value. Since the nature of the return distribution is generally unknown a priori or arbitrarily complex, a common approach finds approximations within a set of representable, parametric distributions. Typically, this involves a projection of the unconstrained distribution onto the set of simplified distributions. We argue that this projection step entails a strong inductive bias when coupled with neural networks and gradient descent, thereby profoundly impacting the generalization behavior of learned models. In order to facilitate reliable uncertainty estimation through diversity, this work studies the combination of several different projections and representations in a distributional ensemble. We establish theoretical properties of such projection ensembles and derive an algorithm that uses ensemble disagreement, measured by the average 1-Wasserstein distance, as a bonus for deep exploration. We evaluate our algorithm on the behavior suite benchmark and find that diverse projection ensembles lead to significant performance improvements over existing methods on a wide variety of tasks with the most pronounced gains in directed exploration problems.

In modern large-scale deep learning, a prevalent and effective workflow for solving low-data problems is adapting powerful pre-trained foundation models (FMs) to new tasks via parameter-efficient fine-tuning (PEFT). However, while empirically effective, the resulting solutions lack generalisation guarantees to certify their accuracy - which may be required for ethical or legal reasons prior to deployment in high-importance applications. In this paper we develop a novel transfer learning approach that is designed to facilitate non-vacuous learning theoretic generalisation guarantees for downstream tasks, even in the low-shot regime. Specifically, we first use upstream tasks to train a distribution over PEFT parameters. We then learn the downstream task by a sample-and-evaluate procedure -- sampling plausible PEFTs from the trained diffusion model and selecting the one with the highest likelihood on the downstream data. Crucially, this confines our model hypothesis to a finite set of PEFT samples. In contrast to learning in the typical continuous hypothesis spaces of neural network weights, this facilitates tighter risk certificates. We instantiate our bound and show non-trivial generalization guarantees compared to existing learning approaches which lead to vacuous bounds in the low-shot regime.

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.

This paper concerns the problem of aligning samples from large language models to human preferences using best-of-n sampling, where we draw n samples, rank them, and return the best one. We consider two fundamental problems. First: what is the relationship between best-of-n and approaches to alignment that train LLMs to output samples with a high expected reward (e.g., RLHF or DPO)? To answer this, we embed both the best-of-n distribution and the sampling distributions learned by alignment procedures in a common class of tiltings of the base LLM distribution. We then show that, within this class, best-of-n is essentially optimal in terms of the trade-off between win-rate against the base model vs KL distance from the base model. That is, best-of-n is the best choice of alignment distribution if the goal is to maximize win rate. However, best-of-n requires drawing n samples for each inference, a substantial cost. To avoid this, the second problem we consider is how to fine-tune a LLM to mimic the best-of-n sampling distribution. We derive BoNBoN Alignment to achieve this by exploiting the special structure of the best-of-n distribution. Experiments show that BoNBoN alignment yields substantial improvements in producing a model that is preferred to the base policy while minimally affecting off-target aspects.

We present a new distribution-free conformal prediction algorithm for sequential data (e.g., time series), called the sequential predictive conformal inference (SPCI). We specifically account for the nature that time series data are non-exchangeable, and thus many existing conformal prediction algorithms are not applicable. The main idea is to adaptively re-estimate the conditional quantile of non-conformity scores (e.g., prediction residuals), upon exploiting the temporal dependence among them. More precisely, we cast the problem of conformal prediction interval as predicting the quantile of a future residual, given a user-specified point prediction algorithm. Theoretically, we establish asymptotic valid conditional coverage upon extending consistency analyses in quantile regression. Using simulation and real-data experiments, we demonstrate a significant reduction in interval width of SPCI compared to other existing methods under the desired empirical coverage.

We study the robust interpolation problem of arbitrary data distributions supported on a bounded space and propose a two-fold law of robustness. Robust interpolation refers to the problem of interpolating n noisy training data points in R^d by a Lipschitz function. Although this problem has been well understood when the samples are drawn from an isoperimetry distribution, much remains unknown concerning its performance under generic or even the worst-case distributions. We prove a Lipschitzness lower bound Omega(n/p) of the interpolating neural network with p parameters on arbitrary data distributions. With this result, we validate the law of robustness conjecture in prior work by Bubeck, Li, and Nagaraj on two-layer neural networks with polynomial weights. We then extend our result to arbitrary interpolating approximators and prove a Lipschitzness lower bound Omega(n^{1/d}) for robust interpolation. Our results demonstrate a two-fold law of robustness: i) we show the potential benefit of overparametrization for smooth data interpolation when n=poly(d), and ii) we disprove the potential existence of an O(1)-Lipschitz robust interpolating function when n=exp(omega(d)).

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.

Meta-learning has emerged as an effective methodology to model several real-world tasks and problems due to its extraordinary effectiveness in the low-data regime. There are many scenarios ranging from the classification of rare diseases to language modelling of uncommon languages where the availability of large datasets is rare. Similarly, for more broader scenarios like self-driving, an autonomous vehicle needs to be trained to handle every situation well. This requires training the ML model on a variety of tasks with good quality data. But often times, we find that the data distribution across various tasks is skewed, i.e.the data follows a long-tail distribution. This leads to the model performing well on some tasks and not performing so well on others leading to model robustness issues. Meta-learning has recently emerged as a potential learning paradigm which can effectively learn from one task and generalize that learning to unseen tasks. In this study, we aim to exploit external knowledge of task relations to improve training stability via effective mini-batching of tasks. We hypothesize that selecting a diverse set of tasks in a mini-batch will lead to a better estimate of the full gradient and hence will lead to a reduction of noise in training.

Currently, many theoretical as well as practically relevant questions towards the transferability and robustness of Convolutional Neural Networks (CNNs) remain unsolved. While ongoing research efforts are engaging these problems from various angles, in most computer vision related cases these approaches can be generalized to investigations of the effects of distribution shifts in image data. In this context, we propose to study the shifts in the learned weights of trained CNN models. Here we focus on the properties of the distributions of dominantly used 3x3 convolution filter kernels. We collected and publicly provide a dataset with over 1.4 billion filters from hundreds of trained CNNs, using a wide range of datasets, architectures, and vision tasks. In a first use case of the proposed dataset, we can show highly relevant properties of many publicly available pre-trained models for practical applications: I) We analyze distribution shifts (or the lack thereof) between trained filters along different axes of meta-parameters, like visual category of the dataset, task, architecture, or layer depth. Based on these results, we conclude that model pre-training can succeed on arbitrary datasets if they meet size and variance conditions. II) We show that many pre-trained models contain degenerated filters which make them less robust and less suitable for fine-tuning on target applications. Data & Project website: https://github.com/paulgavrikov/cnn-filter-db

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N{+}D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D{=}1 and to diffusion models when D{to}infty. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D{to} infty) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64{times}64 datasets, with FID scores of 1.91/2.43 when D{=}2048/128. In class-conditional setting, D{=}2048 yields current state-of-the-art FID of 1.74 on CIFAR-10. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

As the demand for high-quality data in model training grows, researchers and developers are increasingly generating synthetic data to tune and train LLMs. A common assumption about synthetic data is that sampling from instruct-tuned models is sufficient; however, these models struggle to produce diverse outputs-a key requirement for generalization. Despite various prompting methods, in this work we show that achieving meaningful diversity from instruct-tuned models remains challenging. In contrast, we find base models without post-training exhibit greater diversity, but are less capable at instruction following and hence of lower quality. Leveraging this insight, we propose Base-Refine (BARE), a synthetic data generation method that combines the diversity of base models with the quality of instruct-tuned models through a two-stage process. With minimal few-shot examples and curation, BARE generates diverse and high-quality datasets, improving downstream task performance. We show that fine-tuning with as few as 1,000 BARE-generated samples can reach performance comparable to the best similarly sized models on LiveCodeBench tasks. Furthermore, fine-tuning with BARE-generated data achieves a 101% improvement over instruct-only data on GSM8K and a 18.4% improvement over SOTA methods on RAFT.

Visual Auto-Regressive (VAR) models significantly reduce inference steps through the "next-scale" prediction paradigm. However, progressive multi-scale generation incurs substantial memory overhead due to cumulative KV caching, limiting practical deployment. We observe a scale-depth asymmetric dependency in VAR: early scales exhibit extreme sensitivity to network depth, while later scales remain robust to depth reduction. Inspired by this, we propose VARiant: by equidistant sampling, we select multiple subnets ranging from 16 to 2 layers from the original 30-layer VAR-d30 network. Early scales are processed by the full network, while later scales utilize subnet. Subnet and the full network share weights, enabling flexible depth adjustment within a single model. However, weight sharing between subnet and the entire network can lead to optimization conflicts. To address this, we propose a progressive training strategy that breaks through the Pareto frontier of generation quality for both subnets and the full network under fixed-ratio training, achieving joint optimality. Experiments on ImageNet demonstrate that, compared to the pretrained VAR-d30 (FID 1.95), VARiant-d16 and VARiant-d8 achieve nearly equivalent quality (FID 2.05/2.12) while reducing memory consumption by 40-65%. VARiant-d2 achieves 3.5 times speedup and 80% memory reduction at moderate quality cost (FID 2.97). In terms of deployment, VARiant's single-model architecture supports zero-cost runtime depth switching and provides flexible deployment options from high quality to extreme efficiency, catering to diverse application scenarios.

We consider the two related problems of detecting if an example is misclassified or out-of-distribution. We present a simple baseline that utilizes probabilities from softmax distributions. Correctly classified examples tend to have greater maximum softmax probabilities than erroneously classified and out-of-distribution examples, allowing for their detection. We assess performance by defining several tasks in computer vision, natural language processing, and automatic speech recognition, showing the effectiveness of this baseline across all. We then show the baseline can sometimes be surpassed, demonstrating the room for future research on these underexplored detection tasks.

Large transformer-based models are able to perform in-context few-shot learning, without being explicitly trained for it. This observation raises the question: what aspects of the training regime lead to this emergent behavior? Here, we show that this behavior is driven by the distributions of the training data itself. In-context learning emerges when the training data exhibits particular distributional properties such as burstiness (items appear in clusters rather than being uniformly distributed over time) and having large numbers of rarely occurring classes. In-context learning also emerges more strongly when item meanings or interpretations are dynamic rather than fixed. These properties are exemplified by natural language, but are also inherent to naturalistic data in a wide range of other domains. They also depart significantly from the uniform, i.i.d. training distributions typically used for standard supervised learning. In our initial experiments, we found that in-context learning traded off against more conventional weight-based learning, and models were unable to achieve both simultaneously. However, our later experiments uncovered that the two modes of learning could co-exist in a single model when it was trained on data following a skewed Zipfian distribution -- another common property of naturalistic data, including language. In further experiments, we found that naturalistic data distributions were only able to elicit in-context learning in transformers, and not in recurrent models. In sum, our findings indicate how the transformer architecture works together with particular properties of the training data to drive the intriguing emergent in-context learning behaviour of large language models, and how future work might encourage both in-context and in-weights learning in domains beyond language.

Model selection/optimization in conformal inference is challenging, since it may break the exchangeability between labeled and unlabeled data. We study this problem in the context of conformal selection, which uses conformal p-values to select ``interesting'' instances with large unobserved labels from a pool of unlabeled data, while controlling the FDR in finite sample. For validity, existing solutions require the model choice to be independent of the data used to construct the p-values and calibrate the selection set. However, when presented with many model choices and limited labeled data, it is desirable to (i) select the best model in a data-driven manner, and (ii) mitigate power loss due to sample splitting. This paper presents OptCS, a general framework that allows valid statistical testing (selection) after flexible data-driven model optimization. We introduce general conditions under which OptCS constructs valid conformal p-values despite substantial data reuse and handles complex p-value dependencies to maintain finite-sample FDR control via a novel multiple testing procedure. We instantiate this general recipe to propose three FDR-controlling procedures, each optimizing the models differently: (i) selecting the most powerful one among multiple pre-trained candidate models, (ii) using all data for model fitting without sample splitting, and (iii) combining full-sample model fitting and selection. We demonstrate the efficacy of our methods via simulation studies and real applications in drug discovery and alignment of large language models in radiology report generation.

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.

Realistic virtual humans play a crucial role in numerous industries, such as metaverse, intelligent healthcare, and self-driving simulation. But creating them on a large scale with high levels of realism remains a challenge. The utilization of deep implicit function sparks a new era of image-based 3D clothed human reconstruction, enabling pixel-aligned shape recovery with fine details. Subsequently, the vast majority of works locate the surface by regressing the deterministic implicit value for each point. However, should all points be treated equally regardless of their proximity to the surface? In this paper, we propose replacing the implicit value with an adaptive uncertainty distribution, to differentiate between points based on their distance to the surface. This simple ``value to distribution'' transition yields significant improvements on nearly all the baselines. Furthermore, qualitative results demonstrate that the models trained using our uncertainty distribution loss, can capture more intricate wrinkles, and realistic limbs. Code and models are available for research purposes at https://github.com/psyai-net/D-IF_release.