Daily Papers

Convolutional image classifiers can achieve high predictive accuracy, but quantifying their uncertainty remains an unresolved challenge, hindering their deployment in consequential settings. Existing uncertainty quantification techniques, such as Platt scaling, attempt to calibrate the network's probability estimates, but they do not have formal guarantees. We present an algorithm that modifies any classifier to output a predictive set containing the true label with a user-specified probability, such as 90%. The algorithm is simple and fast like Platt scaling, but provides a formal finite-sample coverage guarantee for every model and dataset. Our method modifies an existing conformal prediction algorithm to give more stable predictive sets by regularizing the small scores of unlikely classes after Platt scaling. In experiments on both Imagenet and Imagenet-V2 with ResNet-152 and other classifiers, our scheme outperforms existing approaches, achieving coverage with sets that are often factors of 5 to 10 smaller than a stand-alone Platt scaling baseline.

To provide rigorous uncertainty quantification for online learning models, we develop a framework for constructing uncertainty sets that provably control risk -- such as coverage of confidence intervals, false negative rate, or F1 score -- in the online setting. This extends conformal prediction to apply to a larger class of online learning problems. Our method guarantees risk control at any user-specified level even when the underlying data distribution shifts drastically, even adversarially, over time in an unknown fashion. The technique we propose is highly flexible as it can be applied with any base online learning algorithm (e.g., a deep neural network trained online), requiring minimal implementation effort and essentially zero additional computational cost. We further extend our approach to control multiple risks simultaneously, so the prediction sets we generate are valid for all given risks. To demonstrate the utility of our method, we conduct experiments on real-world tabular time-series data sets showing that the proposed method rigorously controls various natural risks. Furthermore, we show how to construct valid intervals for an online image-depth estimation problem that previous sequential calibration schemes cannot handle.

Visual navigation is a fundamental problem in embodied AI, yet practical deployments demand long-horizon planning capabilities to address multi-objective tasks. A major bottleneck is data scarcity: policies learned from limited data often overfit and fail to generalize OOD. Existing neural network-based agents typically increase architectural complexity that paradoxically become counterproductive in the small-sample regime. This paper introduce NeuRO, a integrated learning-to-optimize framework that tightly couples perception networks with downstream task-level robust optimization. Specifically, NeuRO addresses core difficulties in this integration: (i) it transforms noisy visual predictions under data scarcity into convex uncertainty sets using Partially Input Convex Neural Networks (PICNNs) with conformal calibration, which directly parameterize the optimization constraints; and (ii) it reformulates planning under partial observability as a robust optimization problem, enabling uncertainty-aware policies that transfer across environments. Extensive experiments on both unordered and sequential multi-object navigation tasks demonstrate that NeuRO establishes SoTA performance, particularly in generalization to unseen environments. Our work thus presents a significant advancement for developing robust, generalizable autonomous agents.

Robust optimization safeguards decisions against uncertainty by optimizing against worst-case scenarios, yet their effectiveness hinges on a prespecified robustness level that is often chosen ad hoc, leading to either insufficient protection or overly conservative and costly solutions. Recent approaches using conformal prediction construct data-driven uncertainty sets with finite-sample coverage guarantees, but they still fix coverage targets a priori and offer little guidance for selecting robustness levels. We propose a new framework that provides distribution-free, finite-sample guarantees on both miscoverage and regret for any family of robust predict-then-optimize policies. Our method constructs valid estimators that trace out the miscoverage-regret Pareto frontier, enabling decision-makers to reliably evaluate and calibrate robustness levels according to their cost-risk preferences. The framework is simple to implement, broadly applicable across classical optimization formulations, and achieves sharper finite-sample performance than existing approaches. These results offer the first principled data-driven methodology for guiding robustness selection and empower practitioners to balance robustness and conservativeness in high-stakes decision-making.

The two-stage object pose estimation paradigm first detects semantic keypoints on the image and then estimates the 6D pose by minimizing reprojection errors. Despite performing well on standard benchmarks, existing techniques offer no provable guarantees on the quality and uncertainty of the estimation. In this paper, we inject two fundamental changes, namely conformal keypoint detection and geometric uncertainty propagation, into the two-stage paradigm and propose the first pose estimator that endows an estimation with provable and computable worst-case error bounds. On one hand, conformal keypoint detection applies the statistical machinery of inductive conformal prediction to convert heuristic keypoint detections into circular or elliptical prediction sets that cover the groundtruth keypoints with a user-specified marginal probability (e.g., 90%). Geometric uncertainty propagation, on the other, propagates the geometric constraints on the keypoints to the 6D object pose, leading to a Pose UnceRtainty SEt (PURSE) that guarantees coverage of the groundtruth pose with the same probability. The PURSE, however, is a nonconvex set that does not directly lead to estimated poses and uncertainties. Therefore, we develop RANdom SAmple averaGing (RANSAG) to compute an average pose and apply semidefinite relaxation to upper bound the worst-case errors between the average pose and the groundtruth. On the LineMOD Occlusion dataset we demonstrate: (i) the PURSE covers the groundtruth with valid probabilities; (ii) the worst-case error bounds provide correct uncertainty quantification; and (iii) the average pose achieves better or similar accuracy as representative methods based on sparse keypoints.

Black-box machine learning models are now routinely used in high-risk settings, like medical diagnostics, which demand uncertainty quantification to avoid consequential model failures. Conformal prediction is a user-friendly paradigm for creating statistically rigorous uncertainty sets/intervals for the predictions of such models. Critically, the sets are valid in a distribution-free sense: they possess explicit, non-asymptotic guarantees even without distributional assumptions or model assumptions. One can use conformal prediction with any pre-trained model, such as a neural network, to produce sets that are guaranteed to contain the ground truth with a user-specified probability, such as 90%. It is easy-to-understand, easy-to-use, and general, applying naturally to problems arising in the fields of computer vision, natural language processing, deep reinforcement learning, and so on. This hands-on introduction is aimed to provide the reader a working understanding of conformal prediction and related distribution-free uncertainty quantification techniques with one self-contained document. We lead the reader through practical theory for and examples of conformal prediction and describe its extensions to complex machine learning tasks involving structured outputs, distribution shift, time-series, outliers, models that abstain, and more. Throughout, there are many explanatory illustrations, examples, and code samples in Python. With each code sample comes a Jupyter notebook implementing the method on a real-data example; the notebooks can be accessed and easily run using our codebase.

Deep reinforcement learning (RL) has achieved significant success, yet its application in real-world scenarios is often hindered by a lack of robustness to environmental uncertainties. To solve this challenge, some robust RL algorithms have been proposed, but most are limited to tabular settings. In this work, we propose Distributionally Robust Soft Actor-Critic (DR-SAC), a novel algorithm designed to enhance the robustness of the state-of-the-art Soft Actor-Critic (SAC) algorithm. DR-SAC aims to maximize the expected value with entropy against the worst possible transition model lying in an uncertainty set. A distributionally robust version of the soft policy iteration is derived with a convergence guarantee. For settings where nominal distributions are unknown, such as offline RL, a generative modeling approach is proposed to estimate the required nominal distributions from data. Furthermore, experimental results on a range of continuous control benchmark tasks demonstrate our algorithm achieves up to 9.8 times the average reward of the SAC baseline under common perturbations. Additionally, compared with existing robust reinforcement learning algorithms, DR-SAC significantly improves computing efficiency and applicability to large-scale problems.

In this paper, we study robust decision-making in the latent space of world models (WMs). Robust optimization is a mathematical framework where, given explicitly specified dynamics and physically meaningful disturbances, a robot can select actions that remain effective even under worst-case disturbances. However, applying this principle to the learned latent space of WMs introduces a fundamental challenge: because WMs have fully learned state spaces and dynamics inferred from high-dimensional observations, it is unclear how to define latent-space disturbances that faithfully represent uncertainty in the underlying system. Our key idea is to model a latent-space disturbance as a perturbation to the learned latent dynamics that induces pessimistic but plausible transitions. Specifically, we construct a set of plausible latent dynamics by combining a dynamics-aware similarity metric that captures plausible transitions with out-of-distribution detection that excludes implausible latent states. We calibrate this uncertainty set over latent dynamics using conformal prediction, ensuring that WM imaginations induced by the latent disturbance remain plausible without becoming overly pessimistic. We then jointly optimize robust robot actions and the worst-case latent disturbances through game-theoretic optimization. We leverage this latent-space robust optimization to robustify policy steering, considering two paradigms: latent safety filtering and sample-and-verify steering of a generative control policy. Our controlled simulation experiments show that our latent disturbance enables robust decision-making directly in WM latent spaces, and hardware experiments with a Franka manipulator show that modeling latent disturbances enables robust policy steering, reducing failures by 70% in safety filtering and 54% in sampling-based policy steering. Project website: https://junwon.me/LatentDisturbance/.

Domain generalization (DG) aims to tackle the distribution shift between training domains and unknown target domains. Generating new domains is one of the most effective approaches, yet its performance gain depends on the distribution discrepancy between the generated and target domains. Distributionally robust optimization is promising to tackle distribution discrepancy by exploring domains in an uncertainty set. However, the uncertainty set may be overwhelmingly large, leading to low-confidence prediction in DG. It is because a large uncertainty set could introduce domains containing semantically different factors from training domains. To address this issue, we propose to perform a moderately distributional exploration (MODE) for domain generalization. Specifically, MODE performs distribution exploration in an uncertainty subset that shares the same semantic factors with the training domains. We show that MODE can endow models with provable generalization performance on unknown target domains. The experimental results show that MODE achieves competitive performance compared to state-of-the-art baselines.

Robust Markov decision processes (MDPs) address the challenge of model uncertainty by optimizing the worst-case performance over an uncertainty set of MDPs. In this paper, we focus on the robust average-reward MDPs under the model-free setting. We first theoretically characterize the structure of solutions to the robust average-reward Bellman equation, which is essential for our later convergence analysis. We then design two model-free algorithms, robust relative value iteration (RVI) TD and robust RVI Q-learning, and theoretically prove their convergence to the optimal solution. We provide several widely used uncertainty sets as examples, including those defined by the contamination model, total variation, Chi-squared divergence, Kullback-Leibler (KL) divergence and Wasserstein distance.

We consider the problem of global optimization with noisy zeroth order oracles - a well-motivated problem useful for various applications ranging from hyper-parameter tuning for deep learning to new material design. Existing work relies on Gaussian processes or other non-parametric family, which suffers from the curse of dimensionality. In this paper, we propose a new algorithm GO-UCB that leverages a parametric family of functions (e.g., neural networks) instead. Under a realizable assumption and a few other mild geometric conditions, we show that GO-UCB achieves a cumulative regret of O(T) where T is the time horizon. At the core of GO-UCB is a carefully designed uncertainty set over parameters based on gradients that allows optimistic exploration. Synthetic and real-world experiments illustrate GO-UCB works better than Bayesian optimization approaches in high dimensional cases, even if the model is misspecified.

The Distributionally Robust Markov Decision Process (DRMDP) is a popular framework for addressing dynamics shift in reinforcement learning by learning policies robust to the worst-case transition dynamics within a constrained set. However, solving its dual optimization oracle poses significant challenges, limiting theoretical analysis and computational efficiency. The recently proposed Robust Regularized Markov Decision Process (RRMDP) replaces the uncertainty set constraint with a regularization term on the value function, offering improved scalability and theoretical insights. Yet, existing RRMDP methods rely on unstructured regularization, often leading to overly conservative policies by considering transitions that are unrealistic. To address these issues, we propose a novel framework, the d-rectangular linear robust regularized Markov decision process (d-RRMDP), which introduces a linear latent structure into both transition kernels and regularization. For the offline RL setting, where an agent learns robust policies from a pre-collected dataset in the nominal environment, we develop a family of algorithms, Robust Regularized Pessimistic Value Iteration (R2PVI), employing linear function approximation and f-divergence based regularization terms on transition kernels. We provide instance-dependent upper bounds on the suboptimality gap of R2PVI policies, showing these bounds depend on how well the dataset covers state-action spaces visited by the optimal robust policy under robustly admissible transitions. This term is further shown to be fundamental to d-RRMDPs via information-theoretic lower bounds. Finally, numerical experiments validate that R2PVI learns robust policies and is computationally more efficient than methods for constrained DRMDPs.

Reasoning-capable large language models (LLMs) have recently been adopted as automated judges, but their benefits and costs in LLM-as-a-Judge settings remain unclear. Through controlled comparisons between reasoning and non-reasoning judges, we show that explicit reasoning substantially improves judgment accuracy on tasks requiring structured verification (e.g., math and coding), while offering limited or even negative gains on simpler evaluations and incurring significantly higher computational cost. These findings motivate that reasoning should be used selectively rather than universally, with awareness of possible distribution shift. We propose a Robust Adaptive Cost-Efficient Routing (RACER), which dynamically selects between reasoning and non-reasoning judges under a fixed budget by formulating routing as a constrained distributionally robust optimization problem. RACER explicitly accounts for distribution shift via a KL-divergence uncertainty set, admits an efficient primal--dual algorithm, and enjoys theoretical guarantees including uniqueness of the optimal policy and linear convergence. Extensive experiments show that RACER achieves superior accuracy--cost trade-offs under distribution shift.

Conformal prediction is a powerful tool to generate uncertainty sets with guaranteed coverage using any predictive model, under the assumption that the training and test data are i.i.d.. Recently, it has been shown that adversarial examples are able to manipulate conformal methods to construct prediction sets with invalid coverage rates, as the i.i.d. assumption is violated. To address this issue, a recent work, Randomized Smoothed Conformal Prediction (RSCP), was first proposed to certify the robustness of conformal prediction methods to adversarial noise. However, RSCP has two major limitations: (i) its robustness guarantee is flawed when used in practice and (ii) it tends to produce large uncertainty sets. To address these limitations, we first propose a novel framework called RSCP+ to provide provable robustness guarantee in evaluation, which fixes the issues in the original RSCP method. Next, we propose two novel methods, Post-Training Transformation (PTT) and Robust Conformal Training (RCT), to effectively reduce prediction set size with little computation overhead. Experimental results in CIFAR10, CIFAR100, and ImageNet suggest the baseline method only yields trivial predictions including full label set, while our methods could boost the efficiency by up to 4.36times, 5.46times, and 16.9times respectively and provide practical robustness guarantee. Our codes are available at https://github.com/Trustworthy-ML-Lab/Provably-Robust-Conformal-Prediction.

Robust reinforcement learning is the problem of learning control policies that provide optimal worst-case performance against a span of adversarial environments. It is a crucial ingredient for deploying algorithms in real-world scenarios with prevalent environmental uncertainties and has been a long-standing object of attention in the community, without a standardized set of benchmarks. This contribution endeavors to fill this gap. We introduce the Robust Reinforcement Learning Suite (RRLS), a benchmark suite based on Mujoco environments. RRLS provides six continuous control tasks with two types of uncertainty sets for training and evaluation. Our benchmark aims to standardize robust reinforcement learning tasks, facilitating reproducible and comparable experiments, in particular those from recent state-of-the-art contributions, for which we demonstrate the use of RRLS. It is also designed to be easily expandable to new environments. The source code is available at https://github.com/SuReLI/RRLS{https://github.com/SuReLI/RRLS}.

We consider the distributionally robust optimization (DRO) problem with spectral risk-based uncertainty set and f-divergence penalty. This formulation includes common risk-sensitive learning objectives such as regularized condition value-at-risk (CVaR) and average top-k loss. We present Prospect, a stochastic gradient-based algorithm that only requires tuning a single learning rate hyperparameter, and prove that it enjoys linear convergence for smooth regularized losses. This contrasts with previous algorithms that either require tuning multiple hyperparameters or potentially fail to converge due to biased gradient estimates or inadequate regularization. Empirically, we show that Prospect can converge 2-3times faster than baselines such as stochastic gradient and stochastic saddle-point methods on distribution shift and fairness benchmarks spanning tabular, vision, and language domains.

This paper proposes a two-time scale neurodynamic duplex approach to solve distributionally robust geometric joint chance-constrained optimization problems. The probability distributions of the row vectors are not known in advance and belong to a certain distributional uncertainty set. In our paper, we study three uncertainty sets for the unknown distributions. The neurodynamic duplex is designed based on three projection equations. The main contribution of our work is to propose a neural network-based method to solve distributionally robust joint chance-constrained optimization problems that converges in probability to the global optimum without the use of standard state-of-the-art solving methods. We show that neural networks can be used to solve multiple instances of a problem. In the numerical experiments, we apply the proposed approach to solve a problem of shape optimisation and a telecommunication problem.

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.

As Large Language Models (LLMs) continue to progress toward more advanced forms of intelligence, Reinforcement Learning from Human Feedback (RLHF) is increasingly seen as a key pathway toward achieving Artificial General Intelligence (AGI). However, the reliance on reward-model-based (RM-based) alignment methods introduces significant challenges due to the inherent instability and imperfections of Reward Models (RMs), which can lead to critical issues such as reward hacking and misalignment with human intentions. In this paper, we introduce a reward-robust RLHF framework aimed at addressing these fundamental challenges, paving the way for more reliable and resilient learning in LLMs. Our approach introduces a novel optimization objective that carefully balances performance and robustness by incorporating Bayesian Reward Model Ensembles (BRME) to model the uncertainty set of reward functions. This allows the framework to integrate both nominal performance and minimum reward signals, ensuring more stable learning even with imperfect reward models. Empirical results demonstrate that our framework consistently outperforms traditional RLHF across diverse benchmarks, showing improved accuracy and long-term stability. We also provide a theoretical analysis, demonstrating that reward-robust RLHF approaches the stability of constant reward settings, which proves to be effective in a stochastic-case analysis. Together, these contributions highlight the framework potential to enhance both the performance and stability of LLM alignment with RLHF.

We present a variational free-energy formulation for distributionally robust decision-making with ambiguity in the generative model. The formulation, related to a broad range of learning and control frameworks, yields a minimax optimal control problem where maximization is over an uncertainty set that represents ambiguities. We prove that computing the optimal policy requires solving a non-convex minimization problem and propose an algorithm with convergence guarantees to find the solution. The effectiveness of our results is illustrated via simulations on a pendulum swing-up problem.

Driven by advancements in deep learning, computer-aided diagnoses have made remarkable progress. However, outside controlled laboratory settings, algorithms may encounter several challenges. In the medical domain, these difficulties often stem from limited data availability due to ethical and legal restrictions, as well as the high cost and time required for expert annotations-especially in the face of emerging or rare diseases. In this context, open-set recognition plays a vital role by identifying whether a sample belongs to one of the known classes seen during training or should be rejected as an unknown. Recent studies have shown that features learned in the later stages of deep neural networks are observed to cluster around their class means, which themselves are arranged as individual vertices of a regular simplex [32]. The proposed method introduces a loss function designed to reject samples of unknown classes effectively by penalizing open space regions using auxiliary datasets. This approach achieves significant performance gain across four MedMNIST datasets-BloodMNIST, OCTMNIST, DermaMNIST, TissueMNIST and a publicly available skin dataset [29] outperforming state-of-the-art techniques.

Hydrogen-electrical microgrids are increasingly assuming an important role on the pathway toward decarbonization of energy and transportation systems. This paper studies networked hydrogen-electrical microgrids planning (NHEMP), considering a critical but often-overlooked issue, i.e., the demand-inducing effect (DIE) associated with infrastructure development decisions. Specifically, higher refueling capacities will attract more refueling demand of hydrogen-powered vehicles (HVs). To capture such interactions between investment decisions and induced refueling demand, we introduce a decision-dependent uncertainty (DDU) set and build a trilevel stochastic-robust formulation. The upper-level determines optimal investment strategies for hydrogen-electrical microgrids, the lower-level optimizes the risk-aware operation schedules across a series of stochastic scenarios, and, for each scenario, the middle-level identifies the "worst" situation of refueling demand within an individual DDU set to ensure economic feasibility. Then, an adaptive and exact decomposition algorithm, based on Parametric Column-and-Constraint Generation (PC&CG), is customized and developed to address the computational challenge and to quantitatively analyze the impact of DIE. Case studies on an IEEE exemplary system validate the effectiveness of the proposed NHEMP model and the PC&CG algorithm. It is worth highlighting that DIE can make an important contribution to the economic benefits of NHEMP, yet its significance will gradually decrease when the main bottleneck transits to other system restrictions.

Prediction sets capture uncertainty by predicting sets of labels rather than individual labels, enabling downstream decisions to conservatively account for all plausible outcomes. Conformal inference algorithms construct prediction sets guaranteed to contain the true label with high probability. These guarantees fail to hold in the face of distribution shift, which is precisely when reliable uncertainty quantification can be most useful. We propose a novel algorithm for constructing prediction sets with PAC guarantees in the label shift setting. This method estimates the predicted probabilities of the classes in a target domain, as well as the confusion matrix, then propagates uncertainty in these estimates through a Gaussian elimination algorithm to compute confidence intervals for importance weights. Finally, it uses these intervals to construct prediction sets. We evaluate our approach on five datasets: the CIFAR-10, ChestX-Ray and Entity-13 image datasets, the tabular CDC Heart dataset, and the AGNews text dataset. Our algorithm satisfies the PAC guarantee while producing smaller, more informative, prediction sets compared to several baselines.

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.

Despite their success in many domains, large language models (LLMs) remain under-studied in scenarios requiring optimal decision-making under uncertainty. This is crucial as many real-world applications, ranging from personalized recommendations to healthcare interventions, demand that LLMs not only predict but also actively learn to make optimal decisions through exploration. In this work, we measure LLMs' (in)ability to make optimal decisions in bandits, a state-less reinforcement learning setting relevant to many applications. We develop a comprehensive suite of environments, including both context-free and contextual bandits with varying task difficulties, to benchmark LLMs' performance. Motivated by the existence of optimal exploration algorithms, we propose efficient ways to integrate this algorithmic knowledge into LLMs: by providing explicit algorithm-guided support during inference; and through algorithm distillation via in-context demonstrations and fine-tuning, using synthetic data generated from these algorithms. Impressively, these techniques allow us to achieve superior exploration performance with smaller models, surpassing larger models on various tasks. We conducted an extensive ablation study to shed light on various factors, such as task difficulty and data representation, that influence the efficiency of LLM exploration. Additionally, we conduct a rigorous analysis of the LLM's exploration efficiency using the concept of regret, linking its ability to explore to the model size and underlying algorithm.

Humor recognition has been extensively studied with different methods in the past years. However, existing studies on humor recognition do not understand the mechanisms that generate humor. In this paper, inspired by the incongruity theory, any joke can be divided into two components (the setup and the punchline). Both components have multiple possible semantics, and there is an incongruous relationship between them. We use density matrices to represent the semantic uncertainty of the setup and the punchline, respectively, and design QE-Uncertainty and QE-Incongruity with the help of quantum entropy as features for humor recognition. The experimental results on the SemEval2021 Task 7 dataset show that the proposed features are more effective than the baselines for recognizing humorous and non-humorous texts.

The main objective of Prognostics and Health Management is to estimate the Remaining Useful Lifetime (RUL), namely, the time that a system or a piece of equipment is still in working order before starting to function incorrectly. In recent years, numerous machine learning algorithms have been proposed for RUL estimation, mainly focusing on providing more accurate RUL predictions. However, there are many sources of uncertainty in the problem, such as inherent randomness of systems failure, lack of knowledge regarding their future states, and inaccuracy of the underlying predictive models, making it infeasible to predict the RULs precisely. Hence, it is of utmost importance to quantify the uncertainty alongside the RUL predictions. In this work, we investigate the conformal prediction (CP) framework that represents uncertainty by predicting sets of possible values for the target variable (intervals in the case of RUL) instead of making point predictions. Under very mild technical assumptions, CP formally guarantees that the actual value (true RUL) is covered by the predicted set with a degree of certainty that can be prespecified. We study three CP algorithms to conformalize any single-point RUL predictor and turn it into a valid interval predictor. Finally, we conformalize two single-point RUL predictors, deep convolutional neural networks and gradient boosting, and illustrate their performance on the Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) data sets.

Uncertainty learning and quantification of models are crucial tasks to enhance the trustworthiness of the models. Importantly, the recent surge of generative language models (GLMs) emphasizes the need for reliable uncertainty quantification due to the concerns on generating hallucinated facts. In this paper, we propose to learn neural prediction set models that comes with the probably approximately correct (PAC) guarantee for quantifying the uncertainty of GLMs. Unlike existing prediction set models, which are parameterized by a scalar value, we propose to parameterize prediction sets via neural networks, which achieves more precise uncertainty quantification but still satisfies the PAC guarantee. We demonstrate the efficacy of our method on four types of language datasets and six types of models by showing that our method improves the quantified uncertainty by 63% on average, compared to a standard baseline method.

Active learning (AL) in open set scenarios presents a novel challenge of identifying the most valuable examples in an unlabeled data pool that comprises data from both known and unknown classes. Traditional methods prioritize selecting informative examples with low confidence, with the risk of mistakenly selecting unknown-class examples with similarly low confidence. Recent methods favor the most probable known-class examples, with the risk of picking simple already mastered examples. In this paper, we attempt to query examples that are both likely from known classes and highly informative, and propose a Bidirectional Uncertainty-based Active Learning (BUAL) framework. Specifically, we achieve this by first pushing the unknown class examples toward regions with high-confidence predictions, i.e., the proposed Random Label Negative Learning method. Then, we propose a Bidirectional Uncertainty sampling strategy by jointly estimating uncertainty posed by both positive and negative learning to perform consistent and stable sampling. BUAL successfully extends existing uncertainty-based AL methods to complex open-set scenarios. Extensive experiments on multiple datasets with varying openness demonstrate that BUAL achieves state-of-the-art performance. The code is available at https://github.com/chenchenzong/BUAL.

Active learning (AL), which iteratively queries the most informative examples from a large pool of unlabeled candidates for model training, faces significant challenges in the presence of open-set classes. Existing methods either prioritize query examples likely to belong to known classes, indicating low epistemic uncertainty (EU), or focus on querying those with highly uncertain predictions, reflecting high aleatoric uncertainty (AU). However, they both yield suboptimal performance, as low EU corresponds to limited useful information, and closed-set AU metrics for unknown class examples are less meaningful. In this paper, we propose an Energy-based Active Open-set Annotation (EAOA) framework, which effectively integrates EU and AU to achieve superior performance. EAOA features a (C+1)-class detector and a target classifier, incorporating an energy-based EU measure and a margin-based energy loss designed for the detector, alongside an energy-based AU measure for the target classifier. Another crucial component is the target-driven adaptive sampling strategy. It first forms a smaller candidate set with low EU scores to ensure closed-set properties, making AU metrics meaningful. Subsequently, examples with high AU scores are queried to form the final query set, with the candidate set size adjusted adaptively. Extensive experiments show that EAOA achieves state-of-the-art performance while maintaining high query precision and low training overhead. The code is available at https://github.com/chenchenzong/EAOA.

Healthcare foundation models have largely followed paradigms from natural language processing and computer vision, emphasizing large scale pretraining and deterministic representations over heterogeneous clinical data. However, clinical observations are inherently incomplete, reflecting sparse, irregular, and modality dependent measurements of an underlying physiologic state. In this work, we propose a framework for uncertainty aware foundation modeling that represents each patient not as a point embedding, but as a distribution over plausible latent states. By learning set valued representations and enforcing consistency across partial views of the same patient, the model captures what is invariantly inferable while explicitly encoding epistemic uncertainty. We integrate this formulation with multimodal encoders and scalable self supervised objectives, combining reconstruction, contrastive alignment, and distributional regularization. Across diverse clinical tasks, our approach improves predictive performance, robustness under missing data, and uncertainty calibration relative to strong baselines. These results suggest that modeling what is not observed rather than only what is constitutes a critical inductive bias for healthcare foundation models.

Uncertainty quantification in Knowledge Graph Embedding (KGE) methods is crucial for ensuring the reliability of downstream applications. A recent work applies conformal prediction to KGE methods, providing uncertainty estimates by generating a set of answers that is guaranteed to include the true answer with a predefined confidence level. However, existing methods provide probabilistic guarantees averaged over a reference set of queries and answers (marginal coverage guarantee). In high-stakes applications such as medical diagnosis, a stronger guarantee is often required: the predicted sets must provide consistent coverage per query (conditional coverage guarantee). We propose CondKGCP, a novel method that approximates predicate-conditional coverage guarantees while maintaining compact prediction sets. CondKGCP merges predicates with similar vector representations and augments calibration with rank information. We prove the theoretical guarantees and demonstrate empirical effectiveness of CondKGCP by comprehensive evaluations.

A set of novel approaches for estimating epistemic uncertainty in deep neural networks with a single forward pass has recently emerged as a valid alternative to Bayesian Neural Networks. On the premise of informative representations, these deterministic uncertainty methods (DUMs) achieve strong performance on detecting out-of-distribution (OOD) data while adding negligible computational costs at inference time. However, it remains unclear whether DUMs are well calibrated and can seamlessly scale to real-world applications - both prerequisites for their practical deployment. To this end, we first provide a taxonomy of DUMs, and evaluate their calibration under continuous distributional shifts. Then, we extend them to semantic segmentation. We find that, while DUMs scale to realistic vision tasks and perform well on OOD detection, the practicality of current methods is undermined by poor calibration under distributional shifts.

Accurate uncertainty estimates are essential for deploying deep object detectors in safety-critical systems. The development and evaluation of probabilistic object detectors have been hindered by shortcomings in existing performance measures, which tend to involve arbitrary thresholds or limit the detector's choice of distributions. In this work, we propose to view object detection as a set prediction task where detectors predict the distribution over the set of objects. Using the negative log-likelihood for random finite sets, we present a proper scoring rule for evaluating and training probabilistic object detectors. The proposed method can be applied to existing probabilistic detectors, is free from thresholds, and enables fair comparison between architectures. Three different types of detectors are evaluated on the COCO dataset. Our results indicate that the training of existing detectors is optimized toward non-probabilistic metrics. We hope to encourage the development of new object detectors that can accurately estimate their own uncertainty. Code available at https://github.com/georghess/pmb-nll.

This paper extends Cross Modal Generalization (CMG) to open-set environments by proposing the more challenging Open-set Cross Modal Generalization (OSCMG) task. This task evaluates multimodal unified representations in open-set conditions, addressing the limitations of prior closed-set cross-modal evaluations. OSCMG requires not only cross-modal knowledge transfer but also robust generalization to unseen classes within new modalities, a scenario frequently encountered in real-world applications. Existing multimodal unified representation work lacks consideration for open-set environments. To tackle this, we propose MICU, comprising two key components: Fine-Coarse Masked multimodal InfoNCE (FCMI) and Cross modal Unified Jigsaw Puzzles (CUJP). FCMI enhances multimodal alignment by applying contrastive learning at both holistic semantic and temporal levels, incorporating masking to enhance generalization. CUJP enhances feature diversity and model uncertainty by integrating modality-agnostic feature selection with self-supervised learning, thereby strengthening the model's ability to handle unknown categories in open-set tasks. Extensive experiments on CMG and the newly proposed OSCMG validate the effectiveness of our approach. The code is available at https://github.com/haihuangcode/CMG.

Clouds and haze often occlude optical satellite images, hindering continuous, dense monitoring of the Earth's surface. Although modern deep learning methods can implicitly learn to ignore such occlusions, explicit cloud removal as pre-processing enables manual interpretation and allows training models when only few annotations are available. Cloud removal is challenging due to the wide range of occlusion scenarios -- from scenes partially visible through haze, to completely opaque cloud coverage. Furthermore, integrating reconstructed images in downstream applications would greatly benefit from trustworthy quality assessment. In this paper, we introduce UnCRtainTS, a method for multi-temporal cloud removal combining a novel attention-based architecture, and a formulation for multivariate uncertainty prediction. These two components combined set a new state-of-the-art performance in terms of image reconstruction on two public cloud removal datasets. Additionally, we show how the well-calibrated predicted uncertainties enable a precise control of the reconstruction quality.

As instruction-tuned large language models (LLMs) evolve, aligning pretrained foundation models presents increasing challenges. Existing alignment strategies, which typically leverage diverse and high-quality data sources, often overlook the intrinsic uncertainty of tasks, learning all data samples equally. This may lead to suboptimal data efficiency and model performance. In response, we propose uncertainty-aware learning (UAL) to improve the model alignment of different task scenarios, by introducing the sample uncertainty (elicited from more capable LLMs). We implement UAL in a simple fashion -- adaptively setting the label smoothing value of training according to the uncertainty of individual samples. Analysis shows that our UAL indeed facilitates better token clustering in the feature space, validating our hypothesis. Extensive experiments on widely used benchmarks demonstrate that our UAL significantly and consistently outperforms standard supervised fine-tuning. Notably, LLMs aligned in a mixed scenario have achieved an average improvement of 10.62\% on high-entropy tasks (i.e., AlpacaEval leaderboard), and 1.81\% on complex low-entropy tasks (i.e., MetaMath and GSM8K).

In question-answering tasks, determining when to trust the outputs is crucial to the alignment of large language models (LLMs). Kuhn et al. (2023) introduces semantic entropy as a measure of uncertainty, by incorporating linguistic invariances from the same meaning. It primarily relies on setting threshold to measure the level of semantic equivalence relation. We propose a more nuanced framework that extends beyond such thresholding by developing a Shapley-based uncertainty metric that captures the continuous nature of semantic relationships. We establish three fundamental properties that characterize valid uncertainty metrics and prove that our Shapley uncertainty satisfies these criteria. Through extensive experiments, we demonstrate that our Shapley uncertainty more accurately predicts LLM performance in question-answering and other datasets, compared to similar baseline measures.

Video Temporal Grounding (TG) aims to temporally locate video segments matching a natural language description (a query) in a long video. While Vision-Language Models (VLMs) are effective at holistic semantic matching, they often struggle with fine-grained temporal localisation. Recently, Group Relative Policy Optimisation (GRPO) reformulates the inference process as a reinforcement learning task, enabling fine-grained grounding and achieving strong in-domain performance. However, GRPO relies on labelled data, making it unsuitable in unlabelled domains. Moreover, because videos are large and expensive to store and process, performing full-scale adaptation introduces prohibitive latency and computational overhead, making it impractical for real-time deployment. To overcome both problems, we introduce a Data-Efficient Unlabelled Cross-domain Temporal Grounding method, from which a model is first trained on a labelled source domain, then adapted to a target domain using only a small number of unlabelled videos from the target domain. This approach eliminates the need for target annotation and keeps both computational and storage overhead low enough to run in real time. Specifically, we introduce. Uncertainty-quantified Rollout Policy Adaptation (URPA) for cross-domain knowledge transfer in learning video temporal grounding without target labels. URPA generates multiple candidate predictions using GRPO rollouts, averages them to form a pseudo label, and estimates confidence from the variance across these rollouts. This confidence then weights the training rewards, guiding the model to focus on reliable supervision. Experiments on three datasets across six cross-domain settings show that URPA generalises well using only a few unlabelled target videos. Codes will be released once published.

Subset selection-based methods are widely used to explain deep vision models: they attribute predictions by highlighting the most influential image regions and support object-level explanations. While these methods perform well in in-distribution (ID) settings, their behavior under out-of-distribution (OOD) conditions remains poorly understood. Through extensive experiments across multiple ID-OOD sets, we find that reliability of the existing subset based methods degrades markedly, yielding redundant, unstable, and uncertainty-sensitive explanations. To address these shortcomings, we introduce a framework that combines submodular subset selection with layer-wise, gradient-based uncertainty estimation to improve robustness and fidelity without requiring additional training or auxiliary models. Our approach estimates uncertainty via adaptive weight perturbations and uses these estimates to guide submodular optimization, ensuring diverse and informative subset selection. Empirical evaluations show that, beyond mitigating the weaknesses of existing methods under OOD scenarios, our framework also yields improvements in ID settings. These findings highlight limitations of current subset-based approaches and demonstrate how uncertainty-driven optimization can enhance attribution and object-level interpretability, paving the way for more transparent and trustworthy AI in real-world vision applications.

While 3D body reconstruction methods have made remarkable progress recently, it remains difficult to acquire the sufficiently accurate and numerous 3D supervisions required for training. In this paper, we propose KNOWN, a framework that effectively utilizes body KNOWledge and uNcertainty modeling to compensate for insufficient 3D supervisions. KNOWN exploits a comprehensive set of generic body constraints derived from well-established body knowledge. These generic constraints precisely and explicitly characterize the reconstruction plausibility and enable 3D reconstruction models to be trained without any 3D data. Moreover, existing methods typically use images from multiple datasets during training, which can result in data noise (e.g., inconsistent joint annotation) and data imbalance (e.g., minority images representing unusual poses or captured from challenging camera views). KNOWN solves these problems through a novel probabilistic framework that models both aleatoric and epistemic uncertainty. Aleatoric uncertainty is encoded in a robust Negative Log-Likelihood (NLL) training loss, while epistemic uncertainty is used to guide model refinement. Experiments demonstrate that KNOWN's body reconstruction outperforms prior weakly-supervised approaches, particularly on the challenging minority images.

Epistemic Uncertainty is a measure of the lack of knowledge of a learner which diminishes with more evidence. While existing work focuses on using the variance of the Bayesian posterior due to parameter uncertainty as a measure of epistemic uncertainty, we argue that this does not capture the part of lack of knowledge induced by model misspecification. We discuss how the excess risk, which is the gap between the generalization error of a predictor and the Bayes predictor, is a sound measure of epistemic uncertainty which captures the effect of model misspecification. We thus propose a principled framework for directly estimating the excess risk by learning a secondary predictor for the generalization error and subtracting an estimate of aleatoric uncertainty, i.e., intrinsic unpredictability. We discuss the merits of this novel measure of epistemic uncertainty, and highlight how it differs from variance-based measures of epistemic uncertainty and addresses its major pitfall. Our framework, Direct Epistemic Uncertainty Prediction (DEUP) is particularly interesting in interactive learning environments, where the learner is allowed to acquire novel examples in each round. Through a wide set of experiments, we illustrate how existing methods in sequential model optimization can be improved with epistemic uncertainty estimates from DEUP, and how DEUP can be used to drive exploration in reinforcement learning. We also evaluate the quality of uncertainty estimates from DEUP for probabilistic image classification and predicting synergies of drug combinations.

Hand trajectory forecasting from egocentric views is crucial for enabling a prompt understanding of human intentions when interacting with AR/VR systems. However, existing methods handle this problem in a 2D image space which is inadequate for 3D real-world applications. In this paper, we set up an egocentric 3D hand trajectory forecasting task that aims to predict hand trajectories in a 3D space from early observed RGB videos in a first-person view. To fulfill this goal, we propose an uncertainty-aware state space Transformer (USST) that takes the merits of the attention mechanism and aleatoric uncertainty within the framework of the classical state-space model. The model can be further enhanced by the velocity constraint and visual prompt tuning (VPT) on large vision transformers. Moreover, we develop an annotation workflow to collect 3D hand trajectories with high quality. Experimental results on H2O and EgoPAT3D datasets demonstrate the superiority of USST for both 2D and 3D trajectory forecasting. The code and datasets are publicly released: https://actionlab-cv.github.io/EgoHandTrajPred.

To mitigate the impact of hallucination nature of LLMs, many studies propose detecting hallucinated generation through uncertainty estimation. However, these approaches predominantly operate at the sentence or paragraph level, failing to pinpoint specific spans or entities responsible for hallucinated content. This lack of granularity is especially problematic for long-form outputs that mix accurate and fabricated information. To address this limitation, we explore entity-level hallucination detection. We propose a new data set, HalluEntity, which annotates hallucination at the entity level. Based on the dataset, we comprehensively evaluate uncertainty-based hallucination detection approaches across 17 modern LLMs. Our experimental results show that uncertainty estimation approaches focusing on individual token probabilities tend to over-predict hallucinations, while context-aware methods show better but still suboptimal performance. Through an in-depth qualitative study, we identify relationships between hallucination tendencies and linguistic properties and highlight important directions for future research.

As machine learning (ML) enters high-stakes domains, trustworthy uncertainty quantification (UQ) is essential for safety. In this paper we introduce PCS-UQ, a framework based on the Predictability, Computability, and Stability (PCS) principles for veridical data science. Starting with a candidate set of models or algorithms, PCS-UQ integrates a rigorous prediction-check to screen out unsuitable models in the set and utilizes bootstrap samples, in order to capture both inter-sample variability and algorithmic instability for the prediction-checked algorithms. We then introduce a novel multiplicative calibration scheme to enhance local adaptivity, which basically corresponds to a new score in conformal prediction. Moreover, we produce a compilation of 17 real-world regression datasets with manually-constructed subgroups. On this benchmark, PCS-UQ maintains the target coverage while outperforming or matching conformal methods equipped with oracle-selected algorithms in interval width. PCS-UQ achieves consistent subgroup coverage, outperforming these oracle-selected conformal methods. Notably, PCS-UQ stands out in achieving both competitive interval widths and consistent subgroup coverage.Across 6 classification datasets, PCS-UQ reduces prediction set sizes by 20\%. To scale the framework for deep learning, we propose computationally efficient variants that bypass expensive retraining. On three computer vision benchmarks, these variants reduce prediction set sizes by 20\% over conformal baselines. Finally, we provide theoretical proof that a modified PCS-UQ algorithm preserves valid coverage under exchangeability as a form of split conformal inference.

Contrastively trained encoders have recently been proven to invert the data-generating process: they encode each input, e.g., an image, into the true latent vector that generated the image (Zimmermann et al., 2021). However, real-world observations often have inherent ambiguities. For instance, images may be blurred or only show a 2D view of a 3D object, so multiple latents could have generated them. This makes the true posterior for the latent vector probabilistic with heteroscedastic uncertainty. In this setup, we extend the common InfoNCE objective and encoders to predict latent distributions instead of points. We prove that these distributions recover the correct posteriors of the data-generating process, including its level of aleatoric uncertainty, up to a rotation of the latent space. In addition to providing calibrated uncertainty estimates, these posteriors allow the computation of credible intervals in image retrieval. They comprise images with the same latent as a given query, subject to its uncertainty. Code is available at https://github.com/mkirchhof/Probabilistic_Contrastive_Learning

Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes error, and epistemic uncertainty via the size of the set. In this paper, we extend the notion of calibration, which is commonly used to evaluate the validity of the aleatoric uncertainty representation of a single probabilistic classifier, to assess the validity of an epistemic uncertainty representation obtained by sets of probabilistic classifiers. Broadly speaking, we call a set of probabilistic classifiers calibrated if one can find a calibrated convex combination of these classifiers. To evaluate this notion of calibration, we propose a novel nonparametric calibration test that generalizes an existing test for single probabilistic classifiers to the case of sets of probabilistic classifiers. Making use of this test, we empirically show that ensembles of deep neural networks are often not well calibrated.

Although Neural Radiance Fields (NeRFs) have markedly improved novel view synthesis, accurate uncertainty quantification in their image predictions remains an open problem. The prevailing methods for estimating uncertainty, including the state-of-the-art Density-aware NeRF Ensembles (DANE) [29], quantify uncertainty without calibration. This frequently leads to over- or under-confidence in image predictions, which can undermine their real-world applications. In this paper, we propose a method which, for the first time, achieves calibrated uncertainties for NeRFs. To accomplish this, we overcome a significant challenge in adapting existing calibration techniques to NeRFs: a need to hold out ground truth images from the target scene, reducing the number of images left to train the NeRF. This issue is particularly problematic in sparse-view settings, where we can operate with as few as three images. To address this, we introduce the concept of a meta-calibrator that performs uncertainty calibration for NeRFs with a single forward pass without the need for holding out any images from the target scene. Our meta-calibrator is a neural network that takes as input the NeRF images and uncalibrated uncertainty maps and outputs a scene-specific calibration curve that corrects the NeRF's uncalibrated uncertainties. We show that the meta-calibrator can generalize on unseen scenes and achieves well-calibrated and state-of-the-art uncertainty for NeRFs, significantly beating DANE and other approaches. This opens opportunities to improve applications that rely on accurate NeRF uncertainty estimates such as next-best view planning and potentially more trustworthy image reconstruction for medical diagnosis. The code is available at https://niki-amini-naieni.github.io/instantcalibration.github.io/.

This paper evaluates whether large language models (LLMs) exhibit cognitive fan effects, similar to those discovered by Anderson in humans, after being pre-trained on human textual data. We conduct two sets of in-context recall experiments designed to elicit fan effects. Consistent with human results, we find that LLM recall uncertainty, measured via token probability, is influenced by the fan effect. Our results show that removing uncertainty disrupts the observed effect. The experiments suggest the fan effect is consistent whether the fan value is induced in-context or in the pre-training data. Finally, these findings provide in-silico evidence that fan effects and typicality are expressions of the same phenomena.

Conformant planning is the problem of finding a sequence of actions for achieving a goal in the presence of uncertainty in the initial state or action effects. The problem has been approached as a path-finding problem in belief space where good belief representations and heuristics are critical for scaling up. In this work, a different formulation is introduced for conformant problems with deterministic actions where they are automatically converted into classical ones and solved by an off-the-shelf classical planner. The translation maps literals L and sets of assumptions t about the initial situation, into new literals KL/t that represent that L must be true if t is initially true. We lay out a general translation scheme that is sound and establish the conditions under which the translation is also complete. We show that the complexity of the complete translation is exponential in a parameter of the problem called the conformant width, which for most benchmarks is bounded. The planner based on this translation exhibits good performance in comparison with existing planners, and is the basis for T0, the best performing planner in the Conformant Track of the 2006 International Planning Competition.

Modern machine learning methods including deep learning have achieved great success in predictive accuracy for supervised learning tasks, but may still fall short in giving useful estimates of their predictive {\em uncertainty}. Quantifying uncertainty is especially critical in real-world settings, which often involve input distributions that are shifted from the training distribution due to a variety of factors including sample bias and non-stationarity. In such settings, well calibrated uncertainty estimates convey information about when a model's output should (or should not) be trusted. Many probabilistic deep learning methods, including Bayesian-and non-Bayesian methods, have been proposed in the literature for quantifying predictive uncertainty, but to our knowledge there has not previously been a rigorous large-scale empirical comparison of these methods under dataset shift. We present a large-scale benchmark of existing state-of-the-art methods on classification problems and investigate the effect of dataset shift on accuracy and calibration. We find that traditional post-hoc calibration does indeed fall short, as do several other previous methods. However, some methods that marginalize over models give surprisingly strong results across a broad spectrum of tasks.

Object pose estimation constitutes a critical area within the domain of 3D vision. While contemporary state-of-the-art methods that leverage real-world pose annotations have demonstrated commendable performance, the procurement of such real training data incurs substantial costs. This paper focuses on a specific setting wherein only 3D CAD models are utilized as a priori knowledge, devoid of any background or clutter information. We introduce a novel method, CPPF++, designed for sim-to-real pose estimation. This method builds upon the foundational point-pair voting scheme of CPPF, reformulating it through a probabilistic view. To address the challenge posed by vote collision, we propose a novel approach that involves modeling the voting uncertainty by estimating the probabilistic distribution of each point pair within the canonical space. Furthermore, we augment the contextual information provided by each voting unit through the introduction of N-point tuples. To enhance the robustness and accuracy of the model, we incorporate several innovative modules, including noisy pair filtering, online alignment optimization, and a tuple feature ensemble. Alongside these methodological advancements, we introduce a new category-level pose estimation dataset, named DiversePose 300. Empirical evidence demonstrates that our method significantly surpasses previous sim-to-real approaches and achieves comparable or superior performance on novel datasets. Our code is available on https://github.com/qq456cvb/CPPF2.

In observational settings, where the data generating process and possibly the sample size are not controlled, it is typically impossible to guarantee a priori that quantities of interest will be estimated with sufficient precision. However, even when the data do not determine the quantities of interest, they may still allow determination of what is missing -- unobserved information which, if observed, would meaningfully reduce uncertainty. We propose an interactive visualization system, termed variance deltas, to enable the discovery of such missing information from a Bayesian posterior distribution. This system, which we provide as a software package, represents missing information as subsets of unobserved model quantities, organized into a tree based on how well each subset explains uncertainty about the quantity of interest. This system both automates the construction of candidate subsets from minimal user input and implements interactive operations for the division and combination of subsets, allowing the efficient discovery of interesting and useful explanations. We demonstrate this system by using it to discover nonobvious explanations of uncertainty for (1) a treatment effect parameter in a simulated causal inference problem and (2) a population proportion in a forecasting model of real polling data with many sources of bias.

Motivation: Ab initio protein docking represents a major challenge for optimizing a noisy and costly "black box"-like function in a high-dimensional space. Despite progress in this field, there is no docking method available for rigorous uncertainty quantification (UQ) of its solution quality (e.g. interface RMSD or iRMSD). Results: We introduce a novel algorithm, Bayesian Active Learning (BAL), for optimization and UQ of such black-box functions and flexible protein docking. BAL directly models the posterior distribution of the global optimum (or native structures for protein docking) with active sampling and posterior estimation iteratively feeding each other. Furthermore, we use complex normal modes to represent a homogeneous Euclidean conformation space suitable for high-dimension optimization and construct funnel-like energy models for encounter complexes. Over a protein docking benchmark set and a CAPRI set including homology docking, we establish that BAL significantly improve against both starting points by rigid docking and refinements by particle swarm optimization, providing for one third targets a top-3 near-native prediction. BAL also generates tight confidence intervals with half range around 25% of iRMSD and confidence level at 85%. Its estimated probability of a prediction being native or not achieves binary classification AUROC at 0.93 and AUPRC over 0.60 (compared to 0.14 by chance); and also found to help ranking predictions. To the best of our knowledge, this study represents the first uncertainty quantification solution for protein docking, with theoretical rigor and comprehensive assessment. Source codes are available at https://github.com/Shen-Lab/BAL.

Large, labeled datasets have driven deep learning methods to achieve expert-level performance on a variety of medical imaging tasks. We present CheXpert, a large dataset that contains 224,316 chest radiographs of 65,240 patients. We design a labeler to automatically detect the presence of 14 observations in radiology reports, capturing uncertainties inherent in radiograph interpretation. We investigate different approaches to using the uncertainty labels for training convolutional neural networks that output the probability of these observations given the available frontal and lateral radiographs. On a validation set of 200 chest radiographic studies which were manually annotated by 3 board-certified radiologists, we find that different uncertainty approaches are useful for different pathologies. We then evaluate our best model on a test set composed of 500 chest radiographic studies annotated by a consensus of 5 board-certified radiologists, and compare the performance of our model to that of 3 additional radiologists in the detection of 5 selected pathologies. On Cardiomegaly, Edema, and Pleural Effusion, the model ROC and PR curves lie above all 3 radiologist operating points. We release the dataset to the public as a standard benchmark to evaluate performance of chest radiograph interpretation models. The dataset is freely available at https://stanfordmlgroup.github.io/competitions/chexpert .

Class-wise characteristics of training examples affect the performance of deep classifiers. A well-studied example is when the number of training examples of classes follows a long-tailed distribution, a situation that is likely to yield sub-optimal performance for under-represented classes. This class imbalance problem is conventionally addressed by approaches relying on the class-wise cardinality of training examples, such as data resampling. In this paper, we demonstrate that considering solely the cardinality of classes does not cover all issues causing class imbalance. To measure class imbalance, we propose "Class Uncertainty" as the average predictive uncertainty of the training examples, and we show that this novel measure captures the differences across classes better than cardinality. We also curate SVCI-20 as a novel dataset in which the classes have equal number of training examples but they differ in terms of their hardness; thereby causing a type of class imbalance which cannot be addressed by the approaches relying on cardinality. We incorporate our "Class Uncertainty" measure into a diverse set of ten class imbalance mitigation methods to demonstrate its effectiveness on long-tailed datasets as well as on our SVCI-20. Code and datasets will be made available.

The growing realism and accessibility of manipulated and generated faces threaten the trustworthiness of digital media. To detect such forgeries, deepfake detectors based on vision foundation models have shown promising performance, but they typically rely on a single pretrained representation and are prone to overfitting to particular training distributions. To improve generalization to unseen forgeries, we propose UCF-Net, an uncertainty-aware cascaded fusion network that harnesses CLIP's language-aligned semantic priors and DINO's self-supervised visual-structure priors. UCF-Net extracts hierarchical features across Transformer depths, uses layer-wise expert aggregation to adaptively combine each encoder's multi-level cues, and performs weighted fusion of the resulting representations based on entropy-derived uncertainty. We further consolidate public deepfake datasets into a unified benchmark of approximately 4M images and construct a separate cross-generator evaluation set with over 8K face images from eight recent generators. On the unified benchmark, UCF-Net achieves the best mean AUC among the evaluated methods in both in-domain and cross-domain evaluations. On the cross-generator set, it adapts effectively with limited target-domain data, although zero-shot transfer remains challenging.

Prediction sets have recently been shown to be a promising strategy for quantifying the uncertainty of deep neural networks in a way that provides theoretical guarantees. However, existing techniques have largely targeted settings where the space of labels is simple, so prediction sets can be arbitrary subsets of labels. For structured prediction problems where the space of labels is exponential in size, even prediction sets containing a small fraction of all labels can be exponentially large. In the context of code generation, we propose a solution that considers a restricted set of prediction sets that can compactly be represented as partial programs, which are programs with portions replaced with holes. Given a trained code generation model, our algorithm leverages a programming language's abstract syntax tree to generate a set of programs such that the correct program is in the set with high-confidence. Valuable applications of our algorithm include a Codex-style code generator with holes in uncertain parts of the generated code, which provides a partial program with theoretical guarantees. We evaluate our approach on PICARD (a T5 model for SQL semantic parsing) and Codex (a GPT model for over a dozen programming languages, including Python), demonstrating that our approach generates compact PAC prediction sets. This is the first research contribution that generates PAC prediction sets for generative code models.

We introduce UPose3D, a novel approach for multi-view 3D human pose estimation, addressing challenges in accuracy and scalability. Our method advances existing pose estimation frameworks by improving robustness and flexibility without requiring direct 3D annotations. At the core of our method, a pose compiler module refines predictions from a 2D keypoints estimator that operates on a single image by leveraging temporal and cross-view information. Our novel cross-view fusion strategy is scalable to any number of cameras, while our synthetic data generation strategy ensures generalization across diverse actors, scenes, and viewpoints. Finally, UPose3D leverages the prediction uncertainty of both the 2D keypoint estimator and the pose compiler module. This provides robustness to outliers and noisy data, resulting in state-of-the-art performance in out-of-distribution settings. In addition, for in-distribution settings, UPose3D yields performance rivalling methods that rely on 3D annotated data while being the state-of-the-art among methods relying only on 2D supervision.

We propose a method for jointly inferring labels across a collection of data samples, where each sample consists of an observation and a prior belief about the label. By implicitly assuming the existence of a generative model for which a differentiable predictor is the posterior, we derive a training objective that allows learning under weak beliefs. This formulation unifies various machine learning settings; the weak beliefs can come in the form of noisy or incomplete labels, likelihoods given by a different prediction mechanism on auxiliary input, or common-sense priors reflecting knowledge about the structure of the problem at hand. We demonstrate the proposed algorithms on diverse problems: classification with negative training examples, learning from rankings, weakly and self-supervised aerial imagery segmentation, co-segmentation of video frames, and coarsely supervised text classification.

Uncertainty Quantification (UQ) research has primarily focused on closed-book factual question answering (QA), while contextual QA remains unexplored, despite its importance in real-world applications. In this work, we focus on UQ for the contextual QA task and propose a theoretically grounded approach to quantify epistemic uncertainty. We begin by introducing a task-agnostic, token-level uncertainty measure defined as the cross-entropy between the predictive distribution of the given model and the unknown true distribution. By decomposing this measure, we isolate the epistemic component and approximate the true distribution by a perfectly prompted, idealized model. We then derive an upper bound for epistemic uncertainty and show that it can be interpreted as semantic feature gaps in the given model's hidden representations relative to the ideal model. We further apply this generic framework to the contextual QA task and hypothesize that three features approximate this gap: context-reliance (using the provided context rather than parametric knowledge), context comprehension (extracting relevant information from context), and honesty (avoiding intentional lies). Using a top-down interpretability approach, we extract these features by using only a small number of labeled samples and ensemble them to form a robust uncertainty score. Experiments on multiple QA benchmarks in both in-distribution and out-of-distribution settings show that our method substantially outperforms state-of-the-art unsupervised (sampling-free and sampling-based) and supervised UQ methods, achieving up to a 13-point PRR improvement while incurring a negligible inference overhead.

Detection Transformer (DETR) and its variants show strong performance on object detection, a key task for autonomous systems. However, a critical limitation of these models is that their confidence scores only reflect semantic uncertainty, failing to capture the equally important spatial uncertainty. This results in an incomplete assessment of the detection reliability. On the other hand, Deep Ensembles can tackle this by providing high-quality spatial uncertainty estimates. However, their immense memory consumption makes them impractical for real-world applications. A cheaper alternative, Monte Carlo (MC) Dropout, suffers from high latency due to the need of multiple forward passes during inference to estimate uncertainty. To address these limitations, we introduce GroupEnsemble, an efficient and effective uncertainty estimation method for DETR-like models. GroupEnsemble simultaneously predicts multiple individual detection sets by feeding additional diverse groups of object queries to the transformer decoder during inference. Each query group is transformed by the shared decoder in isolation and predicts a complete detection set for the same input. An attention mask is applied to the decoder to prevent inter-group query interactions, ensuring each group detects independently to achieve reliable ensemble-based uncertainty estimation. By leveraging the decoder's inherent parallelism, GroupEnsemble efficiently estimates uncertainty in a single forward pass without sequential repetition. We validated our method under autonomous driving scenes and common daily scenes using the Cityscapes and COCO datasets, respectively. The results show that a hybrid approach combining MC-Dropout and GroupEnsemble outperforms Deep Ensembles on several metrics at a fraction of the cost. The code is available at https://github.com/yutongy98/GroupEnsemble.

Recent progress in multi-turn reinforcement learning (RL) has significantly improved reasoning LLMs' performances on complex interactive tasks. Despite advances in stabilization techniques such as fine-grained credit assignment and trajectory filtering, instability remains pervasive and often leads to training collapse. We argue that this instability stems from inefficient exploration in multi-turn settings, where policies continue to generate low-information actions that neither reduce uncertainty nor advance task progress. To address this issue, we propose Token- and Turn-level Policy Optimization (T^2PO), an uncertainty-aware framework that explicitly controls exploration at fine-grained levels. At the token level, T^2PO monitors uncertainty dynamics and triggers a thinking intervention once the marginal uncertainty change falls below a threshold. At the turn level, T^2PO identifies interactions with negligible exploration progress and dynamically resamples such turns to avoid wasted rollouts. We evaluate T^2PO in diverse environments, including WebShop, ALFWorld, and Search QA, demonstrating substantial gains in training stability and performance improvements with better exploration efficiency. Code is available at: https://github.com/WillDreamer/T2PO.

Unfair predictions of machine learning (ML) models impede their broad acceptance in real-world settings. Tackling this arduous challenge first necessitates defining what it means for an ML model to be fair. This has been addressed by the ML community with various measures of fairness that depend on the prediction outcomes of the ML models, either at the group level or the individual level. These fairness measures are limited in that they utilize point predictions, neglecting their variances, or uncertainties, making them susceptible to noise, missingness and shifts in data. In this paper, we first show that an ML model may appear to be fair with existing point-based fairness measures but biased against a demographic group in terms of prediction uncertainties. Then, we introduce new fairness measures based on different types of uncertainties, namely, aleatoric uncertainty and epistemic uncertainty. We demonstrate on many datasets that (i) our uncertainty-based measures are complementary to existing measures of fairness, and (ii) they provide more insights about the underlying issues leading to bias.

Accurate retinal vessel (RV) segmentation is a crucial step in the quantitative assessment of retinal vasculature, which is needed for the early detection of retinal diseases and other conditions. Numerous studies have been conducted to tackle the problem of segmenting vessels automatically using a pixel-wise classification approach. The common practice of creating ground truth labels is to categorize pixels as foreground and background. This approach is, however, biased, and it ignores the uncertainty of a human annotator when it comes to annotating e.g. thin vessels. In this work, we propose a simple and effective method that casts the RV segmentation task as an image-level regression. For this purpose, we first introduce a novel Segmentation Annotation Uncertainty-Aware (SAUNA) transform, which adds pixel uncertainty to the ground truth using the pixel's closeness to the annotation boundary and vessel thickness. To train our model with soft labels, we generalize the earlier proposed Jaccard metric loss to arbitrary hypercubes for soft Jaccard index (Intersection-over-Union) optimization. Additionally, we employ a stable version of the Focal-L1 loss for pixel-wise regression. We conduct thorough experiments and compare our method to a diverse set of baselines across 5 retinal image datasets. Our empirical results indicate that the integration of the SAUNA transform and these segmentation losses led to significant performance boosts for different segmentation models. Particularly, our methodology enables UNet-like architectures to substantially outperform computational-intensive baselines. Our implementation is available at https://github.com/Oulu-IMEDS/SAUNA.

Reliable estimation of predictive uncertainty is crucial for machine learning applications, particularly in high-stakes scenarios where hedging against risks is essential. Despite its significance, there is no universal agreement on how to best quantify predictive uncertainty. In this work, we revisit core concepts to propose a framework for information-theoretic measures of predictive uncertainty. Our proposed framework categorizes predictive uncertainty measures according to two factors: (I) The predicting model (II) The approximation of the true predictive distribution. Examining all possible combinations of these two factors, we derive a set of predictive uncertainty measures that includes both known and newly introduced ones. We extensively evaluate these measures across a broad set of tasks, identifying conditions under which certain measures excel. Our findings show the importance of aligning the choice of uncertainty measure with the predicting model on in-distribution (ID) data, the limitations of epistemic uncertainty measures for out-of-distribution (OOD) data, and that the disentanglement between measures varies substantially between ID and OOD data. Together, these insights provide a more comprehensive understanding of predictive uncertainty measures, revealing their implicit assumptions and relationships.

Hallucinations are a persistent problem with Large Language Models (LLMs). As these models become increasingly used in high-stakes domains, such as healthcare and finance, the need for effective hallucination detection is crucial. To this end, we propose a versatile framework for zero-resource hallucination detection that practitioners can apply to real-world use cases. To achieve this, we adapt a variety of existing uncertainty quantification (UQ) techniques, including black-box UQ, white-box UQ, and LLM-as-a-Judge, transforming them as necessary into standardized response-level confidence scores ranging from 0 to 1. To enhance flexibility, we introduce a tunable ensemble approach that incorporates any combination of the individual confidence scores. This approach enables practitioners to optimize the ensemble for a specific use case for improved performance. To streamline implementation, the full suite of scorers is offered in this paper's companion Python toolkit, UQLM. To evaluate the performance of the various scorers, we conduct an extensive set of experiments using several LLM question-answering benchmarks. We find that our tunable ensemble typically surpasses its individual components and outperforms existing hallucination detection methods. Our results demonstrate the benefits of customized hallucination detection strategies for improving the accuracy and reliability of LLMs.

We study how a central bank should dynamically set short-term nominal interest rates to stabilize inflation and unemployment when macroeconomic relationships are uncertain and time-varying. We model monetary policy as a sequential decision-making problem where the central bank observes macroeconomic conditions quarterly and chooses interest rate adjustments. Using publically accessible historical Federal Reserve Economic Data (FRED), we construct a linear-Gaussian transition model and implement a discrete-action Markov Decision Process with a quadratic loss reward function. We chose to compare nine different reinforcement learning style approaches against Taylor Rule and naive baselines, including tabular Q-learning variants, SARSA, Actor-Critic, Deep Q-Networks, Bayesian Q-learning with uncertainty quantification, and POMDP formulations with partial observability. Surprisingly, standard tabular Q-learning achieved the best performance (-615.13 +- 309.58 mean return), outperforming both enhanced RL methods and traditional policy rules. Our results suggest that while sophisticated RL techniques show promise for monetary policy applications, simpler approaches may be more robust in this domain, highlighting important challenges in applying modern RL to macroeconomic policy.

The classification performance of deep neural networks has begun to asymptote at near-perfect levels. However, their ability to generalize outside the training set and their robustness to adversarial attacks have not. In this paper, we make progress on this problem by training with full label distributions that reflect human perceptual uncertainty. We first present a new benchmark dataset which we call CIFAR10H, containing a full distribution of human labels for each image of the CIFAR10 test set. We then show that, while contemporary classifiers fail to exhibit human-like uncertainty on their own, explicit training on our dataset closes this gap, supports improved generalization to increasingly out-of-training-distribution test datasets, and confers robustness to adversarial attacks.

Accurate histopathologic interpretation is key for clinical decision-making; however, current deep learning models for digital pathology are often overconfident and poorly calibrated in out-of-distribution (OOD) settings, which limit trust and clinical adoption. Safety-critical medical imaging workflows benefit from intrinsic uncertainty-aware properties that can accurately reject OOD input. We implement the Spectral-normalized Neural Gaussian Process (SNGP), a set of lightweight modifications that apply spectral normalization and replace the final dense layer with a Gaussian process layer to improve single-model uncertainty estimation and OOD detection. We evaluate SNGP vs. deterministic and MonteCarlo dropout on six datasets across three biomedical classification tasks: white blood cells, amyloid plaques, and colorectal histopathology. SNGP has comparable in-distribution performance while significantly improving uncertainty estimation and OOD detection. Thus, SNGP or related models offer a useful framework for uncertainty-aware classification in digital pathology, supporting safe deployment and building trust with pathologists.

While improving prediction accuracy has been the focus of machine learning in recent years, this alone does not suffice for reliable decision-making. Deploying learning systems in consequential settings also requires calibrating and communicating the uncertainty of predictions. To convey instance-wise uncertainty for prediction tasks, we show how to generate set-valued predictions from a black-box predictor that control the expected loss on future test points at a user-specified level. Our approach provides explicit finite-sample guarantees for any dataset by using a holdout set to calibrate the size of the prediction sets. This framework enables simple, distribution-free, rigorous error control for many tasks, and we demonstrate it in five large-scale machine learning problems: (1) classification problems where some mistakes are more costly than others; (2) multi-label classification, where each observation has multiple associated labels; (3) classification problems where the labels have a hierarchical structure; (4) image segmentation, where we wish to predict a set of pixels containing an object of interest; and (5) protein structure prediction. Lastly, we discuss extensions to uncertainty quantification for ranking, metric learning and distributionally robust learning.

Retrieval-augmented generation (RAG) grounds answers in retrieved passages, yet relevance does not guarantee sufficiency: a topical passage may still fail to justify the answer. We study evidence sufficiency verification for selective RAG answering, in which a verifier receives a question, a candidate answer, and retrieved evidence and decides whether the evidence supports, refutes, or is insufficient for the answer, answering only when support is established. We present SURE-RAG, an aggregation protocol that treats evidence sufficiency as a set-level property: missing hops and unresolved conflicts cannot be detected by scoring passages independently. A shared claim-evidence verifier produces a local relation distribution for each (claim, passage) pair, which SURE-RAG aggregates into four interpretable answer-level feature blocks (coverage, relation strength, uncertainty, and retrieval), producing a three-way decision and an auditable selective score. We evaluate on HotpotQA-RAG v3, a controlled multi-hop benchmark, under an artifact-aware protocol (shortcut baselines, counterfactual swaps, no-oracle checks, and GPT-4o audits). Calibrated SURE-RAG attains 0.9075 Macro-F1 (raw 0.8951 +/- 0.0069), well above DeBERTa mean-pooling (0.6516) and a GPT-4o judge (0.7284), and on par with a strong concat cross-encoder (0.8888 +/- 0.0109) while remaining fully auditable. At 30% coverage, risk falls from 0.2588 to 0.1642, a 37% relative reduction. As a boundary-mapping experiment, we contrast SURE-RAG with GPT-4o on HaluBench unsafe detection: the ranking reverses (0.3343 vs. 0.7389 unsafe-F1), indicating that controlled sufficiency verification and natural hallucination detection are distinct problems.

Background and Objective: Radiation pneumonitis (RP) is a side effect of thoracic radiation therapy. Recently, Machine learning (ML) models enhanced with radiomic and dosiomic features provide better predictions by incorporating spatial information beyond DVHs. However, to improve the clinical decision process, we propose to use uncertainty quantification (UQ) to improve the confidence in model prediction. This study evaluates the impact of post hoc UQ methods on the discriminative performance and calibration of ML models for RP prediction. Methods: This study evaluated four ML models: logistic regression (LR), support vector machines (SVM), extreme gradient boosting (XGB), and random forest (RF), using radiomic, dosiomic, and dosimetric features to predict RP. We applied UQ methods, including Patt scaling, isotonic regression, Venn-ABERS predictor, and Conformal Prediction, to quantify uncertainty. Model performance was assessed through Area Under the Receiver Operating Characteristic curve (AUROC), Area Under the Precision-Recall Curve (AUPRC), and Adaptive Calibration Error (ACE) using Leave-One-Out Cross-Validation (LOO-CV). Results: UQ methods enhanced predictive performance, particularly for high-certainty predictions, while also improving calibration. Radiomic and dosiomic features increased model accuracy but introduced calibration challenges, especially for non-linear models like XGB and RF. Performance gains from UQ methods were most noticeable at higher certainty thresholds. Conclusion: Integrating UQ into ML models with radiomic and dosiomic features improves both predictive accuracy and calibration, supporting more reliable clinical decision-making. The findings emphasize the value of UQ methods in enhancing applicability of predictive models for RP in healthcare settings.

Most existing video anomaly detectors rely solely on RGB frames, which lack the temporal resolution needed to capture abrupt or transient motion cues, key indicators of anomalous events. To address this limitation, we propose Image-Event Fusion for Video Anomaly Detection (IEF-VAD), a framework that synthesizes event representations directly from RGB videos and fuses them with image features through a principled, uncertainty-aware process. The system (i) models heavy-tailed sensor noise with a Student`s-t likelihood, deriving value-level inverse-variance weights via a Laplace approximation; (ii) applies Kalman-style frame-wise updates to balance modalities over time; and (iii) iteratively refines the fused latent state to erase residual cross-modal noise. Without any dedicated event sensor or frame-level labels, IEF-VAD sets a new state of the art across multiple real-world anomaly detection benchmarks. These findings highlight the utility of synthetic event representations in emphasizing motion cues that are often underrepresented in RGB frames, enabling accurate and robust video understanding across diverse applications without requiring dedicated event sensors. Code and models are available at https://github.com/EavnJeong/IEF-VAD.

Accurate and reliable energy time series prediction is of great significance for power generation planning and allocation. At present, deep learning time series prediction has become the mainstream method. However, the multi-scale time dynamics and the irregularity of real data lead to the limitations of the existing methods. Therefore, we propose EnergyPatchTST, which is an extension of the Patch Time Series Transformer specially designed for energy forecasting. The main innovations of our method are as follows: (1) multi-scale feature extraction mechanism to capture patterns with different time resolutions; (2) probability prediction framework to estimate uncertainty through Monte Carlo elimination; (3) integration path of future known variables (such as temperature and wind conditions); And (4) Pre-training and Fine-tuning examples to enhance the performance of limited energy data sets. A series of experiments on common energy data sets show that EnergyPatchTST is superior to other commonly used methods, the prediction error is reduced by 7-12%, and reliable uncertainty estimation is provided, which provides an important reference for time series prediction in the energy field.

Uncertainty quantification (UQ) for large language models (LLMs) is a key building block for safety guardrails of daily LLM applications. Yet, even as LLM agents are increasingly deployed in highly complex tasks, most UQ research still centers on single-turn question-answering. We argue that UQ research must shift to realistic settings with interactive agents, and that a new principled framework for agent UQ is needed. This paper presents the first general formulation of agent UQ that subsumes broad classes of existing UQ setups. Under this formulation, we show that prior works implicitly treat LLM UQ as an uncertainty accumulation process, a viewpoint that breaks down for interactive agents in an open world. In contrast, we propose a novel perspective, a conditional uncertainty reduction process, that explicitly models reducible uncertainty over an agent's trajectory by highlighting "interactivity" of actions. From this perspective, we outline a conceptual framework to provide actionable guidance for designing UQ in LLM agent setups. Finally, we conclude with practical implications of the agent UQ in frontier LLM development and domain-specific applications, as well as open remaining problems.

The rapid progress of multimodal large language models (MLLMs) has led to increasing interest in agent-based systems. While most prior work in medical imaging concentrates on automating routine clinical workflows, we study an underexplored yet clinically significant setting: distinguishing visually hard-to-separate diseases in a zero-shot setting. We benchmark representative agents on two imaging-only proxy diagnostic tasks, (1) melanoma vs. atypical nevus and (2) pulmonary edema vs. pneumonia, where visual features are highly confounded despite substantial differences in clinical management. We introduce a multi-agent framework based on contrastive adjudication. Experimental results show improved diagnostic performance (an 11-percentage-point gain in accuracy on dermoscopy data) and reduced unsupported claims on qualitative samples, although overall performance remains insufficient for clinical deployment. We acknowledge the inherent uncertainty in human annotations and the absence of clinical context, which further limit the translation to real-world settings. Within this controlled setting, this pilot study provides preliminary insights into zero-shot agent performance in visually confounded scenarios.

Large language models (LLMs) are increasingly deployed and democratized on edge devices. To improve the efficiency of on-device deployment, small language models (SLMs) are often adopted due to their efficient decoding latency and reduced energy consumption. However, these SLMs often generate inaccurate responses when handling complex queries. One promising solution is uncertainty-based SLM routing, offloading high-stakes queries to stronger LLMs when resulting in low-confidence responses on SLM. This follows the principle of "If you lack confidence, seek stronger support" to enhance reliability. Relying on more powerful LLMs is yet effective but increases invocation costs. Therefore, striking a routing balance between efficiency and efficacy remains a critical challenge. Additionally, efficiently generalizing the routing strategy to new datasets remains under-explored. In this paper, we conduct a comprehensive investigation into benchmarking and generalization of uncertainty-driven routing strategies from SLMs to LLMs over 1500+ settings. Our findings highlight: First, uncertainty-correctness alignment in different uncertainty quantification (UQ) methods significantly impacts routing performance. Second, uncertainty distributions depend more on both the specific SLM and the chosen UQ method, rather than downstream data. Building on the insight, we propose a calibration data construction instruction pipeline and open-source a constructed hold-out set to enhance routing generalization on new downstream scenarios. The experimental results indicate calibration data effectively bootstraps routing performance without any new data.

In this paper, we propose a general theory of ambiguity-averse MDPs, which treats the uncertain transition probabilities as random variables and evaluates a policy via a risk measure applied to its random return. This ambiguity-averse MDP framework unifies several models of MDPs with epistemic uncertainty for specific choices of risk measures. We extend the concepts of value functions and Bellman operators to our setting. Based on these objects, we establish the consequences of dynamic programming principles in this framework (existence of stationary policies, value and policy iteration algorithms), and we completely characterize law-invariant risk measures compatible with dynamic programming. Our work draws connections among several variants of MDP models and fully delineates what is possible under the dynamic programming paradigm and which risk measures require leaving it.

Uncertainty quantification (UQ) for large language models (LLMs) aims to provide reliable measures of predictive confidence, yet current methods are often unstable under meaning-preserving perturbations. Semantically equivalent paraphrases can induce substantial variability in predictive confidence, even for methods with formal guarantees, such as conformal prediction. To address this issue, we propose a paraphrase-aware UQ framework robust to semantic rewordings. Our approach trains a lightweight proxy model on LLM hidden states and aggregates its predictions across paraphrases to construct label-wise nonconformity scores. Under score exchangeability, conformal calibration retains marginal coverage. This guarantee can also hold under test-only rewording, provided that the paraphrase pipeline satisfies an additional distributional alignment condition. We evaluate three settings (normal, fully reworded, and semi-reworded) which apply rewording to neither dataset, both calibration and test datasets, or only the test dataset, respectively. Across seven multiple-choice QA benchmarks and multiple model families, our method produces compact prediction sets with empirical coverage generally near the nominal target, even in the semi-reworded setting. Ablation studies show that the learned proxy accounts for most of the reduction in set size, while paraphrase-augmented training and inference-time aggregation improve stability under rewording. Code is available at https://github.com/Raina-Xin/PA_Score.

Machine learning classification tasks often benefit from predicting a set of possible labels with confidence scores to capture uncertainty. However, existing methods struggle with the high-dimensional nature of the data and the lack of well-calibrated probabilities from modern classification models. We propose a novel conformal prediction method that employs a rank-based score function suitable for classification models that predict the order of labels correctly, even if not well-calibrated. Our approach constructs prediction sets that achieve the desired coverage rate while managing their size. We provide a theoretical analysis of the expected size of the conformal prediction sets based on the rank distribution of the underlying classifier. Through extensive experiments, we demonstrate that our method outperforms existing techniques on various datasets, providing reliable uncertainty quantification. Our contributions include a novel conformal prediction method, theoretical analysis, and empirical evaluation. This work advances the practical deployment of machine learning systems by enabling reliable uncertainty quantification.

In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order probability distributions, i.e., predictions in the form of distributions on probability distributions. A completely conclusive solution has not yet been found, however, as shown by recent criticisms of commonly used uncertainty measures associated with second-order distributions, identifying undesirable theoretical properties of these measures. In light of these criticisms, we propose a set of formal criteria that meaningful uncertainty measures for predictive uncertainty based on second-order distributions should obey. Moreover, we provide a general framework for developing uncertainty measures to account for these criteria, and offer an instantiation based on the Wasserstein distance, for which we prove that all criteria are satisfied.

The lack of transparency of Deep Neural Networks continues to be a limitation that severely undermines their reliability and usage in high-stakes applications. Promising approaches to overcome such limitations are Prototype-Based Self-Explainable Neural Networks (PSENNs), whose predictions rely on the similarity between the input at hand and a set of prototypical representations of the output classes, offering therefore a deep, yet transparent-by-design, architecture. So far, such models have been designed by considering pointwise estimates for the prototypes, which remain fixed after the learning phase of the model. In this paper, we introduce a probabilistic reformulation of PSENNs, called Prob-PSENN, which replaces point estimates for the prototypes with probability distributions over their values. This provides not only a more flexible framework for an end-to-end learning of prototypes, but can also capture the explanatory uncertainty of the model, which is a missing feature in previous approaches. In addition, since the prototypes determine both the explanation and the prediction, Prob-PSENNs allow us to detect when the model is making uninformed or uncertain predictions, and to obtain valid explanations for them. Our experiments demonstrate that Prob-PSENNs provide more meaningful and robust explanations than their non-probabilistic counterparts, thus enhancing the explainability and reliability of the models.

Quantifying uncertainty in large language models (LLMs) is important for safety-critical applications because it helps spot incorrect answers, known as hallucinations. One major trend of uncertainty quantification methods is based on estimating the entropy of the distribution of the LLM's potential output sequences. This estimation is based on a set of output sequences and associated probabilities obtained by querying the LLM several times. In this paper, we advocate and experimentally show that the probability of unobserved sequences plays a crucial role, and we recommend future research to integrate it to enhance such LLM uncertainty quantification methods.

Perceptual similarity scores that align with human vision are critical for both training and evaluating computer vision models. Deep perceptual losses, such as LPIPS, achieve good alignment but rely on complex, highly non-linear discriminative features with unknown invariances, while hand-crafted measures like SSIM are interpretable but miss key perceptual properties. We introduce the Structured Uncertainty Similarity Score (SUSS); it models each image through a set of perceptual components, each represented by a structured multivariate Normal distribution. These are trained in a generative, self-supervised manner to assign high likelihood to human-imperceptible augmentations. The final score is a weighted sum of component log-probabilities with weights learned from human perceptual datasets. Unlike feature-based methods, SUSS learns image-specific linear transformations of residuals in pixel space, enabling transparent inspection through decorrelated residuals and sampling. SUSS aligns closely with human perceptual judgments, shows strong perceptual calibration across diverse distortion types, and provides localized, interpretable explanations of its similarity assessments. We further demonstrate stable optimization behavior and competitive performance when using SUSS as a perceptual loss for downstream imaging tasks.

An observable in an Effective Field Theory (EFT) is an expansion in a set of small parameters, no different than any other perturbation series. Truncating such a series expansion leaves the leading dropped term as the dominant source of error, and that term itself contains a calculable portion. We explore the partial calculation of this next-order error, available at dim-6^2 in SMEFT with no additional tools needed to simulate it, and explore how to efficiently use that partial calculation to model the next-order uncertainty in full using a minimal number of nuisance parameters. This estimate of the uncertainty of the EFT signal rate naturally imposes EFT validity by ensuring that bounds are driven by kinematic regions where truncation uncertainties are parametrically smaller than the signal. We incorporate the calculable dim-6^2 piece into the signal and cover the remaining higher-dimension uncertainty with a small set of nuisance parameters derived from a scan over Wilson-coefficient values. Our algorithm to determine the relevant nuisance parameters and distributions is automation-friendly and applies to arbitrary truncation choices. We then provide multiple examples of its implementation in high-energy collider processes focused on SMEFT truncated at O(Λ^{-2}), where the dim-6^2 piece is used to estimate the full mathcal O(Λ^{-4}) dependence. In the examples considered here the reduction of nuisance parameters is appreciable, generically reducing the nuisance parameter count by an order of magnitude compared to naïve estimates.

Rapid extraction of structured information from social media is important for humanitarian response, yet existing disaster tweet resources mainly provide document-level category labels without span-level entity annotations. We introduce HUMAID-NER, the first named entity recognition dataset built on the HumAID benchmark, containing 60,000 English disaster tweets annotated in BIO format across ten operationally motivated entity types and yielding approximately 175,000 labelled entity spans. Annotations are generated through a reproducible three-stage hybrid pipeline combining a spaCy transformer model, disaster-domain EntityRuler patterns, and structured regular expressions with priority-based overlap resolution. We also propose a joint multitask learning framework that performs disaster-specific named entity recognition and humanitarian event classification using a shared RoBERTa-large encoder. To reduce task conflict during joint training, the model uses homoscedastic uncertainty weighting with learnable task parameters and a two-stage training schedule that freezes the lower 18 of 24 encoder layers in the second stage. On the HUMAID-NER validation set, the proposed system achieves NER span micro-F1 of 0.841 and classification macro-F1 of 0.761 simultaneously. A real-time web dashboard demonstrates end-to-end deployment. The dataset, models, and pipeline code are released to support reproducibility and future crisis informatics research.

The quality of many modern machine learning models improves as model complexity increases, an effect that has been quantified, for predictive performance, with the non-monotonic double descent learning curve. Here, we address the overarching question: is there an analogous theory of double descent for models which estimate uncertainty? We provide a partially affirmative and partially negative answer in the setting of Gaussian processes (GP). Under standard assumptions, we prove that higher model quality for optimally-tuned GPs (including uncertainty prediction) under marginal likelihood is realized for larger input dimensions, and therefore exhibits a monotone error curve. After showing that marginal likelihood does not naturally exhibit double descent in the input dimension, we highlight related forms of posterior predictive loss that do exhibit non-monotonicity. Finally, we verify empirically that our results hold for real data, beyond our considered assumptions, and we explore consequences involving synthetic covariates.

Uncertainty estimation is a key factor that makes deep learning reliable in practical applications. Recently proposed evidential neural networks explicitly account for different uncertainties by treating the network's outputs as evidence to parameterize the Dirichlet distribution, and achieve impressive performance in uncertainty estimation. However, for high data uncertainty samples but annotated with the one-hot label, the evidence-learning process for those mislabeled classes is over-penalized and remains hindered. To address this problem, we propose a novel method, Fisher Information-based Evidential Deep Learning (I-EDL). In particular, we introduce Fisher Information Matrix (FIM) to measure the informativeness of evidence carried by each sample, according to which we can dynamically reweight the objective loss terms to make the network more focused on the representation learning of uncertain classes. The generalization ability of our network is further improved by optimizing the PAC-Bayesian bound. As demonstrated empirically, our proposed method consistently outperforms traditional EDL-related algorithms in multiple uncertainty estimation tasks, especially in the more challenging few-shot classification settings.

Large language models (LLMs) exhibit a wide range of promising capabilities -- from step-by-step planning to commonsense reasoning -- that may provide utility for robots, but remain prone to confidently hallucinated predictions. In this work, we present KnowNo, which is a framework for measuring and aligning the uncertainty of LLM-based planners such that they know when they don't know and ask for help when needed. KnowNo builds on the theory of conformal prediction to provide statistical guarantees on task completion while minimizing human help in complex multi-step planning settings. Experiments across a variety of simulated and real robot setups that involve tasks with different modes of ambiguity (e.g., from spatial to numeric uncertainties, from human preferences to Winograd schemas) show that KnowNo performs favorably over modern baselines (which may involve ensembles or extensive prompt tuning) in terms of improving efficiency and autonomy, while providing formal assurances. KnowNo can be used with LLMs out of the box without model-finetuning, and suggests a promising lightweight approach to modeling uncertainty that can complement and scale with the growing capabilities of foundation models. Website: https://robot-help.github.io

Semi-supervised crowd counting is an important yet challenging task. A popular approach is to iteratively generate pseudo-labels for unlabeled data and add them to the training set. The key is to use uncertainty to select reliable pseudo-labels. In this paper, we propose a novel method to calibrate model uncertainty for crowd counting. Our method takes a supervised uncertainty estimation strategy to train the model through a surrogate function. This ensures the uncertainty is well controlled throughout the training. We propose a matching-based patch-wise surrogate function to better approximate uncertainty for crowd counting tasks. The proposed method pays a sufficient amount of attention to details, while maintaining a proper granularity. Altogether our method is able to generate reliable uncertainty estimation, high quality pseudolabels, and achieve state-of-the-art performance in semisupervised crowd counting.

We introduce a method to measure uncertainty in large language models. For tasks like question answering, it is essential to know when we can trust the natural language outputs of foundation models. We show that measuring uncertainty in natural language is challenging because of "semantic equivalence" -- different sentences can mean the same thing. To overcome these challenges we introduce semantic entropy -- an entropy which incorporates linguistic invariances created by shared meanings. Our method is unsupervised, uses only a single model, and requires no modifications to off-the-shelf language models. In comprehensive ablation studies we show that the semantic entropy is more predictive of model accuracy on question answering data sets than comparable baselines.

Binary classification involves predicting the label of an instance based on whether the model score for the positive class exceeds a threshold chosen based on the application requirements (e.g., maximizing recall for a precision bound). However, model scores are often not aligned with the true positivity rate. This is especially true when the training involves a differential sampling across classes or there is distributional drift between train and test settings. In this paper, we provide theoretical analysis and empirical evidence of the dependence of model score estimation bias on both uncertainty and score itself. Further, we formulate the decision boundary selection in terms of both model score and uncertainty, prove that it is NP-hard, and present algorithms based on dynamic programming and isotonic regression. Evaluation of the proposed algorithms on three real-world datasets yield 25%-40% gain in recall at high precision bounds over the traditional approach of using model score alone, highlighting the benefits of leveraging uncertainty.

In an educational setting, an estimate of the difficulty of multiple-choice questions (MCQs), a commonly used strategy to assess learning progress, constitutes very useful information for both teachers and students. Since human assessment is costly from multiple points of view, automatic approaches to MCQ item difficulty estimation are investigated, yielding however mixed success until now. Our approach to this problem takes a different angle from previous work: asking various Large Language Models to tackle the questions included in two different MCQ datasets, we leverage model uncertainty to estimate item difficulty. By using both model uncertainty features as well as textual features in a Random Forest regressor, we show that uncertainty features contribute substantially to difficulty prediction, where difficulty is inversely proportional to the number of students who can correctly answer a question. In addition to showing the value of our approach, we also observe that our model achieves state-of-the-art results on the BEA publicly available dataset.

Hallucination in large language models (LLMs) can be detected by assessing the uncertainty of model outputs, typically measured using entropy. Semantic entropy (SE) enhances traditional entropy estimation by quantifying uncertainty at the semantic cluster level. However, as modern LLMs generate longer one-sentence responses, SE becomes less effective because it overlooks two crucial factors: intra-cluster similarity (the spread within a cluster) and inter-cluster similarity (the distance between clusters). To address these limitations, we propose a simple black-box uncertainty quantification method inspired by nearest neighbor estimates of entropy. Our approach can also be easily extended to white-box settings by incorporating token probabilities. Additionally, we provide theoretical results showing that our method generalizes semantic entropy. Extensive empirical results demonstrate its effectiveness compared to semantic entropy across two recent LLMs (Phi3 and Llama3) and three common text generation tasks: question answering, text summarization, and machine translation. Our code is available at https://github.com/BigML-CS-UCLA/SNNE.

Expressing confidence is challenging for embodied agents navigating dynamic multimodal environments, where uncertainty arises from both perception and decision-making processes. We present the first work investigating embodied confidence elicitation in open-ended multimodal environments. We introduce Elicitation Policies, which structure confidence assessment across inductive, deductive, and abductive reasoning, along with Execution Policies, which enhance confidence calibration through scenario reinterpretation, action sampling, and hypothetical reasoning. Evaluating agents in calibration and failure prediction tasks within the Minecraft environment, we show that structured reasoning approaches, such as Chain-of-Thoughts, improve confidence calibration. However, our findings also reveal persistent challenges in distinguishing uncertainty, particularly under abductive settings, underscoring the need for more sophisticated embodied confidence elicitation methods.

Accurate confidence calibration in Large Language Models (LLMs) is critical for safe use in high-stakes domains, where clear verbalized confidence enhances user trust. Traditional methods that mimic reference confidence expressions often fail to capture the reasoning needed for accurate confidence assessment. We propose natural language critiques as a solution, ideally suited for confidence calibration, as precise gold confidence labels are hard to obtain and often require multiple generations. This paper studies how natural language critiques can enhance verbalized confidence, addressing: (1) What to critique: uncertainty (question-focused) or confidence (answer-specific)? Analysis shows confidence suits multiple-choice tasks, while uncertainty excels in open-ended scenarios. (2) How to critique: self-critique or critique calibration training? We propose Self-Critique, enabling LLMs to critique and optimize their confidence beyond mere accuracy, and CritiCal, a novel Critique Calibration training method that leverages natural language critiques to improve confidence calibration, moving beyond direct numerical optimization. Experiments show that CritiCal significantly outperforms Self-Critique and other competitive baselines, even surpassing its teacher model, GPT-4o, in complex reasoning tasks. CritiCal also shows robust generalization in out-of-distribution settings, advancing LLM's reliability.

Large language models (LLMs) are increasingly used in high-stakes settings, where overconfident responses can mislead users. Reliable confidence estimation has been shown to enhance trust and task accuracy. Yet existing methods face practical barriers: logits are often hidden, multi-sampling is computationally expensive, and verbalized numerical uncertainty (e.g., giving a 0-100 score) deviates from natural communication. We revisit linguistic confidence (LC), where models express uncertainty through hedging language (e.g., probably, might), offering a lightweight and human-centered alternative. To advance this direction, we (1) release the first diverse, large-scale dataset of hedging expressions with human-annotated confidence scores, and (2) propose a lightweight mapper that converts hedges into confidence scores at near-zero cost. Building on these resources, we (3) conduct the first systematic study of LC across modern LLMs and QA benchmarks, revealing that while most LLMs underperform in expressing reliable LC, carefully designed prompting achieves competitive calibration and discriminability. Finally, we (4) introduce a fine-tuning framework that further improves LC reliability. Taken together, our work positions linguistic confidence as a scalable, efficient, and human-aligned approach to LLM uncertainty estimation, and calls for deeper exploration of this promising yet underexplored direction.

Concept Bottleneck Models (CBMs) predict through human-interpretable concepts, but they typically output point concept probabilities that conflate epistemic uncertainty (reducible model underspecification) with aleatoric uncertainty (irreducible input ambiguity). This makes concept-level uncertainty hard to interpret and, more importantly, hard to act upon. We introduce CREDENCE (Credal Ensemble Concept Estimation), a CBM framework that decomposes concept uncertainty by construction. CREDENCE represents each concept as a credal prediction (a probability interval), derives epistemic uncertainty from disagreement across diverse concept heads, and estimates aleatoric uncertainty via a dedicated ambiguity output trained to match annotator disagreement when available. The resulting signals support prescriptive decisions: automate low-uncertainty cases, prioritize data collection for high-epistemic cases, route high-aleatoric cases to human review, and abstain when both are high. Across several tasks, we show that epistemic uncertainty is positively associated with prediction errors, whereas aleatoric uncertainty closely tracks annotator disagreement, providing guidance beyond error correlation. Our implementation is available at the following link: https://github.com/Tankiit/Credal_Sets/tree/ensemble-credal-cbm

Sparse rewards and heterogeneous task sequences remain persistent challenges in Reinforcement Learning (RL), often resulting in slow convergence, weak generalization, and inefficient exploration. We propose Uncertainty-Aware LLM-Guided Policy Shaping (ULPS), a novel framework that integrates a calibrated Large Language Model (LLM) into the RL training loop to provide structured, uncertainty-modulated behavioral guidance. ULPS employs an A*-based oracle to synthesize optimal symbolic trajectories, which are used to fine-tune a BERT-based language model. During training, this model supplies action suggestions whose influence is conditioned on epistemic uncertainty estimated via Monte Carlo (MC) dropout. An entropy-based blending mechanism adaptively balances LLM guidance and the learned policy (via Proximal Policy Optimization, PPO), allowing the agent to prioritize reliable priors while preserving adaptability. We evaluate ULPS on the MiniGridUnlockPickup benchmark and observe consistent improvements in success rate, reward efficiency, and sample complexity over unguided, uncalibrated, and standard RL baselines. ULPS achieves more than 9% improvement in execution accuracy after fine-tuning, requires fewer environment interactions, and yields higher reward AUC. Our results demonstrate that integrating symbolic A* trajectories, pretrained language priors, and uncertainty-aware control offers a principled and effective approach to multi-task reinforcement learning in sparse-reward domains, with potential extensibility to partially observable and multi-agent settings.

Large Language Models (LLMs) are increasingly deployed to autonomously solve real-world tasks. A key ingredient for this is the LLM Function-Calling paradigm, a widely used approach for equipping LLMs with tool-use capabilities. However, an LLM calling functions incorrectly can have severe implications, especially when their effects are irreversible, e.g., transferring money or deleting data. Hence, it is of paramount importance to consider the LLM's confidence that a function call solves the task correctly prior to executing it. Uncertainty Quantification (UQ) methods can be used to quantify this confidence and prevent potentially incorrect function calls. In this work, we present what is, to our knowledge, the first evaluation of UQ methods for LLM Function-Calling (FC). While multi-sample UQ methods, such as Semantic Entropy, show strong performance for natural language Q&A tasks, we find that in the FC setting, it offers no clear advantage over simple single-sample UQ methods. Additionally, we find that the particularities of FC outputs can be leveraged to improve the performance of existing UQ methods in this setting. Specifically, multi-sample UQ methods benefit from clustering FC outputs based on their abstract syntax tree parsing, while single-sample UQ methods can be improved by selecting only semantically meaningful tokens when calculating logit-based uncertainty scores.

This paper focuses on the unsupervised domain adaptation of transferring the knowledge from the source domain to the target domain in the context of semantic segmentation. Existing approaches usually regard the pseudo label as the ground truth to fully exploit the unlabeled target-domain data. Yet the pseudo labels of the target-domain data are usually predicted by the model trained on the source domain. Thus, the generated labels inevitably contain the incorrect prediction due to the discrepancy between the training domain and the test domain, which could be transferred to the final adapted model and largely compromises the training process. To overcome the problem, this paper proposes to explicitly estimate the prediction uncertainty during training to rectify the pseudo label learning for unsupervised semantic segmentation adaptation. Given the input image, the model outputs the semantic segmentation prediction as well as the uncertainty of the prediction. Specifically, we model the uncertainty via the prediction variance and involve the uncertainty into the optimization objective. To verify the effectiveness of the proposed method, we evaluate the proposed method on two prevalent synthetic-to-real semantic segmentation benchmarks, i.e., GTA5 -> Cityscapes and SYNTHIA -> Cityscapes, as well as one cross-city benchmark, i.e., Cityscapes -> Oxford RobotCar. We demonstrate through extensive experiments that the proposed approach (1) dynamically sets different confidence thresholds according to the prediction variance, (2) rectifies the learning from noisy pseudo labels, and (3) achieves significant improvements over the conventional pseudo label learning and yields competitive performance on all three benchmarks.

Uncertainty estimation is a promising approach to detect hallucinations in large language models (LLMs). Recent approaches commonly depend on model internal states to estimate uncertainty. However, they suffer from strict assumptions on how hidden states should evolve across layers, and from information loss by solely focusing on last or mean tokens. To address these issues, we present Sequential Internal Variance Representation (SIVR), a supervised hallucination detection framework that leverages token-wise, layer-wise features derived from hidden states. SIVR adopts a more basic assumption that uncertainty manifests in the degree of dispersion or variance of internal representations across layers, rather than relying on specific assumptions, which makes the method model and task agnostic. It additionally aggregates the full sequence of per-token variance features, learning temporal patterns indicative of factual errors and thereby preventing information loss. Experimental results demonstrate SIVR consistently outperforms strong baselines. Most importantly, SIVR enjoys stronger generalisation and avoids relying on large training sets, highlighting the potential for practical deployment. Our code repository is available online at https://github.com/ponhvoan/internal-variance.

Recent advances in multimodal large language models have increased interest in interaction paradigms for video understanding. The evolution from offline to streaming and proactive interaction has gradually shifted models from passive responders toward more proactive agents that can decide when to answer. However, existing proactive paradigms typically assume that the information required to answer a query is complete, leaving models to only wait or answer. In the real world, however, information is often incomplete due to uncertainty from either the video or the user. In proactive paradigms, such uncertainty can cause the model to wait forever or generate highly hallucinatory responses. We therefore argue that proactive interaction should be redefined with a third action: ask, allowing models to actively ask for missing information. To study when and what models should ask before answering, we introduce AskStream, the first multi-turn benchmark spanning video and user uncertainty for streaming video understanding, with four task categories and eight subtasks. It contains 438 videos with 2,714 manually annotated frame-level time windows across three types: wait, ask, and answer. Across both multiple-choice and open-ended settings, even the strongest model attains only 52.18% on our proposed Ask-F1 metric, highlighting substantial limitations in proactive information seeking under uncertainty.

Machine learning models in modern mass-market applications are often updated over time. One of the foremost challenges faced is that, despite increasing overall performance, these updates may flip specific model predictions in unpredictable ways. In practice, researchers quantify the number of unstable predictions between models pre and post update -- i.e., predictive churn. In this paper, we study this effect through the lens of predictive multiplicity -- i.e., the prevalence of conflicting predictions over the set of near-optimal models (the Rashomon set). We show how traditional measures of predictive multiplicity can be used to examine expected churn over this set of prospective models -- i.e., the set of models that may be used to replace a baseline model in deployment. We present theoretical results on the expected churn between models within the Rashomon set from different perspectives. And we characterize expected churn over model updates via the Rashomon set, pairing our analysis with empirical results on real-world datasets -- showing how our approach can be used to better anticipate, reduce, and avoid churn in consumer-facing applications. Further, we show that our approach is useful even for models enhanced with uncertainty awareness.

Deep Neural Networks (DNNs) have demonstrated remarkable performance across various domains, including computer vision and natural language processing. However, they often struggle to accurately quantify the uncertainty of their predictions, limiting their broader adoption in critical real-world applications. Uncertainty Quantification (UQ) for Deep Learning seeks to address this challenge by providing methods to improve the reliability of uncertainty estimates. Although numerous techniques have been proposed, a unified tool offering a seamless workflow to evaluate and integrate these methods remains lacking. To bridge this gap, we introduce Torch-Uncertainty, a PyTorch and Lightning-based framework designed to streamline DNN training and evaluation with UQ techniques and metrics. In this paper, we outline the foundational principles of our library and present comprehensive experimental results that benchmark a diverse set of UQ methods across classification, segmentation, and regression tasks. Our library is available at https://github.com/ENSTA-U2IS-AI/Torch-Uncertainty

We present a scheme to obtain an inexpensive and reliable estimate of the uncertainty associated with the predictions of a machine-learning model of atomic and molecular properties. The scheme is based on resampling, with multiple models being generated based on sub-sampling of the same training data. The accuracy of the uncertainty prediction can be benchmarked by maximum likelihood estimation, which can also be used to correct for correlations between resampled models, and to improve the performance of the uncertainty estimation by a cross-validation procedure. In the case of sparse Gaussian Process Regression models, this resampled estimator can be evaluated at negligible cost. We demonstrate the reliability of these estimates for the prediction of molecular energetics, and for the estimation of nuclear chemical shieldings in molecular crystals. Extension to estimate the uncertainty in energy differences, forces, or other correlated predictions is straightforward. This method can be easily applied to other machine learning schemes, and will be beneficial to make data-driven predictions more reliable, and to facilitate training-set optimization and active-learning strategies.

Discrete diffusion models iteratively denoise a noisy sequence of categorical data such as text, enabling any-order generation with self-correction and in-filling capabilities. This makes them promising candidates for reasoning, planning, and constrained-generation tasks like coding and math. Yet masked and uniform diffusion erase a token's identity in a single corruption event, so their noisy states cannot explicitly represent partially resolved uncertainty in which several alternatives remain plausible. We close this gap with Binary Discrete Diffusion, a family of continuous-time discrete-diffusion processes whose noisy state is a set of candidate tokens per position, represented as a binary membership vector. Binary diffusion changes candidate sets through additions and removals, allowing information to be lost and recovered gradually while the diffusion state itself represents partial uncertainty. On Sudoku-Extreme, Boxoban, and graph coloring, the symmetric formulation of binary diffusion consistently outperforms strong, well-tuned masked and uniform baselines under matched architectures and controlled training, sampling, and tuning budgets, with its largest gains on the hardest instances, while remaining competitive on language modeling (Text8, TinyStories, OpenWebText). These results support candidate sets as an effective intermediate representation for iterative reasoning and show that the corruption kernel can materially change the computation learned by the reverse model.

Numerous deep learning applications benefit from multi-task learning with multiple regression and classification objectives. In this paper we make the observation that the performance of such systems is strongly dependent on the relative weighting between each task's loss. Tuning these weights by hand is a difficult and expensive process, making multi-task learning prohibitive in practice. We propose a principled approach to multi-task deep learning which weighs multiple loss functions by considering the homoscedastic uncertainty of each task. This allows us to simultaneously learn various quantities with different units or scales in both classification and regression settings. We demonstrate our model learning per-pixel depth regression, semantic and instance segmentation from a monocular input image. Perhaps surprisingly, we show our model can learn multi-task weightings and outperform separate models trained individually on each task.

Graph Neural Networks (GNNs) are able to achieve high classification accuracy on many important real world datasets, but provide no rigorous notion of predictive uncertainty. Quantifying the confidence of GNN models is difficult due to the dependence between datapoints induced by the graph structure. We leverage recent advances in conformal prediction to construct prediction sets for node classification in inductive learning scenarios. We do this by taking an existing approach for conformal classification that relies on exchangeable data and modifying it by appropriately weighting the conformal scores to reflect the network structure. We show through experiments on standard benchmark datasets using popular GNN models that our approach provides tighter and better calibrated prediction sets than a naive application of conformal prediction.

The prevalence and importance of algorithmic two-sided marketplaces has drawn attention to the issue of fairness in such settings. Algorithmic decisions are used in assigning students to schools, users to advertisers, and applicants to job interviews. These decisions should heed the preferences of individuals, and simultaneously be fair with respect to their merits (synonymous with fit, future performance, or need). Merits conditioned on observable features are always uncertain, a fact that is exacerbated by the widespread use of machine learning algorithms to infer merit from the observables. As our key contribution, we carefully axiomatize a notion of individual fairness in the two-sided marketplace setting which respects the uncertainty in the merits; indeed, it simultaneously recognizes uncertainty as the primary potential cause of unfairness and an approach to address it. We design a linear programming framework to find fair utility-maximizing distributions over allocations, and we show that the linear program is robust to perturbations in the estimated parameters of the uncertain merit distributions, a key property in combining the approach with machine learning techniques.

A crucial requirement for reliable deployment of deep learning models for safety-critical applications is the ability to identify out-of-distribution (OOD) data points, samples which differ from the training data and on which a model might underperform. Previous work has attempted to tackle this problem using uncertainty estimation techniques. However, there is empirical evidence that a large family of these techniques do not detect OOD reliably in classification tasks. This paper gives a theoretical explanation for said experimental findings and illustrates it on synthetic data. We prove that such techniques are not able to reliably identify OOD samples in a classification setting, since their level of confidence is generalized to unseen areas of the feature space. This result stems from the interplay between the representation of ReLU networks as piece-wise affine transformations, the saturating nature of activation functions like softmax, and the most widely-used uncertainty metrics.

Safety and robustness are crucial factors in developing trustworthy autonomous vehicles. One essential aspect of addressing these factors is to equip vehicles with the capability to predict future trajectories for all moving objects in the surroundings and quantify prediction uncertainties. In this paper, we propose the Sequential Neural Variational Agent (SeNeVA), a generative model that describes the distribution of future trajectories for a single moving object. Our approach can distinguish Out-of-Distribution data while quantifying uncertainty and achieving competitive performance compared to state-of-the-art methods on the Argoverse 2 and INTERACTION datasets. Specifically, a 0.446 meters minimum Final Displacement Error, a 0.203 meters minimum Average Displacement Error, and a 5.35% Miss Rate are achieved on the INTERACTION test set. Extensive qualitative and quantitative analysis is also provided to evaluate the proposed model. Our open-source code is available at https://github.com/PurdueDigitalTwin/seneva.

We introduce BSDetector, a method for detecting bad and speculative answers from a pretrained Large Language Model by estimating a numeric confidence score for any output it generated. Our uncertainty quantification technique works for any LLM accessible only via a black-box API, whose training data remains unknown. By expending a bit of extra computation, users of any LLM API can now get the same response as they would ordinarily, as well as a confidence estimate that cautions when not to trust this response. Experiments on both closed and open-form Question-Answer benchmarks reveal that BSDetector more accurately identifies incorrect LLM responses than alternative uncertainty estimation procedures (for both GPT-3 and ChatGPT). By sampling multiple responses from the LLM and considering the one with the highest confidence score, we can additionally obtain more accurate responses from the same LLM, without any extra training steps. In applications involving automated evaluation with LLMs, accounting for our confidence scores leads to more reliable evaluation in both human-in-the-loop and fully-automated settings (across both GPT 3.5 and 4).

A single unexpected object on the road can cause an accident or may lead to injuries. To prevent this, we need a reliable mechanism for finding anomalous objects on the road. This task, called anomaly segmentation, can be a stepping stone to safe and reliable autonomous driving. Current approaches tackle anomaly segmentation by assigning an anomaly score to each pixel and by grouping anomalous regions using simple heuristics. However, pixel grouping is a limiting factor when it comes to evaluating the segmentation performance of individual anomalous objects. To address the issue of grouping multiple anomaly instances into one, we propose an approach that produces accurate anomaly instance masks. Our approach centers on an out-of-distribution segmentation model for identifying uncertain regions and a strong generalist segmentation model for anomaly instances segmentation. We investigate ways to use uncertain regions to guide such a segmentation model to perform segmentation of anomalous instances. By incorporating strong object priors from a generalist model we additionally improve the per-pixel anomaly segmentation performance. Our approach outperforms current pixel-level anomaly segmentation methods, achieving an AP of 80.08% and 88.98% on the Fishyscapes Lost and Found and the RoadAnomaly validation sets respectively. Project page: https://vision.rwth-aachen.de/ugains

Although large language models (LLMs) are capable of performing various tasks, they still suffer from producing plausible but incorrect responses. To improve the reliability of LLMs, recent research has focused on uncertainty quantification to predict whether a response is correct or not. However, most uncertainty quantification methods have been evaluated on questions requiring a single clear answer, ignoring the existence of data uncertainty that arises from irreducible randomness. Instead, these methods only consider model uncertainty, which arises from a lack of knowledge. In this paper, we investigate previous uncertainty quantification methods under the presence of data uncertainty. Our contributions are two-fold: 1) proposing a new Multi-Answer Question Answering dataset, MAQA, consisting of world knowledge, mathematical reasoning, and commonsense reasoning tasks to evaluate uncertainty quantification regarding data uncertainty, and 2) assessing 5 uncertainty quantification methods of diverse white- and black-box LLMs. Our findings show that entropy and consistency-based methods estimate the model uncertainty well even under data uncertainty, while other methods for white- and black-box LLMs struggle depending on the tasks. Additionally, methods designed for white-box LLMs suffer from overconfidence in reasoning tasks compared to simple knowledge queries. We believe our observations will pave the way for future work on uncertainty quantification in realistic setting.

Selecting an effective training signal for machine learning tasks is difficult: expert annotations are expensive, and crowd-sourced annotations may not be reliable. Recent work has demonstrated that learning from a distribution over labels acquired from crowd annotations can be effective both for performance and uncertainty estimation. However, this has mainly been studied using a limited set of soft-labeling methods in an in-domain setting. Additionally, no one method has been shown to consistently perform well across tasks, making it difficult to know a priori which to choose. To fill these gaps, this paper provides the first large-scale empirical study on learning from crowd labels in the out-of-domain setting, systematically analyzing 8 soft-labeling methods on 4 language and vision tasks. Additionally, we propose to aggregate soft-labels via a simple average in order to achieve consistent performance across tasks. We demonstrate that this yields classifiers with improved predictive uncertainty estimation in most settings while maintaining consistent raw performance compared to learning from individual soft-labeling methods or taking a majority vote of the annotations. We additionally highlight that in regimes with abundant or minimal training data, the selection of soft labeling method is less important, while for highly subjective labels and moderate amounts of training data, aggregation yields significant improvements in uncertainty estimation over individual methods. Code can be found at https://github.com/copenlu/aggregating-crowd-annotations-ood.

Supervised learning for empathy regression is challenged by noisy self-reported empathy scores. While many algorithms have been proposed for learning with noisy labels in textual classification problems, the regression counterpart is relatively under-explored. We propose UPLME, an uncertainty-aware probabilistic language modelling framework to capture label noise in the regression setting of empathy detection. UPLME includes a probabilistic language model that predicts both empathy score and heteroscedastic uncertainty and is trained using Bayesian concepts with variational model ensembling. We further introduce two novel loss components: one penalises degenerate Uncertainty Quantification (UQ), and another enforces the similarity between the input pairs on which we predict empathy. UPLME provides state-of-the-art performance (Pearson Correlation Coefficient: 0.558rightarrow0.580 and 0.629rightarrow0.634) in terms of the performance reported in the literature in two public benchmarks, having label noise. Through synthetic label noise injection, we show that UPLME is effective in separating noisy and clean samples based on the predicted uncertainty. UPLME further outperform (Calibration error: 0.571rightarrow0.376) a recent variational model ensembling-based UQ method designed for regression problems.

Utility functions or their equivalents (value functions, objective functions, loss functions, reward functions, preference orderings) are a central tool in most current machine learning systems. These mechanisms for defining goals and guiding optimization run into practical and conceptual difficulty when there are independent, multi-dimensional objectives that need to be pursued simultaneously and cannot be reduced to each other. Ethicists have proved several impossibility theorems that stem from this origin; those results appear to show that there is no way of formally specifying what it means for an outcome to be good for a population without violating strong human ethical intuitions (in such cases, the objective function is a social welfare function). We argue that this is a practical problem for any machine learning system (such as medical decision support systems or autonomous weapons) or rigidly rule-based bureaucracy that will make high stakes decisions about human lives: such systems should not use objective functions in the strict mathematical sense. We explore the alternative of using uncertain objectives, represented for instance as partially ordered preferences, or as probability distributions over total orders. We show that previously known impossibility theorems can be transformed into uncertainty theorems in both of those settings, and prove lower bounds on how much uncertainty is implied by the impossibility results. We close by proposing two conjectures about the relationship between uncertainty in objectives and severe unintended consequences from AI systems.

Recently, diffusion policy has shown impressive results in handling multi-modal tasks in robotic manipulation. However, it has fundamental limitations in out-of-distribution failures that persist due to compounding errors and its limited capability to extrapolate. One way to address these limitations is robot-gated DAgger, an interactive imitation learning with a robot query system to actively seek expert help during policy rollout. While robot-gated DAgger has high potential for learning at scale, existing methods like Ensemble-DAgger struggle with highly expressive policies: They often misinterpret policy disagreements as uncertainty at multi-modal decision points. To address this problem, we introduce Diff-DAgger, an efficient robot-gated DAgger algorithm that leverages the training objective of diffusion policy. We evaluate Diff-DAgger across different robot tasks including stacking, pushing, and plugging, and show that Diff-DAgger improves the task failure prediction by 39.0%, the task completion rate by 20.6%, and reduces the wall-clock time by a factor of 7.8. We hope that this work opens up a path for efficiently incorporating expressive yet data-hungry policies into interactive robot learning settings. The project website is available at: https://diffdagger.github.io.