Daily Papers

Multimodal large language models (MLLMs) must resolve conflicts when different modalities provide contradictory information, a process we term modality following. Prior work measured this behavior only with coarse dataset-level statistics, overlooking the influence of model's confidence in unimodal reasoning. In this paper, we introduce a new framework that decomposes modality following into two fundamental factors: relative reasoning uncertainty (the case-specific confidence gap between unimodal predictions) and inherent modality preference( a model's stable bias when uncertainties are balanced). To validate this framework, we construct a controllable dataset that systematically varies the reasoning difficulty of visual and textual inputs. Using entropy as a fine-grained uncertainty metric, we uncover a universal law: the probability of following a modality decreases monotonically as its relative uncertainty increases. At the relative difficulty level where the model tends to follow both modalities with comparable probability what we call the balance point, a practical indicator of the model's inherent preference. Unlike traditional macro-level ratios, this measure offers a more principled and less confounded way to characterize modality bias, disentangling it from unimodal capabilities and dataset artifacts. Further, by probing layer-wise predictions, we reveal the internal mechanism of oscillation: in ambiguous regions near the balance point, models vacillate between modalities across layers, explaining externally observed indecision. Together, these findings establish relative uncertainty and inherent preference as the two governing principles of modality following, offering both a quantitative framework and mechanistic insight into how MLLMs resolve conflicting information.

Recent progress in large language models (LLMs) has focused on test-time scaling to improve reasoning via increased inference computation, but often at the cost of efficiency. We revisit test-time behavior and uncover a simple yet underexplored phenomenon: reasoning uncertainty is highly localized-only a small subset of high-entropy tokens dominantly affects output correctness. Motivated by this, we propose Minimal Test-Time Intervention (MTI), a training-free framework that enhances reasoning accuracy and stability with minimal overhead. MTI includes: (i) Selective CFG intervention, applying classifier-free guidance only at uncertain positions; and (ii) Lightweight negative-prompt guidance, reusing the main model's KV cache to approximate unconditional decoding efficiently. MTI yields consistent gains across general, coding, and STEM tasks-e.g., +1.35% average improvement on eight benchmarks for Qwen3-8B-Base and +5% on AIME2024 using Qwen3-32B-Reasoning-while remaining highly efficient.

Visual reasoning in multimodal large language models (MLLMs) has primarily been studied in static, fully observable settings, limiting their effectiveness in real-world environments where information is often incomplete due to occlusion or limited field of view. Humans, in contrast, actively explore and interact with their environment-moving, examining, and manipulating objects-to gather information through a closed-loop process integrating perception, reasoning, and action. Inspired by this human capability, we introduce the Active Visual Reasoning (AVR) task, extending visual reasoning to partially observable, interactive environments. AVR necessitates agents to: (1) actively acquire information via sequential physical actions, (2) integrate observations across multiple steps for coherent reasoning, and (3) dynamically adjust decisions based on evolving visual feedback. To rigorously evaluate AVR, we introduce CLEVR-AVR, a simulation benchmark featuring multi-round interactive environments designed to assess both reasoning correctness and information-gathering efficiency. We present AVR-152k, a large-scale dataset that offers rich Chain-of-Thought (CoT) annotations detailing iterative reasoning for uncertainty identification, action-conditioned information gain prediction, and information-maximizing action selection, crucial for training agents in a higher-order Markov Decision Process. Building on this, we develop PhysVLM-AVR, an MLLM achieving state-of-the-art performance on CLEVR-AVR, embodied reasoning (OpenEQA, RoboVQA), and passive visual reasoning (GeoMath, Geometry30K). Our analysis also reveals that current embodied MLLMs, despite detecting information incompleteness, struggle to actively acquire and integrate new information through interaction, highlighting a fundamental gap in active reasoning capabilities.

Multimodal large language models (MLLMs) have recently demonstrated remarkable reasoning abilities with reinforcement learning paradigm. Although several multimodal reasoning models have been explored in the medical domain, most of them focus exclusively on basic reasoning, which refers to shallow inference based on visual feature matching. However, real-world clinical diagnosis extends beyond basic reasoning, demanding reasoning processes that integrate heterogeneous clinical information (such as chief complaints and medical history) with multimodal medical imaging data. To bridge this gap, we introduce MM-Retinal-Reason, the first ophthalmic multimodal dataset with the full spectrum of perception and reasoning. It encompasses both basic reasoning tasks and complex reasoning tasks, aiming to enhance visual-centric fundamental reasoning capabilities and emulate realistic clinical thinking patterns. Building upon MM-Retinal-Reason, we propose OphthaReason, the first ophthalmology-specific multimodal reasoning model with step-by-step reasoning traces. To enable flexible adaptation to both basic and complex reasoning tasks, we specifically design a novel method called Uncertainty-Aware Dynamic Thinking (UADT), which estimates sample-level uncertainty via entropy and dynamically modulates the model's exploration depth using a shaped advantage mechanism. Comprehensive experiments demonstrate that our model achieves state-of-the-art performance on both basic and complex reasoning tasks, outperforming general-purpose MLLMs, medical MLLMs, RL-based medical MLLMs, and ophthalmic MLLMs by at least 24.92\%, 15.00\%, 21.20\%, and 17.66\%. Project Page: https://github.com/lxirich/OphthaReason{link}.

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

We revisit the weakly supervised cross-modal face-name alignment task; that is, given an image and a caption, we label the faces in the image with the names occurring in the caption. Whereas past approaches have learned the latent alignment between names and faces by uncertainty reasoning over a set of images and their respective captions, in this paper, we rely on appropriate loss functions to learn the alignments in a neural network setting and propose SECLA and SECLA-B. SECLA is a Symmetry-Enhanced Contrastive Learning-based Alignment model that can effectively maximize the similarity scores between corresponding faces and names in a weakly supervised fashion. A variation of the model, SECLA-B, learns to align names and faces as humans do, that is, learning from easy to hard cases to further increase the performance of SECLA. More specifically, SECLA-B applies a two-stage learning framework: (1) Training the model on an easy subset with a few names and faces in each image-caption pair. (2) Leveraging the known pairs of names and faces from the easy cases using a bootstrapping strategy with additional loss to prevent forgetting and learning new alignments at the same time. We achieve state-of-the-art results for both the augmented Labeled Faces in the Wild dataset and the Celebrity Together dataset. In addition, we believe that our methods can be adapted to other multimodal news understanding tasks.

Bayesian inference provides a principled framework for learning from complex data and reasoning under uncertainty. It has been widely applied in machine learning tasks such as medical diagnosis, drug design, and policymaking. In these common applications, data can be highly sensitive. Differential privacy (DP) offers data analysis tools with powerful worst-case privacy guarantees and has been developed as the leading approach in privacy-preserving data analysis. In this paper, we study Metropolis-Hastings (MH), one of the most fundamental MCMC methods, for large-scale Bayesian inference under differential privacy. While most existing private MCMC algorithms sacrifice accuracy and efficiency to obtain privacy, we provide the first exact and fast DP MH algorithm, using only a minibatch of data in most iterations. We further reveal, for the first time, a three-way trade-off among privacy, scalability (i.e. the batch size), and efficiency (i.e. the convergence rate), theoretically characterizing how privacy affects the utility and computational cost in Bayesian inference. We empirically demonstrate the effectiveness and efficiency of our algorithm in various experiments.

Discovering novel high-entropy alloys (HEAs) with desirable properties is challenging due to the vast compositional space and complex phase formation mechanisms. Efficient exploration of this space requires a strategic approach that integrates heterogeneous knowledge sources. Here, we propose a framework that systematically combines knowledge extracted from computational material datasets with domain knowledge distilled from scientific literature using large language models (LLMs). A central feature of this approach is the explicit consideration of element substitutability, identifying chemically similar elements that can be interchanged to potentially stabilize desired HEAs. Dempster-Shafer theory, a mathematical framework for reasoning under uncertainty, is employed to model and combine substitutabilities based on aggregated evidence from multiple sources. The framework predicts the phase stability of candidate HEA compositions and is systematically evaluated on both quaternary alloy systems, demonstrating superior performance compared to baseline machine learning models and methods reliant on single-source evidence in cross-validation experiments. By leveraging multi-source knowledge, the framework retains robust predictive power even when key elements are absent from the training data, underscoring its potential for knowledge transfer and extrapolation. Furthermore, the enhanced interpretability of the methodology offers insights into the fundamental factors governing HEA formation. Overall, this work provides a promising strategy for accelerating HEA discovery by integrating computational and textual knowledge sources, enabling efficient exploration of vast compositional spaces with improved generalization and interpretability.

Statistical shape modeling (SSM) enables population-based quantitative analysis of anatomical shapes, informing clinical diagnosis. Deep learning approaches predict correspondence-based SSM directly from unsegmented 3D images but require calibrated uncertainty quantification, motivating Bayesian formulations. Variational information bottleneck DeepSSM (VIB-DeepSSM) is an effective, principled framework for predicting probabilistic shapes of anatomy from images with aleatoric uncertainty quantification. However, VIB is only half-Bayesian and lacks epistemic uncertainty inference. We derive a fully Bayesian VIB formulation and demonstrate the efficacy of two scalable implementation approaches: concrete dropout and batch ensemble. Additionally, we introduce a novel combination of the two that further enhances uncertainty calibration via multimodal marginalization. Experiments on synthetic shapes and left atrium data demonstrate that the fully Bayesian VIB network predicts SSM from images with improved uncertainty reasoning without sacrificing accuracy.

Solving complex tasks usually requires LLMs to generate long multi-step reasoning chains. Previous work has shown that verifying the correctness of individual reasoning steps can further improve the performance and efficiency of LLMs on such tasks and enhance solution interpretability. However, existing verification approaches, such as Process Reward Models (PRMs), are either computationally expensive, limited to specific domains, or require large-scale human or model-generated annotations. Thus, we propose a lightweight alternative for step-level reasoning verification based on data-driven uncertainty scores. We train transformer-based uncertainty quantification heads (UHeads) that use the internal states of a frozen LLM to estimate the uncertainty of its reasoning steps during generation. The approach is fully automatic: target labels are generated either by another larger LLM (e.g., DeepSeek R1) or in a self-supervised manner by the original model itself. UHeads are both effective and lightweight, containing less than 10M parameters. Across multiple domains, including mathematics, planning, and general knowledge question answering, they match or even surpass the performance of PRMs that are up to 810x larger. Our findings suggest that the internal states of LLMs encode their uncertainty and can serve as reliable signals for reasoning verification, offering a promising direction toward scalable and generalizable introspective LLMs.

Large Language Models (LLMs) have achieved impressive performance on reasoning-intensive tasks, yet optimizing their reasoning efficiency remains an open challenge. While Test-Time Scaling (TTS) improves reasoning quality, it often leads to overthinking, wasting tokens on redundant computations. This work investigates how to efficiently and adaptively guide LLM test-time scaling without additional training. Inspired by the concept of momentum in physics, we propose Momentum Uncertainty-guided Reasoning (MUR), which dynamically allocates thinking budgets to critical reasoning steps by tracking and aggregating stepwise uncertainty over time. To support flexible inference-time control, we introduce gamma-control, a simple mechanism that tunes the reasoning budget via a single hyperparameter. We provide in-depth theoretical proof to support the superiority of MUR in terms of stability and biases. MUR is comprehensively evaluated against various TTS methods across four challenging benchmarks (MATH-500, AIME24, AIME25, and GPQA-diamond) using different sizes of recent Qwen3 models (1.7B, 4B, and 8B). Results demonstrate that MUR reduces computation by over 50% on average while improving accuracy by 0.62-3.37%.

This work presents a first evaluation of two state-of-the-art Large Reasoning Models (LRMs), OpenAI's o3-mini and DeepSeek R1, on analogical reasoning, focusing on well-established nonverbal human IQ tests based on Raven's progressive matrices. We benchmark with the I-RAVEN dataset and its more difficult extension, I-RAVEN-X, which tests the ability to generalize to longer reasoning rules and ranges of the attribute values. To assess the influence of visual uncertainties on these nonverbal analogical reasoning tests, we extend the I-RAVEN-X dataset, which otherwise assumes an oracle perception. We adopt a two-fold strategy to simulate this imperfect visual perception: 1) we introduce confounding attributes which, being sampled at random, do not contribute to the prediction of the correct answer of the puzzles and 2) smoothen the distributions of the input attributes' values. We observe a sharp decline in OpenAI's o3-mini task accuracy, dropping from 86.6% on the original I-RAVEN to just 17.0% -- approaching random chance -- on the more challenging I-RAVEN-X, which increases input length and range and emulates perceptual uncertainty. This drop occurred despite spending 3.4x more reasoning tokens. A similar trend is also observed for DeepSeek R1: from 80.6% to 23.2%. On the other hand, a neuro-symbolic probabilistic abductive model, ARLC, that achieves state-of-the-art performances on I-RAVEN, can robustly reason under all these out-of-distribution tests, maintaining strong accuracy with only a modest reduction from 98.6% to 88.0%. Our code is available at https://github.com/IBM/raven-large-language-models.

Parallel test-time scaling (TTS) is a pivotal approach for enhancing large language models (LLMs), typically by sampling multiple token-based chains-of-thought in parallel and aggregating outcomes through voting or search. Recent advances in latent reasoning, where intermediate reasoning unfolds in continuous vector spaces, offer a more efficient alternative to explicit Chain-of-Thought, yet whether such latent models can similarly benefit from parallel TTS remains open, mainly due to the absence of sampling mechanisms in continuous space, and the lack of probabilistic signals for advanced trajectory aggregation. \ This work enables parallel TTS for latent reasoning models by addressing the above issues. For sampling, we introduce two uncertainty-inspired stochastic strategies: Monte Carlo Dropout and Additive Gaussian Noise. For aggregation, we design a Latent Reward Model (LatentRM) trained with step-wise contrastive objective to score and guide latent reasoning. Extensive experiments and visualization analyses show that both sampling strategies scale effectively with compute and exhibit distinct exploration dynamics, while LatentRM enables effective trajectory selection. Together, our explorations open a new direction for scalable inference in continuous spaces. Code released at https://github.com/YRYangang/LatentTTS.

Recent advances in inference time scaling with extended long chain-of thought have significantly improved the reasoning capabilities of both general and medical large language models (LLMs). However, these models tend to engage in lengthy reasoning processes regardless of the difficulty of the input question, leading to increased inference costs in real-world applications. Therefore, enabling adaptive thinking where models think less for simpler questions and think more for complex ones is critical for the effective use of medical LLMs in practice. Despite its importance, there is a lack of end-to-end approaches designed to enhance the adaptive thinking capabilities of medical LLMs while providing a comprehensive examination of the trade-off between performance and computational cost. To bridge this gap, we propose AdaThink-Med, the first end-to-end framework designed to enhance adaptive thinking ability in medical reasoning models with uncertainty-guided length calibration. AdaThink-Med first generates multiple candidate outputs for each question, evaluates the correctness and uncertainty of each candidate, and then estimates problem difficulty via an uncertainty-guided length calibration module. For outputs with low difficulty and correct answers, the framework penalizes longer reasoning paths; whereas for those with high difficulty and incorrect answers, it encourages extending the chain of thought to explore alternative solutions. On six public medical QA benchmarks, AdaThink-Med achieves up to 6.4x length reduction on average while retaining performance with only minimal degradation. Intriguingly, we observe that AdaThink-Med spontaneously develops two distinct reasoning modes, which we characterize as "non-thinking" and "thinking", demonstrating the model's ability to suppress redundant reasoning processes dynamically.

While Large Language Models (LLMs) can solve many NLP tasks in zero-shot settings, applications involving embodied agents remain problematic. In particular, complex plans that require multi-step reasoning become difficult and too costly as the context window grows. Planning requires understanding the likely effects of one's actions and identifying whether the current environment satisfies the goal state. While symbolic planners find optimal solutions quickly, they require a complete and accurate representation of the planning problem, severely limiting their use in practical scenarios. In contrast, modern LLMs cope with noisy observations and high levels of uncertainty when reasoning about a task. Our work presents LLM Dynamic Planner (LLM-DP): a neuro-symbolic framework where an LLM works hand-in-hand with a traditional planner to solve an embodied task. Given action-descriptions, LLM-DP solves Alfworld faster and more efficiently than a naive LLM ReAct baseline.

Reinforcement learning with verifiable rewards (RLVR) improves reasoning in large language models (LLMs) but struggles with exploration, an issue that still persists for multimodal LLMs (MLLMs). Current methods treat the visual input as a fixed, deterministic condition, overlooking a critical source of ambiguity and struggling to build policies robust to plausible visual variations. We introduce VOGUE (Visual Uncertainty Guided Exploration), a novel method that shifts exploration from the output (text) to the input (visual) space. By treating the image as a stochastic context, VOGUE quantifies the policy's sensitivity to visual perturbations using the symmetric KL divergence between a "raw" and "noisy" branch, creating a direct signal for uncertainty-aware exploration. This signal shapes the learning objective via an uncertainty-proportional bonus, which, combined with a token-entropy bonus and an annealed sampling schedule, effectively balances exploration and exploitation. Implemented within GRPO on two model scales (Qwen2.5-VL-3B/7B), VOGUE boosts pass@1 accuracy by an average of 2.6% on three visual math benchmarks and 3.7% on three general-domain reasoning benchmarks, while simultaneously increasing pass@4 performance and mitigating the exploration decay commonly observed in RL fine-tuning. Our work shows that grounding exploration in the inherent uncertainty of visual inputs is an effective strategy for improving multimodal reasoning.

Large language models (LLMs) show remarkable promise for democratizing automated reasoning by generating formal specifications. However, a fundamental tension exists: LLMs are probabilistic, while formal verification demands deterministic guarantees. This paper addresses this epistemological gap by comprehensively investigating failure modes and uncertainty quantification (UQ) in LLM-generated formal artifacts. Our systematic evaluation of five frontier LLMs reveals Satisfiability Modulo Theories (SMT) based autoformalization's domain-specific impact on accuracy (from +34.8% on logical tasks to -44.5% on factual ones), with known UQ techniques like the entropy of token probabilities failing to identify these errors. We introduce a probabilistic context-free grammar (PCFG) framework to model LLM outputs, yielding a refined uncertainty taxonomy. We find uncertainty signals are task-dependent (e.g., grammar entropy for logic, AUROC>0.93). Finally, a lightweight fusion of these signals enables selective verification, drastically reducing errors (14-100%) with minimal abstention, transforming LLM-driven formalization into a reliable engineering discipline.

Large language models have demonstrated remarkable capabilities in complex mathematical reasoning tasks, but they inevitably generate errors throughout multi-step solutions. Process-level Reward Models (PRMs) have shown great promise by providing supervision and evaluation at each intermediate step, thereby effectively improving the models' reasoning abilities. However, training effective PRMs requires high-quality process reward data, yet existing methods for constructing such data are often labour-intensive or inefficient. In this paper, we propose an uncertainty-driven framework for automated process reward data construction, encompassing both data generation and annotation processes for PRMs. Additionally, we identify the limitations of both majority vote and PRMs, and introduce two generic uncertainty-aware output aggregation methods: Hybrid Majority Reward Vote and Weighted Reward Frequency Vote, which combine the strengths of majority vote with PRMs. Extensive experiments on ProcessBench, MATH, and GSMPlus show the effectiveness and efficiency of the proposed PRM data construction framework, and demonstrate that the two output aggregation methods further improve the mathematical reasoning abilities across diverse PRMs. The code and data will be publicly available at https://github.com/Jiuzhouh/UnPRM.

Balancing exploration and exploitation is a central goal in reinforcement learning (RL). Despite recent advances in enhancing language model (LM) reasoning, most methods lean toward exploitation, and increasingly encounter performance plateaus. In this work, we revisit entropy -- a signal of exploration in RL -- and examine its relationship to exploratory reasoning in LMs. Through empirical analysis, we uncover strong positive correlations between high-entropy regions and three types of exploratory reasoning actions: (1) pivotal tokens that determine or connect logical steps, (2) reflective actions such as self-verification and correction, and (3) rare behaviors under-explored by the base LMs. Motivated by this, we introduce a minimal modification to standard RL with only one line of code: augmenting the advantage function with an entropy-based term. Unlike traditional maximum-entropy methods which encourage exploration by promoting uncertainty, we encourage exploration by promoting longer and deeper reasoning chains. Notably, our method achieves significant gains on the Pass@K metric -- an upper-bound estimator of LM reasoning capabilities -- even when evaluated with extremely large K values, pushing the boundaries of LM reasoning.

Large language models (LLMs) excel in many tasks but struggle to accurately quantify uncertainty in their generated responses. This limitation makes it challenging to detect misinformation and ensure reliable decision-making. Existing uncertainty quantification (UQ) methods for LLMs are primarily prompt-wise rather than response-wise, often requiring multiple response samples, which incurs high computational costs. Moreover, LLMs have been shown to be overconfident, particularly when using reasoning steps to derive their answers. In this work, we propose CoT-UQ, a response-wise UQ framework that integrates LLMs' inherent reasoning capabilities through Chain-of-Thought (CoT) into the UQ process. CoT-UQ captures critical information during inference by extracting keywords from each reasoning step and assessing their importance to the final answer. This key reasoning information is then aggregated to produce a final uncertainty estimate. We conduct extensive experiments based on LLaMA Family with model sizes varying from 8B to 13B across logical and mathematical reasoning tasks. Experimental results demonstrate that CoT-UQ significantly outperforms existing UQ methods, achieving an average improvement of 5.9% AUROC compared to current UQ methods. The code is available at: https://github.com/ZBox1005/CoT-UQ.

Accurate greenhouse gas (GHG) emission reporting is critical for governments, businesses, and investors. However, adoption remains limited particularly among small and medium enterprises due to high implementation costs, fragmented emission factor databases, and a lack of robust sector classification methods. To address these challenges, we introduce Group Reasoning Emission Estimation Networks (GREEN), an AI-driven carbon accounting framework that standardizes enterprise-level emission estimation, constructs a large-scale benchmark dataset, and leverages a novel reasoning approach with large language models (LLMs). Specifically, we compile textual descriptions for 20,850 companies with validated North American Industry Classification System (NAICS) labels and align these with an economic model of carbon intensity factors. By reframing sector classification as an information retrieval task, we fine-tune Sentence-BERT models using a contrastive learning loss. To overcome the limitations of single-stage models in handling thousands of hierarchical categories, we propose a Group Reasoning method that ensembles LLM classifiers based on the natural NAICS ontology, decomposing the task into multiple sub-classification steps. We theoretically prove that this approach reduces classification uncertainty and computational complexity. Experiments on 1,114 NAICS categories yield state-of-the-art performance (83.68% Top-1, 91.47% Top-10 accuracy), and case studies on 20 companies report a mean absolute percentage error (MAPE) of 45.88%. The project is available at: https://huggingface.co/datasets/Yvnminc/ExioNAICS.

Accurately quantifying a large language model's (LLM) predictive uncertainty is crucial for judging the reliability of its answers. While most existing research focuses on short, directly answerable questions with closed-form outputs (e.g., multiple-choice), involving intermediate reasoning steps in LLM responses is increasingly important. This added complexity complicates uncertainty quantification (UQ) because the probabilities assigned to answer tokens are conditioned on a vast space of preceding reasoning tokens. Direct marginalization is infeasible, and the dependency inflates probability estimates, causing overconfidence in UQ. To address this, we propose UQAC, an efficient method that narrows the reasoning space to a tractable size for marginalization. UQAC iteratively constructs an "attention chain" of tokens deemed "semantically crucial" to the final answer via a backtracking procedure. Starting from the answer tokens, it uses attention weights to identify the most influential predecessors, then iterates this process until reaching the input tokens. Similarity filtering and probability thresholding further refine the resulting chain, allowing us to approximate the marginal probabilities of the answer tokens, which serve as the LLM's confidence. We validate UQAC on multiple reasoning benchmarks with advanced open-source LLMs, demonstrating that it consistently delivers reliable UQ estimates with high computational efficiency.

It is important for Large Language Models to be aware of the boundary of their knowledge, the mechanism of identifying known and unknown queries. This type of awareness can help models perform adaptive inference, such as invoking RAG, engaging in slow and deep thinking, or adopting the abstention mechanism, which is beneficial to the development of efficient and trustworthy AI. In this work, we propose a method to detect knowledge boundaries via Query-Level Uncertainty, which aims to determine if the model is able to address a given query without generating any tokens. To this end, we introduce a novel and training-free method called Internal Confidence, which leverages self-evaluations across layers and tokens. Empirical results on both factual QA and mathematical reasoning tasks demonstrate that our internal confidence can outperform several baselines. Furthermore, we showcase that our proposed method can be used for efficient RAG and model cascading, which is able to reduce inference costs while maintaining performance.

Process reward models (PRMs) play a central role in guiding inference-time scaling algorithms for large language models (LLMs). However, we observe that even state-of-the-art PRMs can be poorly calibrated and often overestimate success probabilities. To address this, we present a calibration approach, performed via quantile regression, that adjusts PRM outputs to better align with true success probabilities. Leveraging these calibrated success estimates and their associated confidence bounds, we introduce an instance-adaptive scaling (IAS) framework that dynamically adjusts the inference budget based on the estimated likelihood that a partial reasoning trajectory will yield a correct final answer. Unlike conventional methods that allocate a fixed number of reasoning trajectories per query, this approach successfully adapts to each instance and reasoning step when using our calibrated PRMs. Experiments on mathematical reasoning benchmarks show that (i) our PRM calibration method successfully achieves small calibration error, outperforming the baseline methods, (ii) calibration is crucial for enabling effective adaptive scaling, and (iii) the proposed IAS strategy reduces inference costs while maintaining final answer accuracy, utilizing less compute on more confident problems as desired.

Complex question-answering (QA) systems face significant challenges in retrieving and reasoning over information that addresses multi-faceted queries. While large language models (LLMs) have advanced the reasoning capabilities of these systems, the bounded-recall problem persists, where procuring all relevant documents in first-stage retrieval remains a challenge. Missing pertinent documents at this stage leads to performance degradation that cannot be remedied in later stages, especially given the limited context windows of LLMs which necessitate high recall at smaller retrieval depths. In this paper, we introduce SUNAR, a novel approach that leverages LLMs to guide a Neighborhood Aware Retrieval process. SUNAR iteratively explores a neighborhood graph of documents, dynamically promoting or penalizing documents based on uncertainty estimates from interim LLM-generated answer candidates. We validate our approach through extensive experiments on two complex QA datasets. Our results show that SUNAR significantly outperforms existing retrieve-and-reason baselines, achieving up to a 31.84% improvement in performance over existing state-of-the-art methods for complex QA.

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.

Large language models (LLMs) exhibit advanced reasoning skills, enabling robots to comprehend natural language instructions and strategically plan high-level actions through proper grounding. However, LLM hallucination may result in robots confidently executing plans that are misaligned with user goals or even unsafe in critical scenarios. Additionally, inherent ambiguity in natural language instructions can introduce uncertainty into the LLM's reasoning and planning processes.We propose introspective planning, a systematic approach that align LLM's uncertainty with the inherent ambiguity of the task. Our approach constructs a knowledge base containing introspective reasoning examples as post-hoc rationalizations of human-selected safe and compliant plans, which are retrieved during deployment. Evaluations on three tasks, including a newly introduced safe mobile manipulation benchmark, demonstrate that introspection substantially improves both compliance and safety over state-of-the-art LLM-based planning methods. Furthermore, we empirically show that introspective planning, in combination with conformal prediction, achieves tighter confidence bounds, maintaining statistical success guarantees while minimizing unnecessary user clarification requests. The webpage and code are accessible at https://introplan.github.io.

Transformers have become the gold standard for many natural language processing tasks and, in particular, for multi-hop question answering (MHQA). This task includes processing a long document and reasoning over the multiple parts of it. The landscape of MHQA approaches can be classified into two primary categories. The first group focuses on extracting supporting evidence, thereby constraining the QA model's context to predicted facts. Conversely, the second group relies on the attention mechanism of the long input encoding model to facilitate multi-hop reasoning. However, attention-based token representations lack explicit global contextual information to connect reasoning steps. To address these issues, we propose GEMFormer, a two-stage method that first collects relevant information over the entire document to the memory and then combines it with local context to solve the task. Our experimental results show that fine-tuning a pre-trained model with memory-augmented input, including the most certain global elements, improves the model's performance on three MHQA datasets compared to the baseline. We also found that the global explicit memory contains information from supporting facts required for the correct answer.

Implicit policies parameterized by generative models, such as Diffusion Policy, have become the standard for policy learning and Vision-Language-Action (VLA) models in robotics. However, these approaches often suffer from high computational cost, exposure bias, and unstable inference dynamics, which lead to divergence under distribution shifts. Energy-Based Models (EBMs) address these issues by learning energy landscapes end-to-end and modeling equilibrium dynamics, offering improved robustness and reduced exposure bias. Yet, policies parameterized by EBMs have historically struggled to scale effectively. Recent work on Energy-Based Transformers (EBTs) demonstrates the scalability of EBMs to high-dimensional spaces, but their potential for solving core challenges in physically embodied models remains underexplored. We introduce a new energy-based architecture, EBT-Policy, that solves core issues in robotic and real-world settings. Across simulated and real-world tasks, EBT-Policy consistently outperforms diffusion-based policies, while requiring less training and inference computation. Remarkably, on some tasks it converges within just two inference steps, a 50x reduction compared to Diffusion Policy's 100. Moreover, EBT-Policy exhibits emergent capabilities not seen in prior models, such as zero-shot recovery from failed action sequences using only behavior cloning and without explicit retry training. By leveraging its scalar energy for uncertainty-aware inference and dynamic compute allocation, EBT-Policy offers a promising path toward robust, generalizable robot behavior under distribution shifts.

Recently evolved large reasoning models (LRMs) show powerful performance in solving complex tasks with long chain-of-thought (CoT) reasoning capability. As these LRMs are mostly developed by post-training on formal reasoning tasks, whether they generalize the reasoning capability to help reduce hallucination in fact-seeking tasks remains unclear and debated. For instance, DeepSeek-R1 reports increased performance on SimpleQA, a fact-seeking benchmark, while OpenAI-o3 observes even severer hallucination. This discrepancy naturally raises the following research question: Are reasoning models more prone to hallucination? This paper addresses the question from three perspectives. (1) We first conduct a holistic evaluation for the hallucination in LRMs. Our analysis reveals that LRMs undergo a full post-training pipeline with cold start supervised fine-tuning (SFT) and verifiable reward RL generally alleviate their hallucination. In contrast, both distillation alone and RL training without cold start fine-tuning introduce more nuanced hallucinations. (2) To explore why different post-training pipelines alters the impact on hallucination in LRMs, we conduct behavior analysis. We characterize two critical cognitive behaviors that directly affect the factuality of a LRM: Flaw Repetition, where the surface-level reasoning attempts repeatedly follow the same underlying flawed logic, and Think-Answer Mismatch, where the final answer fails to faithfully match the previous CoT process. (3) Further, we investigate the mechanism behind the hallucination of LRMs from the perspective of model uncertainty. We find that increased hallucination of LRMs is usually associated with the misalignment between model uncertainty and factual accuracy. Our work provides an initial understanding of the hallucination in LRMs.

Large language models (LLMs) exhibit varying levels of confidence across input prompts (questions): some lead to consistent, semantically similar answers, while others yield diverse or contradictory outputs. This variation reflects LLM's uncertainty about the input prompt, a signal of how confidently the model understands a given problem. However, vanilla Group Relative Policy Optimization (GRPO) treats all prompts equally during policy updates, ignoring this important information about the model's knowledge boundaries. To address this limitation, we propose SEED-GRPO (Semantic Entropy EnhanceD GRPO), which explicitly measures LLMs' uncertainty of the input prompts semantic entropy. Semantic entropy measures the diversity of meaning in multiple generated answers given a prompt and uses this to modulate the magnitude of policy updates. This uncertainty-aware training mechanism enables dynamic adjustment of policy update magnitudes based on question uncertainty. It allows more conservative updates on high-uncertainty questions while maintaining the original learning signal on confident ones. Experimental results on five mathematical reasoning benchmarks (AIME24 56.7, AMC 68.7, MATH 83.4, Minerva 34.2, and OlympiadBench 48.0) demonstrate that SEED-GRPO achieves new state-of-the-art performance in average accuracy, validating the effectiveness of uncertainty-aware policy optimization.

Recent advancements in large language models (LLMs) often rely on generating intermediate reasoning steps to enhance accuracy. However, little work has examined how reasoning utility contributes to the final answer's correctness. Due to the stochastic nature of autoregressive generation, generating more context does not guarantee increased confidence in the answer. If we could predict, during generation, whether a reasoning step will be useful, we could stop early or prune ineffective steps, avoiding distractions in the final decision. We present an oracle study on MATH dataset, using Qwen2.5-32B and GPT-4o to generate reasoning chains, and then employing a separate model (Qwen3-8B) to quantify the utility of these chains for final accuracy. Specifically, we measure the model's uncertainty on the answer span Y at each reasoning step using conditional entropy (expected negative log-likelihood over the vocabulary) with context expanding step by step. Our results show a clear pattern: conditional entropy that decreases over steps is strongly associated with correct answers, whereas flat or increasing entropy often results in wrong answers. We also corroborate that incorrect reasoning paths tend to be longer than correct ones, suggesting that longer reasoning does not necessarily yield better outcomes. These findings serve as a foundation to inspire future work on designing efficient reasoning pipelines that detect and avoid unproductive reasoning early.

The field of controllable image generation has seen significant advancements, with various architectures improving generation layout consistency with control signals. However, contemporary methods still face challenges in bridging the semantic gap between input text prompts with sparse semantics and the target images, often over-relying on low-level control signals to infer regional details. To address this challenge, we propose ControlThinker, a novel framework that employs a "comprehend-then-generate" paradigm. Firstly, by incentivizing the visual reasoning capability of a MLLM, latent semantics from control images are mined to enrich text prompts. This enriched semantic understanding then seamlessly aids in image generation without the need for additional complex modifications. To further tackle the uncertainty arising from the ambiguity of control images, we encourage broader exploration of reasoning trajectories and select the optimal one using a metric-based output reward model (ORM). Extensive experimental results demonstrate that ControlThinker effectively mitigates the semantic gap between raw text prompts and target images, resulting in improved visual quality and semantic consistency across a wide range of benchmarks. The code and models are available at https://github.com/Maplebb/ControlThinker.

LLMs are ideal for decision-making thanks to their ability to reason over long contexts. However, challenges arise when processing speech transcripts that describe complex scenarios, as they are verbose and include repetition, hedging, and vagueness. E.g., during a company's earnings call, an executive might project a positive revenue outlook to reassure investors, despite uncertainty regarding future earnings. It is crucial for LLMs to incorporate this uncertainty systematically when making decisions. In this paper, we introduce DeFine, a modular framework that constructs probabilistic factor profiles from complex scenarios. It then integrates these profiles with analogical reasoning, leveraging insights from similar past experiences to guide LLMs in making critical decisions in new situations. Our framework separates the tasks of quantifying uncertainty and incorporating it into LLM decision-making. This approach is particularly useful in areas such as consulting and financial deliberation, where making decisions under uncertainty is vital.

Transcending human cognitive limitations represents a critical frontier in LLM training. Proprietary agentic systems like DeepResearch have demonstrated superhuman capabilities on extremely complex information-seeking benchmarks such as BrowseComp, a feat previously unattainable. We posit that their success hinges on a sophisticated reasoning pattern absent in open-source models: the ability to systematically reduce extreme uncertainty when navigating vast information landscapes. Based on this insight, we introduce WebSailor, a complete post-training methodology designed to instill this crucial capability. Our approach involves generating novel, high-uncertainty tasks through structured sampling and information obfuscation, RFT cold start, and an efficient agentic RL training algorithm, Duplicating Sampling Policy Optimization (DUPO). With this integrated pipeline, WebSailor significantly outperforms all opensource agents in complex information-seeking tasks, matching proprietary agents' performance and closing the capability gap.

Uncertainty estimation is crucial for evaluating Large Language Models (LLMs), particularly in high-stakes domains where incorrect answers result in significant consequences. Numerous approaches consider this problem, while focusing on a specific type of uncertainty, ignoring others. We investigate what estimates, specifically token-wise entropy and model-as-judge (MASJ), would work for multiple-choice question-answering tasks for different question topics. Our experiments consider three LLMs: Phi-4, Mistral, and Qwen of different sizes from 1.5B to 72B and 14 topics. While MASJ performs similarly to a random error predictor, the response entropy predicts model error in knowledge-dependent domains and serves as an effective indicator of question difficulty: for biology ROC AUC is 0.73. This correlation vanishes for the reasoning-dependent domain: for math questions ROC-AUC is 0.55. More principally, we found out that the entropy measure required a reasoning amount. Thus, data-uncertainty related entropy should be integrated within uncertainty estimates frameworks, while MASJ requires refinement. Moreover, existing MMLU-Pro samples are biased, and should balance required amount of reasoning for different subdomains to provide a more fair assessment of LLMs performance.

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.

Table reasoning with the large language models (LLMs) is a fundamental path toward building intelligent systems that can understand and analyze over structured data. While recent progress has shown promising results, they still suffer from two key limitations: (i) the reasoning processes lack the depth and iterative refinement characteristic of human cognition; and (ii) the reasoning processes exhibit instability, which compromises their reliability in downstream applications. In this work, we present STaR (slow-thinking for table reasoning), a new framework achieving cognitive table reasoning, in which LLMs are equipped with slow-thinking capabilities by explicitly modeling step-by-step thinking and uncertainty-aware inference. During training, STaR employs two-stage difficulty-aware reinforcement learning (DRL), progressively learning from simple to complex queries under a composite reward. During inference, STaR performs trajectory-level uncertainty quantification by integrating token-level confidence and answer consistency, enabling selection of more credible reasoning paths. Extensive experiments on benchmarks demonstrate that STaR achieves superior performance and enhanced reasoning stability. Moreover, strong generalization over out-of-domain datasets further demonstrates STaR's potential as a reliable and cognitively inspired solution for table reasoning with LLMs.

Spatial reasoning is a core aspect of human intelligence that allows perception, inference and planning in 3D environments. However, current vision-language models (VLMs) struggle to maintain geometric coherence and cross-view consistency for spatial reasoning in multi-view settings. We attribute this gap to the lack of fine-grained benchmarks that isolate multi-view reasoning from single-view perception and temporal factors. To address this, we present ReMindView-Bench, a cognitively grounded benchmark for evaluating how VLMs construct, align and maintain spatial mental models across complementary viewpoints. ReMindView-Bench systematically varies viewpoint spatial pattern and query type to probe key factors of spatial cognition. Evaluations of 15 current VLMs reveals consistent failures in cross-view alignment and perspective-taking in multi-view spatial reasoning, motivating deeper analysis on the reasoning process. Explicit phase-wise analysis using LLM-as-a-judge and self-consistency prompting shows that VLMs perform well on in-frame perception but degrade sharply when integrating information across views. Implicit analysis, including linear probing and entropy dynamics, further show progressive loss of task-relevant information and uncertainty separation between correct and incorrect trajectories. These results provide a cognitively grounded diagnosis of VLM spatial reasoning and reveal how multi-view spatial mental models are formed, degraded and destabilized across reasoning phases. The ReMindView-Bench benchmark is available at https://huggingface.co/datasets/Xue0823/ReMindView-Bench, and the source codes of benchmark construction and VLM reasoning analysis are available at https://github.com/pittisl/ReMindView-Bench.

Large Reasoning Models (LRMs) extend large language models with explicit, multi-step reasoning traces to enhance transparency and performance on complex tasks. However, these reasoning traces can be redundant or logically inconsistent, making them a new source of hallucination that is difficult to detect. Existing hallucination detection methods focus primarily on answer-level uncertainty and often fail to detect hallucinations or logical inconsistencies arising from the model's reasoning trace. This oversight is particularly problematic for LRMs, where the explicit thinking trace is not only an important support to the model's decision-making process but also a key source of potential hallucination. To this end, we propose RACE (Reasoning and Answer Consistency Evaluation), a novel framework specifically tailored for hallucination detection in LRMs. RACE operates by extracting essential reasoning steps and computing four diagnostic signals: inter-sample consistency of reasoning traces, entropy-based answer uncertainty, semantic alignment between reasoning and answers, and internal coherence of reasoning. This joint analysis enables fine-grained hallucination detection even when the final answer appears correct. Experiments across datasets and different LLMs demonstrate that RACE outperforms existing hallucination detection baselines, offering a robust and generalizable solution for evaluating LRMs. Our code is available at: https://github.com/bebr2/RACE.

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.

Most reasoning benchmarks for LLMs emphasize factual accuracy or step-by-step logic. In finance, however, professionals must not only converge on optimal decisions but also generate creative, plausible futures under uncertainty. We introduce ConDiFi, a benchmark that jointly evaluates divergent and convergent thinking in LLMs for financial tasks. ConDiFi features 607 macro-financial prompts for divergent reasoning and 990 multi-hop adversarial MCQs for convergent reasoning. Using this benchmark, we evaluated 14 leading models and uncovered striking differences. Despite high fluency, GPT-4o underperforms on Novelty and Actionability. In contrast, models like DeepSeek-R1 and Cohere Command R+ rank among the top for generating actionable, insights suitable for investment decisions. ConDiFi provides a new perspective to assess reasoning capabilities essential to safe and strategic deployment of LLMs in finance.

Large Language Models (LLMs) exhibit impressive reasoning abilities, yet their reliance on structured step-by-step processing reveals a critical limitation. While human cognition fluidly adapts between intuitive, heuristic (System 1) and analytical, deliberative (System 2) reasoning depending on the context, LLMs lack this dynamic flexibility. This rigidity can lead to brittle and unreliable performance when faced with tasks that deviate from their trained patterns. To address this, we create a dataset of 2,000 samples with valid System 1 and System 2 answers, explicitly align LLMs with these reasoning styles, and evaluate their performance across reasoning benchmarks. Our results reveal an accuracy-efficiency trade-off: System 2-aligned models excel in arithmetic and symbolic reasoning, while System 1-aligned models perform better in commonsense tasks. A mechanistic analysis of model responses shows that System 1 models employ more definitive answers, whereas System 2 models demonstrate greater uncertainty. Interpolating between these extremes produces a monotonic transition in reasoning accuracy, preserving coherence. This work challenges the assumption that step-by-step reasoning is always optimal and highlights the need for adapting reasoning strategies based on task demands.

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

For Large Language Models (LLMs) to be reliably deployed in both everyday and high-stakes domains, knowing when not to answer is equally critical as answering correctly. Real-world user queries, which can be underspecified, ill-posed, or fundamentally unanswerable, require LLMs to reason about uncertainty and selectively abstain -- i.e., refuse to answer definitively. However, abstention remains understudied, without a systematic evaluation framework for modern LLMs. In this work, we introduce AbstentionBench, a large-scale benchmark for holistically evaluating abstention across 20 diverse datasets, including questions with unknown answers, underspecification, false premises, subjective interpretations, and outdated information. Evaluating 20 frontier LLMs reveals abstention is an unsolved problem, and one where scaling models is of little use. While recent reasoning LLMs have shown impressive results in complex problem solving, surprisingly, we find that reasoning fine-tuning degrades abstention (by 24% on average), even for math and science domains on which reasoning models are explicitly trained. We find that while a carefully crafted system prompt can boost abstention in practice, it does not resolve models' fundamental inability to reason about uncertainty. We release AbstentionBench to foster research into advancing LLM reliability.

Chain-of-thought (CoT) reasoning enables large language models (LLMs) to break down complex problems into interpretable intermediate steps, significantly enhancing model transparency and performance in reasoning tasks. However, conventional CoT methods rely on heuristic sampling without structured modeling of reasoning transitions, constraining their ability to systematically explore and discover diverse and effective reasoning trajectories. In this work, we introduce CTRLS, a framework that formulates CoT reasoning as a Markov decision process (MDP) with latent state transitions, enabling principled and state-aware exploration via distributional reinforcement learning. By modelling reasoning actions as explicit probability distributions in latent space, our approach explicitly models epistemic uncertainty, facilitating robust exploration of the reasoning space. As part of our framework, we introduce an on-policy reinforcement learning strategy incorporating epsilon-greedy exploration and entropy-based regularization to iteratively refine latent state transitions without requiring additional fine-tuning of the underlying LLM. Theoretical analyses provide evidence lower bounds (ELBO), theoretically grounding our transition-aware modeling of latent reasoning dynamics. Further experiments demonstrate improvements in reasoning accuracy, diversity, and exploration efficiency across benchmark reasoning tasks.

Integrating large language models (LLMs) like DeepSeek R1 into healthcare requires rigorous evaluation of their reasoning alignment with clinical expertise. This study assesses DeepSeek R1's medical reasoning against expert patterns using 100 MedQA clinical cases. The model achieved 93% diagnostic accuracy, demonstrating systematic clinical judgment through differential diagnosis, guideline-based treatment selection, and integration of patient-specific factors. However, error analysis of seven incorrect cases revealed persistent limitations: anchoring bias, challenges reconciling conflicting data, insufficient exploration of alternatives, overthinking, knowledge gaps, and premature prioritization of definitive treatment over intermediate care. Crucially, reasoning length correlated with accuracy - shorter responses (<5,000 characters) were more reliable, suggesting extended explanations may signal uncertainty or rationalization of errors. While DeepSeek R1 exhibits foundational clinical reasoning capabilities, recurring flaws highlight critical areas for refinement, including bias mitigation, knowledge updates, and structured reasoning frameworks. These findings underscore LLMs' potential to augment medical decision-making through artificial reasoning but emphasize the need for domain-specific validation, interpretability safeguards, and confidence metrics (e.g., response length thresholds) to ensure reliability in real-world applications.

Traditional evaluations of multimodal large language models (LLMs) have been limited by their focus on single-image reasoning, failing to assess crucial aspects like contextual understanding, reasoning stability, and uncertainty calibration. This study addresses these limitations by introducing a novel benchmark that integrates multi-image reasoning tasks with rejection-based evaluation and positional bias detection. To evaluate these dimensions, we further introduce entropy as a novel metric for quantifying reasoning consistency across reordered answer variants. We applied this benchmark to assess Grok 3, ChatGPT-4o, ChatGPT-o1, Gemini 2.0 Flash Experimental, DeepSeek Janus models, Qwen2.5-VL-72B-Instruct, QVQ-72B-Preview, and Pixtral 12B across eight visual reasoning tasks, including difference spotting and diagram interpretation. Our findings reveal ChatGPT-o1 leading in overall accuracy (82.5\%) and rejection accuracy (70.0\%), closely followed by Gemini 2.0 Flash Experimental (70.8\%). QVQ-72B-Preview demonstrated superior rejection accuracy (85.5\%). Notably, Pixtral 12B (51.7\%) showed promise in specific domains, while Janus models exhibited challenges in bias and uncertainty calibration, reflected in low rejection accuracies and high entropy scores. High entropy scores in Janus models (Janus 7B: 0.8392, Janus 1B: 0.787) underscore their susceptibility to positional bias and unstable reasoning, contrasting with the low entropy and robust reasoning of ChatGPT models. The study further demonstrates that model size is not the sole determinant of performance, as evidenced by Grok 3 underperformance despite its substantial parameter count. By employing multi-image contexts, rejection mechanisms, and entropy-based consistency metrics, this benchmark sets a new standard for evaluating multimodal LLMs, enabling a more robust and reliable assessment of next-generation AI systems.

Large language models (LLMs) often fail to ask effective questions under uncertainty, making them unreliable in domains where proactive information-gathering is essential for decisionmaking. We present ALFA, a framework that improves LLM question-asking by (i) decomposing the notion of a "good" question into a set of theory-grounded attributes (e.g., clarity, relevance), (ii) controllably synthesizing attribute-specific question variations, and (iii) aligning models via preference-based optimization to explicitly learn to ask better questions along these fine-grained attributes. Focusing on clinical reasoning as a case study, we introduce the MediQ-AskDocs dataset, composed of 17k real-world clinical interactions augmented with 80k attribute-specific preference pairs of follow-up questions, as well as a novel expert-annotated interactive healthcare QA task to evaluate question-asking abilities. Models aligned with ALFA reduce diagnostic errors by 56.6% on MediQ-AskDocs compared to SOTA instruction-tuned LLMs, with a question-level win-rate of 64.4% and strong generalizability. Our findings suggest that explicitly guiding question-asking with structured, fine-grained attributes offers a scalable path to improve LLMs, especially in expert application domains.

There is a growing literature on reasoning by large language models (LLMs), but the discussion on the uncertainty in their responses is still lacking. Our aim is to assess the extent of confidence that LLMs have in their answers and how it correlates with accuracy. Confidence is measured (i) qualitatively in terms of persistence in keeping their answer when prompted to reconsider, and (ii) quantitatively in terms of self-reported confidence score. We investigate the performance of three LLMs -- GPT4o, GPT4-turbo and Mistral -- on two benchmark sets of questions on causal judgement and formal fallacies and a set of probability and statistical puzzles and paradoxes. Although the LLMs show significantly better performance than random guessing, there is a wide variability in their tendency to change their initial answers. There is a positive correlation between qualitative confidence and accuracy, but the overall accuracy for the second answer is often worse than for the first answer. There is a strong tendency to overstate the self-reported confidence score. Confidence is only partially explained by the underlying token-level probability. The material effects of prompting on qualitative confidence and the strong tendency for overconfidence indicate that current LLMs do not have any internally coherent sense of confidence.

Large language models (LLMs) have revolutionized the field of natural language processing with their impressive reasoning and question-answering capabilities. However, these models are sometimes prone to generating credible-sounding but incorrect information, a phenomenon known as LLM hallucinations. Reliable uncertainty estimation in LLMs is essential for fostering trust in their generated responses and serves as a critical tool for the detection and prevention of erroneous or hallucinated outputs. To achieve reliable and well-calibrated uncertainty quantification in open-ended and free-form natural language generation, we propose an uncertainty-aware fine-tuning approach for LLMs. This approach enhances the model's ability to provide reliable uncertainty estimates without compromising accuracy, thereby guiding them to produce more trustworthy responses. We introduce a novel uncertainty-aware causal language modeling loss function, grounded in the principles of decision theory. Through rigorous evaluation on multiple free-form question-answering datasets and models, we demonstrate that our uncertainty-aware fine-tuning approach yields better calibrated uncertainty estimates in natural language generation tasks than fine-tuning with the standard causal language modeling loss. Furthermore, the experimental results show that the proposed method significantly improves the model's ability to detect hallucinations and identify out-of-domain prompts.

The rapid development of large language models (LLMs) has shown promising practical results. However, their low interpretability often leads to errors in unforeseen circumstances, limiting their utility. Many works have focused on creating comprehensive evaluation systems, but previous benchmarks have primarily assessed problem-solving abilities while neglecting the response's uncertainty, which may result in unreliability. Recent methods for measuring LLM reliability are resource-intensive and unable to test black-box models. To address this, we propose UBENCH, a comprehensive benchmark for evaluating LLM reliability. UBENCH includes 3,978 multiple-choice questions covering knowledge, language, understanding, and reasoning abilities. Experimental results show that UBENCH has achieved state-of-the-art performance, while its single-sampling method significantly saves computational resources compared to baseline methods that require multiple samplings. Additionally, based on UBENCH, we evaluate the reliability of 15 popular LLMs, finding GLM4 to be the most outstanding, closely followed by GPT-4. We also explore the impact of Chain-of-Thought prompts, role-playing prompts, option order, and temperature on LLM reliability, analyzing the varying effects on different LLMs.

Without explicit feedback, humans can rapidly learn the meaning of words. Children can acquire a new word after just a few passive exposures, a process known as fast mapping. This word learning capability is believed to be the most fundamental building block of multimodal understanding and reasoning. Despite recent advancements in multimodal learning, a systematic and rigorous evaluation is still missing for human-like word learning in machines. To fill in this gap, we introduce the MachinE Word Learning (MEWL) benchmark to assess how machines learn word meaning in grounded visual scenes. MEWL covers human's core cognitive toolkits in word learning: cross-situational reasoning, bootstrapping, and pragmatic learning. Specifically, MEWL is a few-shot benchmark suite consisting of nine tasks for probing various word learning capabilities. These tasks are carefully designed to be aligned with the children's core abilities in word learning and echo the theories in the developmental literature. By evaluating multimodal and unimodal agents' performance with a comparative analysis of human performance, we notice a sharp divergence in human and machine word learning. We further discuss these differences between humans and machines and call for human-like few-shot word learning in machines.

Multimodal semantic understanding often has to deal with uncertainty, which means the obtained messages tend to refer to multiple targets. Such uncertainty is problematic for our interpretation, including inter- and intra-modal uncertainty. Little effort has studied the modeling of this uncertainty, particularly in pre-training on unlabeled datasets and fine-tuning in task-specific downstream datasets. In this paper, we project the representations of all modalities as probabilistic distributions via a Probability Distribution Encoder (PDE) by utilizing sequence-level interactions. Compared to the existing deterministic methods, such uncertainty modeling can convey richer multimodal semantic information and more complex relationships. Furthermore, we integrate uncertainty modeling with popular pre-training frameworks and propose suitable pre-training tasks: Distribution-based Vision-Language Contrastive learning (D-VLC), Distribution-based Masked Language Modeling (D-MLM), and Distribution-based Image-Text Matching (D-ITM). The fine-tuned models are applied to challenging downstream tasks, including image-text retrieval, visual question answering, visual reasoning, and visual entailment, and achieve state-of-the-art results.

Numerous applications of large language models (LLMs) rely on their ability to perform step-by-step reasoning. However, the reasoning behavior of LLMs remains poorly understood, posing challenges to research, development, and safety. To address this gap, we introduce landscape of thoughts-the first visualization tool for users to inspect the reasoning paths of chain-of-thought and its derivatives on any multi-choice dataset. Specifically, we represent the states in a reasoning path as feature vectors that quantify their distances to all answer choices. These features are then visualized in two-dimensional plots using t-SNE. Qualitative and quantitative analysis with the landscape of thoughts effectively distinguishes between strong and weak models, correct and incorrect answers, as well as different reasoning tasks. It also uncovers undesirable reasoning patterns, such as low consistency and high uncertainty. Additionally, users can adapt our tool to a model that predicts the property they observe. We showcase this advantage by adapting our tool to a lightweight verifier that evaluates the correctness of reasoning paths. The code is publicly available at: https://github.com/tmlr-group/landscape-of-thoughts.

When language models (LMs) are trained via reinforcement learning (RL) to generate natural language "reasoning chains", their performance improves on a variety of difficult question answering tasks. Today, almost all successful applications of RL for reasoning use binary reward functions that evaluate the correctness of LM outputs. Because such reward functions do not penalize guessing or low-confidence outputs, they often have the unintended side-effect of degrading calibration and increasing the rate at which LMs generate incorrect responses (or "hallucinate") in other problem domains. This paper describes RLCR (Reinforcement Learning with Calibration Rewards), an approach to training reasoning models that jointly improves accuracy and calibrated confidence estimation. During RLCR, LMs generate both predictions and numerical confidence estimates after reasoning. They are trained to optimize a reward function that augments a binary correctness score with a Brier score -- a scoring rule for confidence estimates that incentivizes calibrated prediction. We first prove that this reward function (or any analogous reward function that uses a bounded, proper scoring rule) yields models whose predictions are both accurate and well-calibrated. We next show that across diverse datasets, RLCR substantially improves calibration with no loss in accuracy, on both in-domain and out-of-domain evaluations -- outperforming both ordinary RL training and classifiers trained to assign post-hoc confidence scores. While ordinary RL hurts calibration, RLCR improves it. Finally, we demonstrate that verbalized confidence can be leveraged at test time to improve accuracy and calibration via confidence-weighted scaling methods. Our results show that explicitly optimizing for calibration can produce more generally reliable reasoning models.

Large Language Models (LLMs) have attained human-level accuracy on medical question-answer (QA) benchmarks. However, their limitations in navigating open-ended clinical scenarios have recently been shown, raising concerns about the robustness and generalizability of LLM reasoning across diverse, real-world medical tasks. To probe potential LLM failure modes in clinical problem-solving, we present the medical abstraction and reasoning corpus (M-ARC). M-ARC assesses clinical reasoning through scenarios designed to exploit the Einstellung effect -- the fixation of thought arising from prior experience, targeting LLM inductive biases toward inflexible pattern matching from their training data rather than engaging in flexible reasoning. We find that LLMs, including current state-of-the-art o1 and Gemini models, perform poorly compared to physicians on M-ARC, often demonstrating lack of commonsense medical reasoning and a propensity to hallucinate. In addition, uncertainty estimation analyses indicate that LLMs exhibit overconfidence in their answers, despite their limited accuracy. The failure modes revealed by M-ARC in LLM medical reasoning underscore the need to exercise caution when deploying these models in clinical settings.

Recent progress in multimodal large language models (MLLMs) has demonstrated promising performance on medical benchmarks and in preliminary trials as clinical assistants. Yet, our pilot audit of diagnostic cases uncovers a critical failure mode: instability in early evidence interpretation precedes hallucination, creating branching reasoning trajectories that cascade into globally inconsistent conclusions. This highlights the need for clinical reasoning agents that constrain stochasticity and hallucination while producing auditable decision flows. We introduce MedMMV, a controllable multimodal multi-agent framework for reliable and verifiable clinical reasoning. MedMMV stabilizes reasoning through diversified short rollouts, grounds intermediate steps in a structured evidence graph under the supervision of a Hallucination Detector, and aggregates candidate paths with a Combined Uncertainty scorer. On six medical benchmarks, MedMMV improves accuracy by up to 12.7% and, more critically, demonstrates superior reliability. Blind physician evaluations confirm that MedMMV substantially increases reasoning truthfulness without sacrificing informational content. By controlling instability through a verifiable, multi-agent process, our framework provides a robust path toward deploying trustworthy AI systems in high-stakes domains like clinical decision support.

Understanding sources of a model's uncertainty regarding its predictions is crucial for effective human-AI collaboration. Prior work proposes using numerical uncertainty or hedges ("I'm not sure, but ..."), which do not explain uncertainty that arises from conflicting evidence, leaving users unable to resolve disagreements or rely on the output. We introduce CLUE (Conflict-and-Agreement-aware Language-model Uncertainty Explanations), the first framework to generate natural language explanations of model uncertainty by (i) identifying relationships between spans of text that expose claim-evidence or inter-evidence conflicts and agreements that drive the model's predictive uncertainty in an unsupervised way, and (ii) generating explanations via prompting and attention steering that verbalize these critical interactions. Across three language models and two fact-checking datasets, we show that CLUE produces explanations that are more faithful to the model's uncertainty and more consistent with fact-checking decisions than prompting for uncertainty explanations without span-interaction guidance. Human evaluators judge our explanations to be more helpful, more informative, less redundant, and more logically consistent with the input than this baseline. CLUE requires no fine-tuning or architectural changes, making it plug-and-play for any white-box language model. By explicitly linking uncertainty to evidence conflicts, it offers practical support for fact-checking and generalises readily to other tasks that require reasoning over complex information.

Time series reasoning treats time as a first-class axis and incorporates intermediate evidence directly into the answer. This survey defines the problem and organizes the literature by reasoning topology with three families: direct reasoning in one step, linear chain reasoning with explicit intermediates, and branch-structured reasoning that explores, revises, and aggregates. The topology is crossed with the main objectives of the field, including traditional time series analysis, explanation and understanding, causal inference and decision making, and time series generation, while a compact tag set spans these axes and captures decomposition and verification, ensembling, tool use, knowledge access, multimodality, agent loops, and LLM alignment regimes. Methods and systems are reviewed across domains, showing what each topology enables and where it breaks down in faithfulness or robustness, along with curated datasets, benchmarks, and resources that support study and deployment (https://github.com/blacksnail789521/Time-Series-Reasoning-Survey). Evaluation practices that keep evidence visible and temporally aligned are highlighted, and guidance is distilled on matching topology to uncertainty, grounding with observable artifacts, planning for shift and streaming, and treating cost and latency as design budgets. We emphasize that reasoning structures must balance capacity for grounding and self-correction against computational cost and reproducibility, while future progress will likely depend on benchmarks that tie reasoning quality to utility and on closed-loop testbeds that trade off cost and risk under shift-aware, streaming, and long-horizon settings. Taken together, these directions mark a shift from narrow accuracy toward reliability at scale, enabling systems that not only analyze but also understand, explain, and act on dynamic worlds with traceable evidence and credible outcomes.

Large Vision-Language Models (LVLMs) have demonstrated impressive general capabilities across a wide range of multi-modal tasks. However, the reasoning processes of LVLMs often suffer from unreliable outputs and limited interpretability. To address this, grounded visual reasoning has emerged as a promising paradigm that enforces responses anchored on salient visual evidence regions. However, existing approaches typically rely on costly supervision such as bounding box annotations, chain-of-thought rationale or external tool calls, limiting their scalability. In this work, we propose Ground-R1, a reinforcement learning framework that enables grounded visual reasoning without requiring explicit evidence or rationale annotations. Ground-R1 consists of a grounding phase that generates evidence region rollouts based on format constraints, and an answering phase that produces responses guided by both answer correctness and format adherence rewards. Extensive experiments across multiple visual reasoning benchmarks manifest that Ground-R1 achieves superior performance and exhibits emergent cognitive behaviors such as uncertainty awareness, spatial perception, and iterative refinement, offering a scalable and interpretable alternative to existing approaches.

Multi-hop question answering (QA) requires models to retrieve and reason over multiple pieces of evidence. While Retrieval-Augmented Generation (RAG) has made progress in this area, existing methods often suffer from two key limitations: (1) fixed or overly frequent retrieval steps, and (2) ineffective use of previously retrieved knowledge. We propose MIND (Memory-Informed and INteractive Dynamic RAG), a framework that addresses these challenges through: (i) prompt-based entity extraction to identify reasoning-relevant elements, (ii) dynamic retrieval triggering based on token-level entropy and attention signals, and (iii) memory-aware filtering, which stores high-confidence facts across reasoning steps to enable consistent multi-hop generation.

The remarkable performance of large language models (LLMs) in content generation, coding, and common-sense reasoning has spurred widespread integration into many facets of society. However, integration of LLMs raises valid questions on their reliability and trustworthiness, given their propensity to generate hallucinations: plausible, factually-incorrect responses, which are expressed with striking confidence. Previous work has shown that hallucinations and other non-factual responses generated by LLMs can be detected by examining the uncertainty of the LLM in its response to the pertinent prompt, driving significant research efforts devoted to quantifying the uncertainty of LLMs. This survey seeks to provide an extensive review of existing uncertainty quantification methods for LLMs, identifying their salient features, along with their strengths and weaknesses. We present existing methods within a relevant taxonomy, unifying ostensibly disparate methods to aid understanding of the state of the art. Furthermore, we highlight applications of uncertainty quantification methods for LLMs, spanning chatbot and textual applications to embodied artificial intelligence applications in robotics. We conclude with open research challenges in uncertainty quantification of LLMs, seeking to motivate future research.

Empowering large language models to accurately express confidence in their answers is essential for trustworthy decision-making. Previous confidence elicitation methods, which primarily rely on white-box access to internal model information or model fine-tuning, have become less suitable for LLMs, especially closed-source commercial APIs. This leads to a growing need to explore the untapped area of black-box approaches for LLM uncertainty estimation. To better break down the problem, we define a systematic framework with three components: prompting strategies for eliciting verbalized confidence, sampling methods for generating multiple responses, and aggregation techniques for computing consistency. We then benchmark these methods on two key tasks-confidence calibration and failure prediction-across five types of datasets (e.g., commonsense and arithmetic reasoning) and five widely-used LLMs including GPT-4 and LLaMA 2 Chat. Our analysis uncovers several key insights: 1) LLMs, when verbalizing their confidence, tend to be overconfident, potentially imitating human patterns of expressing confidence. 2) As model capability scales up, both calibration and failure prediction performance improve. 3) Employing our proposed strategies, such as human-inspired prompts, consistency among multiple responses, and better aggregation strategies can help mitigate this overconfidence from various perspectives. 4) Comparisons with white-box methods indicate that while white-box methods perform better, the gap is narrow, e.g., 0.522 to 0.605 in AUROC. Despite these advancements, none of these techniques consistently outperform others, and all investigated methods struggle in challenging tasks, such as those requiring professional knowledge, indicating significant scope for improvement. We believe this study can serve as a strong baseline and provide insights for eliciting confidence in black-box LLMs.

Visual Question Answering (VQA) models often perform poorly on out-of-distribution data and struggle on domain generalization. Due to the multi-modal nature of this task, multiple factors of variation are intertwined, making generalization difficult to analyze. This motivates us to introduce a virtual benchmark, Super-CLEVR, where different factors in VQA domain shifts can be isolated in order that their effects can be studied independently. Four factors are considered: visual complexity, question redundancy, concept distribution and concept compositionality. With controllably generated data, Super-CLEVR enables us to test VQA methods in situations where the test data differs from the training data along each of these axes. We study four existing methods, including two neural symbolic methods NSCL and NSVQA, and two non-symbolic methods FiLM and mDETR; and our proposed method, probabilistic NSVQA (P-NSVQA), which extends NSVQA with uncertainty reasoning. P-NSVQA outperforms other methods on three of the four domain shift factors. Our results suggest that disentangling reasoning and perception, combined with probabilistic uncertainty, form a strong VQA model that is more robust to domain shifts. The dataset and code are released at https://github.com/Lizw14/Super-CLEVR.

Recent reasoning Large Language Models (LLMs) demonstrate remarkable problem-solving abilities but often generate long thinking traces whose utility is unclear. Our work aims to improve their efficiency, enabling them to reach high performance without overthinking. First, we analyze the entropy of token probabilities in reasoning traces. Across three models, we observe a consistent U-shaped entropy pattern: high entropy on easy problems despite high accuracy, low entropy on problems with medium difficulty, and high entropy on hard problems reflecting uncertainty. Specifically, we notice 22--25\% entropy reduction from easy to medium difficulty regions, suggesting an {overthinking} phenomenon on easy instances. Building on these insights, we introduce DiffAdapt, a lightweight framework that selects Easy/Normal/Hard inference strategies per question based on their difficulty and reasoning trace entropy. Each inference strategy consists of a fixed prompt, temperature and maximum token length. In contrast to existing efficiency optimization methods, our approach does not fine-tune base LLM but a small probe that classifies LLM's final hidden state, allowing inexpensive adaptation. We comprehensively evaluate our method on five models and eight benchmarks. Our method achieves comparable or improved accuracy while reducing token usage by up to 22.4\%, establishing a practical path toward compute-efficient reasoning.

Existing reasoning segmentation approaches typically fine-tune multimodal large language models (MLLMs) using image-text pairs and corresponding mask labels. However, they exhibit limited generalization to out-of-distribution scenarios without an explicit reasoning process. Although recent efforts leverage reinforcement learning through group-relative policy optimization (GRPO) to enhance reasoning ability, they often suffer from overthinking - producing uniformly verbose reasoning chains irrespective of task complexity. This results in elevated computational costs and limited control over reasoning quality. To address this problem, we propose PixelThink, a simple yet effective scheme that integrates externally estimated task difficulty and internally measured model uncertainty to regulate reasoning generation within a reinforcement learning paradigm. The model learns to compress reasoning length in accordance with scene complexity and predictive confidence. To support comprehensive evaluation, we introduce ReasonSeg-Diff, an extended benchmark with annotated reasoning references and difficulty scores, along with a suite of metrics designed to assess segmentation accuracy, reasoning quality, and efficiency jointly. Experimental results demonstrate that the proposed approach improves both reasoning efficiency and overall segmentation performance. Our work contributes novel perspectives towards efficient and interpretable multimodal understanding. The code and model will be publicly available.

Long video understanding has emerged as an increasingly important yet challenging task in computer vision. Agent-based approaches are gaining popularity for processing long videos, as they can handle extended sequences and integrate various tools to capture fine-grained information. However, existing methods still face several challenges: (1) they often rely solely on the reasoning ability of large language models (LLMs) without dedicated mechanisms to enhance reasoning in long video scenarios; and (2) they remain vulnerable to errors or noise from external tools. To address these issues, we propose a specialized chain-of-thought (CoT) process tailored for long video analysis. Our proposed CoT with plan-adjust mode enables the LLM to incrementally plan and adapt its information-gathering strategy. We further incorporate heuristic uncertainty estimation of both the LLM and external tools to guide the CoT process. This allows the LLM to assess the reliability of newly collected information, refine its collection strategy, and make more robust decisions when synthesizing final answers. Empirical experiments show that our uncertainty-aware CoT effectively mitigates noise from external tools, leading to more reliable outputs. We implement our approach in a system called VideoAgent2, which also includes additional modules such as general context acquisition and specialized tool design. Evaluation on three dedicated long video benchmarks (and their subsets) demonstrates that VideoAgent2 outperforms the previous state-of-the-art agent-based method, VideoAgent, by an average of 13.1% and achieves leading performance among all zero-shot approaches

Improving the multi-step reasoning ability of Large Language Models (LLMs) is a critical yet challenging task. The dominant paradigm, outcome-supervised reinforcement learning (RLVR), rewards only correct final answers, often propagating flawed reasoning and suffering from sparse reward signals. While process-level reward models (PRMs) provide denser, step-by-step feedback, they lack generalizability and interpretability, requiring task-specific segmentation of the reasoning process. To this end, we propose the Dimension-level Reward Model (DRM), a new supervision framework that bridges the gap between these two approaches. DRM evaluates the quality of a reasoning process along three fundamental, complementary, and interpretable dimensions: Confidence for uncertainty calibration, Relevance for semantic alignment, and Coherence for logical consistency. Together, these dimensions capture aspects beyond final answer correctness and enable interpretable assessment without requiring ground truth answers. Experimental results show that DRM provides effective supervision signals, guides the optimization of LLMs and enhances their reasoning ability. In particular, DRM-supervised training achieves consistent gains on both in-distribution and out-of-distribution open-domain tasks, including mathematics, question answering, code execution, and puzzles. Our findings demonstrate that multidimensional supervision of the reasoning process can improve the generalized reasoning ability of LLMs beyond the training distribution.

Advancing LLM reasoning skills has captivated wide interest. However, current post-training techniques rely heavily on supervisory signals, such as outcome supervision or auxiliary reward models, which face the problem of scalability and high annotation costs. This motivates us to enhance LLM reasoning without the need for external supervision. We introduce a generalizable and purely unsupervised self-training framework, named Genius. Without external auxiliary, Genius requires to seek the optimal response sequence in a stepwise manner and optimize the LLM. To explore the potential steps and exploit the optimal ones, Genius introduces a stepwise foresight re-sampling strategy to sample and estimate the step value by simulating future outcomes. Further, we recognize that the unsupervised setting inevitably induces the intrinsic noise and uncertainty. To provide a robust optimization, we propose an advantage-calibrated optimization (ACO) loss function to mitigate estimation inconsistencies. Combining these techniques together, Genius provides an advanced initial step towards self-improve LLM reasoning with general queries and without supervision, revolutionizing reasoning scaling laws given the vast availability of general queries. The code will be released at https://github.com/xufangzhi/Genius.

Large Language Models (LLMs) have shown impressive reasoning capabilities in well-defined problems with clear solutions, such as mathematics and coding. However, they still struggle with complex real-world scenarios like business negotiations, which require strategic reasoning-an ability to navigate dynamic environments and align long-term goals amidst uncertainty. Existing methods for strategic reasoning face challenges in adaptability, scalability, and transferring strategies to new contexts. To address these issues, we propose explicit policy optimization (EPO) for strategic reasoning, featuring an LLM that provides strategies in open-ended action space and can be plugged into arbitrary LLM agents to motivate goal-directed behavior. To improve adaptability and policy transferability, we train the strategic reasoning model via multi-turn reinforcement learning (RL) using process rewards and iterative self-play, without supervised fine-tuning (SFT) as a preliminary step. Experiments across social and physical domains demonstrate EPO's ability of long-term goal alignment through enhanced strategic reasoning, achieving state-of-the-art performance on social dialogue and web navigation tasks. Our findings reveal various collaborative reasoning mechanisms emergent in EPO and its effectiveness in generating novel strategies, underscoring its potential for strategic reasoning in real-world applications.

Model merging aggregates Large Language Models (LLMs) finetuned on different tasks into a stronger one. However, parameter conflicts between models leads to performance degradation in averaging. While model routing addresses this issue by selecting individual models during inference, it imposes excessive storage and compute costs, and fails to leverage the common knowledge from different models. In this work, we observe that different layers exhibit varying levels of parameter conflicts. Building on this insight, we average layers with minimal parameter conflicts and use a novel task-level expert routing for layers with significant conflicts. To further reduce storage costs, inspired by task arithmetic sparsity, we decouple multiple fine-tuned experts into a dense expert and several sparse experts. Considering the out-of-distribution samples, we select and merge appropriate experts based on the task uncertainty of the input data. We conduct extensive experiments on both LLaMA and Qwen with varying parameter scales, and evaluate on real-world reasoning tasks. Results demonstrate that our method consistently achieves significant performance improvements while requiring less system cost compared to existing methods.

Modern Vision-Language Models (VLMs) have achieved impressive performance in various tasks, yet they often struggle with compositional reasoning, the ability to decompose and recombine concepts to solve novel problems. While neuro-symbolic approaches offer a promising direction, they are typically constrained by crisp logical execution or predefined predicates, which limit flexibility. In this work, we introduce NePTune, a neuro-symbolic framework that overcomes these limitations through a hybrid execution model that integrates the perception capabilities of foundation vision models with the compositional expressiveness of symbolic reasoning. NePTune dynamically translates natural language queries into executable Python programs that blend imperative control flow with soft logic operators capable of reasoning over VLM-generated uncertainty. Operating in a training-free manner, NePTune, with a modular design, decouples perception from reasoning, yet its differentiable operations support fine-tuning. We evaluate NePTune on multiple visual reasoning benchmarks and various domains, utilizing adversarial tests, and demonstrate a significant improvement over strong base models, as well as its effective compositional generalization and adaptation capabilities in novel environments.

Large Language Models (LLMs) have achieved remarkable success in complex reasoning tasks, but their inference remains computationally inefficient. We observe a common failure mode in many prevalent LLMs, overthinking, where models generate verbose and tangential reasoning traces even for simple queries. Recent works have tried to mitigate this by enforcing fixed token budgets, however, this can lead to underthinking, especially on harder problems. Through empirical analysis, we identify that this inefficiency often stems from unclear problem-solving strategies. To formalize this, we develop a theoretical model, BBAM (Bayesian Budget Allocation Model), which models reasoning as a sequence of sub-questions with varying uncertainty, and introduce the E^3 metric to capture the trade-off between correctness and computation efficiency. Building on theoretical results from BBAM, we propose Plan-and-Budget, a model-agnostic, test-time framework that decomposes complex queries into sub-questions and allocates token budgets based on estimated complexity using adaptive scheduling. Plan-and-Budget improves reasoning efficiency across a range of tasks and models, achieving up to +70% accuracy gains, -39% token reduction, and +187.5% improvement in E^3. Notably, it elevates a smaller model (DS-Qwen-32B) to match the efficiency of a larger model (DS-LLaMA-70B)-demonstrating Plan-and-Budget's ability to close performance gaps without retraining. Our code is available at anonymous.4open.science/r/P-and-B-6513/.

Large Language Models (LLMs) are increasingly becoming ubiquitous, yet their ability to reason about and retain temporal information remains limited. This hinders their application in real-world scenarios where understanding the sequential nature of events is crucial. This paper experiments with state-of-the-art models on a novel, large-scale temporal dataset, TempUN, to reveal significant limitations in temporal retention and reasoning abilities. Interestingly, closed-source models indicate knowledge gaps more frequently, potentially suggesting a trade-off between uncertainty awareness and incorrect responses. Further, exploring various fine-tuning approaches yielded no major performance improvements. The associated dataset and code are available at the following URL (https://github.com/lingoiitgn/TempUN).

Anomaly segmentation is a critical task for driving applications, and it is approached traditionally as a per-pixel classification problem. However, reasoning individually about each pixel without considering their contextual semantics results in high uncertainty around the objects' boundaries and numerous false positives. We propose a paradigm change by shifting from a per-pixel classification to a mask classification. Our mask-based method, Mask2Anomaly, demonstrates the feasibility of integrating an anomaly detection method in a mask-classification architecture. Mask2Anomaly includes several technical novelties that are designed to improve the detection of anomalies in masks: i) a global masked attention module to focus individually on the foreground and background regions; ii) a mask contrastive learning that maximizes the margin between an anomaly and known classes; and iii) a mask refinement solution to reduce false positives. Mask2Anomaly achieves new state-of-the-art results across a range of benchmarks, both in the per-pixel and component-level evaluations. In particular, Mask2Anomaly reduces the average false positives rate by 60% wrt the previous state-of-the-art. Github page: https://github.com/shyam671/Mask2Anomaly-Unmasking-Anomalies-in-Road-Scene-Segmentation.

Task-oriented dialogue systems often face difficulties when user utterances seem semantically complete but lack necessary structural information for appropriate system action. This arises because users frequently do not fully understand their own needs, while systems require precise intent definitions. Current LLM-based agents cannot effectively distinguish between linguistically complete and contextually triggerable expressions, lacking frameworks for collaborative intent formation. We present STORM, a framework modeling asymmetric information dynamics through conversations between UserLLM (full internal access) and AgentLLM (observable behavior only). STORM produces annotated corpora capturing expression trajectories and latent cognitive transitions, enabling systematic analysis of collaborative understanding development. Our contributions include: (1) formalizing asymmetric information processing in dialogue systems; (2) modeling intent formation tracking collaborative understanding evolution; and (3) evaluation metrics measuring internal cognitive improvements alongside task performance. Experiments across four language models reveal that moderate uncertainty (40-60%) can outperform complete transparency in certain scenarios, with model-specific patterns suggesting reconsideration of optimal information completeness in human-AI collaboration. These findings contribute to understanding asymmetric reasoning dynamics and inform uncertainty-calibrated dialogue system design.

The ability to acknowledge the inevitable uncertainty in their knowledge and reasoning is a prerequisite for AI systems to be truly truthful and reliable. In this paper, we present a taxonomy of uncertainty specific to vision-language AI systems, distinguishing between epistemic uncertainty (arising from a lack of information) and aleatoric uncertainty (due to inherent unpredictability), and further explore finer categories within. Based on this taxonomy, we synthesize a benchmark dataset, CertainlyUncertain, featuring 178K visual question answering (VQA) samples as contrastive pairs. This is achieved by 1) inpainting images to make previously answerable questions into unanswerable ones; and 2) using image captions to prompt large language models for both answerable and unanswerable questions. Additionally, we introduce a new metric confidence-weighted accuracy, that is well correlated with both accuracy and calibration error, to address the shortcomings of existing metrics.

Large Language Models (LLMs) empowered with retrieval mechanisms have achieved strong progress in open-domain question answering (QA). Yet, the conventional retrieve--then--answer paradigm often suffers from two key limitations: (1) low signal-to-noise ratio in retrieved evidence, where useful information is buried under irrelevant content, and (2) error accumulation in multi-hop reasoning when incomplete or noisy passages are involved. To address these challenges, we present EviNote-RAG, an agentic RAG framework that introduces a structured retrieve--note--answer pipeline. Instead of directly reasoning over raw retrievals, the model is trained to compose Supportive-Evidence Notes (SENs), concise, human-like notes that preserve only answer-relevant information, highlight uncertainty, and explicitly state when no useful evidence exists. This distillation process is further reinforced by the Evidence Quality Reward (EQR), an entailment-based signal that evaluates whether SENs logically support the final answer. Together, SENs and EQR guide the model toward faithful and robust reasoning, while reducing the impact of noise. Experiments on in-domain and out-of-domain QA benchmarks show that EviNote-RAG consistently outperforms strong baselines in accuracy, generalization, and training stability. In particular, it achieves state-of-the-art results while enhancing robustness and efficiency, yielding relative F1 gains of 20\% on HotpotQA (+0.093), 40\% on Bamboogle (+0.151), and 91\% on 2Wiki (+0.256) via denser rewards and reduced verbosity.

Though Large Language Models (LLMs) have demonstrated the powerful capabilities of few-shot learning through prompting methods, supervised training is still necessary for complex reasoning tasks. Because of their extensive parameters and memory consumption, both Parameter-Efficient Fine-Tuning (PEFT) methods and Memory-Efficient Fine-Tuning methods have been proposed for LLMs. Nevertheless, the issue of large annotated data consumption, the aim of Data-Efficient Fine-Tuning, remains unexplored. One obvious way is to combine the PEFT method with active learning. However, the experimental results show that such a combination is not trivial and yields inferior results. Through probe experiments, such observation might be explained by two main reasons: uncertainty gap and poor model calibration. Therefore, in this paper, we propose a novel approach to effectively integrate uncertainty-based active learning and LoRA. Specifically, for the uncertainty gap, we introduce a dynamic uncertainty measurement that combines the uncertainty of the base model and the uncertainty of the full model during the iteration of active learning. For poor model calibration, we incorporate the regularization method during LoRA training to keep the model from being over-confident, and the Monte-Carlo dropout mechanism is employed to enhance the uncertainty estimation. Experimental results show that the proposed approach outperforms existing baseline models on three complex reasoning tasks.

Transcending human cognitive limitations represents a critical frontier in LLM training. Proprietary agentic systems like DeepResearch have demonstrated superhuman capabilities on extremely complex information-seeking benchmarks such as BrowseComp, a feat previously unattainable. We posit that their success hinges on a sophisticated reasoning pattern absent in open-source models: the ability to systematically reduce extreme uncertainty when navigating vast information landscapes. Based on this insight, we introduce WebSailor, a complete post-training methodology designed to instill this crucial capability. Our approach involves generating novel, high-uncertainty tasks through structured sampling and information obfuscation, RFT cold start, and an efficient agentic RL training algorithm, Duplicating Sampling Policy Optimization (DUPO). With this integrated pipeline, WebSailor significantly outperforms all open-source agents in complex information-seeking tasks, matching proprietary agents' performance and closing the capability gap.

Multiple-choice exam questions with "None of the above" (NA) options have been extensively studied in educational testing, in which existing research suggests that they better assess true knowledge. However, their impact on Large Language Models (LLMs) evaluation remains underexplored. Through systematic experiments with 28 LLMs on the MMLU benchmark, we examine how NA options affect model performance and confidence calibration. Our analysis reveals that NA options, when used as the correct answer, lead to a consistent 30-50\% performance drop across models regardless of scale--suggesting that LLMs lack the meta-cognitive ability to systematically evaluate and reject all given options when none are correct. This degradation shows strong domain dependence, with minimal impact on mathematical reasoning (14.6\% drop) but severe effects on tasks requiring uncertainty handling like business ethics (48.1\% drop). Our results highlight important implications for benchmark design and raise questions about LLMs' ability to handle uncertainty in real-world applications.

Probabilistic model checking is a technique for formal automated reasoning about software or hardware systems that operate in the context of uncertainty or stochasticity. It builds upon ideas and techniques from a diverse range of fields, from logic, automata and graph theory, to optimisation, numerical methods and control. In recent years, probabilistic model checking has also been extended to integrate ideas from game theory, notably using models such as stochastic games and solution concepts such as equilibria, to formally verify the interaction of multiple rational agents with distinct objectives. This provides a means to reason flexibly about agents acting in either an adversarial or a collaborative fashion, and opens up opportunities to tackle new problems within, for example, artificial intelligence, robotics and autonomous systems. In this paper, we summarise some of the advances in this area, and highlight applications for which they have already been used. We discuss how the strengths of probabilistic model checking apply, or have the potential to apply, to the multi-agent setting and outline some of the key challenges required to make further progress in this field.

Large language models (LLMs) achieve strong performance across benchmarks--from knowledge quizzes and math reasoning to web-agent tasks--but these tests occur in static settings, lacking real dynamics and uncertainty. Consequently, they evaluate isolated reasoning or problem-solving rather than decision-making under uncertainty. To address this, we introduce LiveTradeBench, a live trading environment for evaluating LLM agents in realistic and evolving markets. LiveTradeBench follows three design principles: (i) Live data streaming of market prices and news, eliminating dependence on offline backtesting and preventing information leakage while capturing real-time uncertainty; (ii) a portfolio-management abstraction that extends control from single-asset actions to multi-asset allocation, integrating risk management and cross-asset reasoning; and (iii) multi-market evaluation across structurally distinct environments--U.S. stocks and Polymarket prediction markets--differing in volatility, liquidity, and information flow. At each step, an agent observes prices, news, and its portfolio, then outputs percentage allocations that balance risk and return. Using LiveTradeBench, we run 50-day live evaluations of 21 LLMs across families. Results show that (1) high LMArena scores do not imply superior trading outcomes; (2) models display distinct portfolio styles reflecting risk appetite and reasoning dynamics; and (3) some LLMs effectively leverage live signals to adapt decisions. These findings expose a gap between static evaluation and real-world competence, motivating benchmarks that test sequential decision making and consistency under live uncertainty.

Parallel thinking expands exploration breadth, complementing the deep exploration of information-seeking (IS) agents to further enhance problem-solving capability. However, conventional parallel thinking faces two key challenges in this setting: inefficiency from repeatedly rolling out from scratch, and difficulty in integrating long-horizon reasoning trajectories during answer generation, as limited context capacity prevents full consideration of the reasoning process. To address these issues, we propose ParallelMuse, a two-stage paradigm designed for deep IS agents. The first stage, Functionality-Specified Partial Rollout, partitions generated sequences into functional regions and performs uncertainty-guided path reuse and branching to enhance exploration efficiency. The second stage, Compressed Reasoning Aggregation, exploits reasoning redundancy to losslessly compress information relevant to answer derivation and synthesize a coherent final answer. Experiments across multiple open-source agents and benchmarks demonstrate up to 62% performance improvement with a 10--30% reduction in exploratory token consumption.

We introduce FailureSensorIQ, a novel Multi-Choice Question-Answering (MCQA) benchmarking system designed to assess the ability of Large Language Models (LLMs) to reason and understand complex, domain-specific scenarios in Industry 4.0. Unlike traditional QA benchmarks, our system focuses on multiple aspects of reasoning through failure modes, sensor data, and the relationships between them across various industrial assets. Through this work, we envision a paradigm shift where modeling decisions are not only data-driven using statistical tools like correlation analysis and significance tests, but also domain-driven by specialized LLMs which can reason about the key contributors and useful patterns that can be captured with feature engineering. We evaluate the Industrial knowledge of over a dozen LLMs-including GPT-4, Llama, and Mistral-on FailureSensorIQ from different lens using Perturbation-Uncertainty-Complexity analysis, Expert Evaluation study, Asset-Specific Knowledge Gap analysis, ReAct agent using external knowledge-bases. Even though closed-source models with strong reasoning capabilities approach expert-level performance, the comprehensive benchmark reveals a significant drop in performance that is fragile to perturbations, distractions, and inherent knowledge gaps in the models. We also provide a real-world case study of how LLMs can drive the modeling decisions on 3 different failure prediction datasets related to various assets. We release: (a) expert-curated MCQA for various industrial assets, (b) FailureSensorIQ benchmark and Hugging Face leaderboard based on MCQA built from non-textual data found in ISO documents, and (c) LLMFeatureSelector, an LLM-based feature selection scikit-learn pipeline. The software is available at https://github.com/IBM/FailureSensorIQ.

Uncertainty quantification is essential for assessing the reliability and trustworthiness of modern AI systems. Among existing approaches, verbalized uncertainty, where models express their confidence through natural language, has emerged as a lightweight and interpretable solution in large language models (LLMs). However, its effectiveness in vision-language models (VLMs) remains insufficiently studied. In this work, we conduct a comprehensive evaluation of verbalized confidence in VLMs, spanning three model categories, four task domains, and three evaluation scenarios. Our results show that current VLMs often display notable miscalibration across diverse tasks and settings. Notably, visual reasoning models (i.e., thinking with images) consistently exhibit better calibration, suggesting that modality-specific reasoning is critical for reliable uncertainty estimation. To further address calibration challenges, we introduce Visual Confidence-Aware Prompting, a two-stage prompting strategy that improves confidence alignment in multimodal settings. Overall, our study highlights the inherent miscalibration in VLMs across modalities. More broadly, our findings underscore the fundamental importance of modality alignment and model faithfulness in advancing reliable multimodal systems.

The collaborative paradigm of large and small language models (LMs) effectively balances performance and cost, yet its pivotal challenge lies in precisely pinpointing the moment of invocation when hallucinations arise in small LMs. Previous optimization efforts primarily focused on post-processing techniques, which were separate from the reasoning process of LMs, resulting in high computational costs and limited effectiveness. In this paper, we propose a practical invocation evaluation metric called AttenHScore, which calculates the accumulation and propagation of hallucinations during the generation process of small LMs, continuously amplifying potential reasoning errors. By dynamically adjusting the detection threshold, we achieve more accurate real-time invocation of large LMs. Additionally, considering the limited reasoning capacity of small LMs, we leverage uncertainty-aware knowledge reorganization to assist them better capture critical information from different text chunks. Extensive experiments reveal that our AttenHScore outperforms most baseline in enhancing real-time hallucination detection capabilities across multiple QA datasets, especially when addressing complex queries. Moreover, our strategies eliminate the need for additional model training and display flexibility in adapting to various transformer-based LMs.

Rate control algorithms are at the heart of video conferencing platforms, determining target bitrates that match dynamic network characteristics for high quality. Recent data-driven strategies have shown promise for this challenging task, but the performance degradation they introduce during training has been a nonstarter for many production services, precluding adoption. This paper aims to bolster the practicality of data-driven rate control by presenting an alternative avenue for experiential learning: leveraging purely existing telemetry logs produced by the incumbent algorithm in production. We observe that these logs contain effective decisions, although often at the wrong times or in the wrong order. To realize this approach despite the inherent uncertainty that log-based learning brings (i.e., lack of feedback for new decisions), our system, Mowgli, combines a variety of robust learning techniques (i.e., conservatively reasoning about alternate behavior to minimize risk and using a richer model formulation to account for environmental noise). Across diverse networks (emulated and real-world), Mowgli outperforms the widely deployed GCC algorithm, increasing average video bitrates by 15-39% while reducing freeze rates by 60-100%.

Human cognition excels at transcending sensory input and forming latent representations that structure our understanding of the world. Although Large Language Models (LLMs) can produce chain-of-thought reasoning, they lack a principled framework to capture latent structures and model uncertainty, especially in compositional reasoning tasks. We propose Verbalized Probabilistic Graphical Modeling (vPGM), a Bayesian prompting framework that guides LLMs to simulate key principles of Probabilistic Graphical Models (PGMs) in natural language. Unlike many traditional probabilistic methods requiring substantial domain expertise or specialized training, vPGM bypasses expert-driven model design, making it well-suited for scenarios with limited assumptions or scarce data. We evaluated our model on several compositional reasoning tasks, both close-ended and open-ended. Our results indicate that the model effectively enhances confidence calibration and text generation quality.

This paper introduces Self-aware Knowledge Retrieval (SeaKR), a novel adaptive RAG model that extracts self-aware uncertainty of LLMs from their internal states. SeaKR activates retrieval when the LLMs present high self-aware uncertainty for generation. To effectively integrate retrieved knowledge snippets, SeaKR re-ranks them based on LLM's self-aware uncertainty to preserve the snippet that reduces their uncertainty to the utmost. To facilitate solving complex tasks that require multiple retrievals, SeaKR utilizes their self-aware uncertainty to choose among different reasoning strategies. Our experiments on both complex and simple Question Answering datasets show that SeaKR outperforms existing adaptive RAG methods. We release our code at https://github.com/THU-KEG/SeaKR.

Reinforcement Learning from Verifiable Rewards (RLVR) improves the reasoning abilities of Large Language Models (LLMs) but it struggles with unstable exploration. We propose FR3E (First Return, Entropy-Eliciting Explore), a structured exploration framework that identifies high-uncertainty decision points in reasoning trajectories and performs targeted rollouts to construct semantically grounded intermediate feedback. Our method provides targeted guidance without relying on dense supervision. Empirical results on mathematical reasoning benchmarks(AIME24) show that FR3E promotes more stable training, produces longer and more coherent responses, and increases the proportion of fully correct trajectories. These results highlight the framework's effectiveness in improving LLM reasoning through more robust and structured exploration.

Large language models (LLMs) increasingly solve complex reasoning tasks via long chain-of-thought, but their forward-only autoregressive generation process is fragile; early token errors can cascade, which creates a clear need for self-reflection mechanisms. However, existing self-reflection either performs revisions over full drafts or learns self-correction via expensive training, both fundamentally reactive and inefficient. To address this, we propose Self-Reflective Generation at Test Time (SRGen), a lightweight test-time framework that reflects before generating at uncertain points. During token generation, SRGen utilizes dynamic entropy thresholding to identify high-uncertainty tokens. For each identified token, it trains a specific corrective vector, which fully exploits the already generated context for a self-reflective generation to correct the token probability distribution. By retrospectively analyzing the partial output, this self-reflection enables more trustworthy decisions, thereby significantly reducing the probability of errors at highly uncertain points. Evaluated on challenging mathematical reasoning benchmarks and a diverse set of LLMs, SRGen can consistently strengthen model reasoning: improvements in single-pass quality also translate into stronger self-consistency voting. Especially, on AIME2024 with DeepSeek-R1-Distill-Qwen-7B, SRGen yields absolute improvements of +12.0% on Pass@1 and +13.3% on Cons@5. Moreover, our findings position SRGen as a plug-and-play method that integrates reflection into the generation process for reliable LLM reasoning, achieving consistent gains with bounded overhead and broad composability with other training-time (e.g., RLHF) and test-time (e.g., SLOT) techniques.

The pervasiveness of large language models and generative AI in online media has amplified the need for effective automated fact-checking to assist fact-checkers in tackling the increasing volume and sophistication of misinformation. The complex nature of fact-checking demands that automated fact-checking systems provide explanations that enable fact-checkers to scrutinise their outputs. However, it is unclear how these explanations should align with the decision-making and reasoning processes of fact-checkers to be effectively integrated into their workflows. Through semi-structured interviews with fact-checking professionals, we bridge this gap by: (i) providing an account of how fact-checkers assess evidence, make decisions, and explain their processes; (ii) examining how fact-checkers use automated tools in practice; and (iii) identifying fact-checker explanation requirements for automated fact-checking tools. The findings show unmet explanation needs and identify important criteria for replicable fact-checking explanations that trace the model's reasoning path, reference specific evidence, and highlight uncertainty and information gaps.

This paper introduces the Univariate Gaussian Mixture Model Neural Network (uGMM-NN), a novel neural architecture that embeds probabilistic reasoning directly into the computational units of deep networks. Unlike traditional neurons, which apply weighted sums followed by fixed nonlinearities, each uGMM-NN node parameterizes its activations as a univariate Gaussian mixture, with learnable means, variances, and mixing coefficients. This design enables richer representations by capturing multimodality and uncertainty at the level of individual neurons, while retaining the scalability of standard feedforward networks. We demonstrate that uGMM-NN can achieve competitive discriminative performance compared to conventional multilayer perceptrons, while additionally offering a probabilistic interpretation of activations. The proposed framework provides a foundation for integrating uncertainty-aware components into modern neural architectures, opening new directions for both discriminative and generative modeling.

Artificial intelligence commonly refers to the science and engineering of artificial systems that can carry out tasks generally associated with requiring aspects of human intelligence, such as playing games, translating languages, and driving cars. In recent years, there have been exciting advances in learning-based, data-driven approaches towards AI, and machine learning and deep learning have enabled computer systems to perceive the world in unprecedented ways. Reinforcement learning has enabled breakthroughs in complex games such as Go and challenging robotics tasks such as quadrupedal locomotion. A key aspect of intelligence is to not only make predictions, but reason about the uncertainty in these predictions, and to consider this uncertainty when making decisions. This is what this manuscript on "Probabilistic Artificial Intelligence" is about. The first part covers probabilistic approaches to machine learning. We discuss the differentiation between "epistemic" uncertainty due to lack of data and "aleatoric" uncertainty, which is irreducible and stems, e.g., from noisy observations and outcomes. We discuss concrete approaches towards probabilistic inference and modern approaches to efficient approximate inference. The second part of the manuscript is about taking uncertainty into account in sequential decision tasks. We consider active learning and Bayesian optimization -- approaches that collect data by proposing experiments that are informative for reducing the epistemic uncertainty. We then consider reinforcement learning and modern deep RL approaches that use neural network function approximation. We close by discussing modern approaches in model-based RL, which harness epistemic and aleatoric uncertainty to guide exploration, while also reasoning about safety.

Large language models (LLMs) demonstrate impressive reasoning abilities, but translating reasoning into actions in the real world remains challenging. In particular, it remains unclear how to complete a given task provably within a minimum number of interactions with the external environment, e.g., through an internal mechanism of reasoning. To this end, we propose a principled framework with provable regret guarantees to orchestrate reasoning and acting, which we call "reason for future, act for now" (RAFA). Specifically, we design a prompt template for reasoning that learns from the memory buffer and plans a future trajectory over a long horizon ("reason for future"). At each step, the LLM agent takes the initial action of the planned trajectory ("act for now"), stores the collected feedback in the memory buffer, and reinvokes the reasoning routine to replan the future trajectory from the new state. The key idea is to cast reasoning in LLMs as learning and planning in Bayesian adaptive Markov decision processes (MDPs). Correspondingly, we prompt LLMs to form an updated posterior of the unknown environment from the memory buffer (learning) and generate an optimal trajectory for multiple future steps that maximizes a value function (planning). The learning and planning subroutines are performed in an "in-context" manner to emulate the actor-critic update for MDPs. Our theoretical analysis proves that the novel combination of long-term reasoning and short-term acting achieves a T regret. In particular, the regret bound highlights an intriguing interplay between the prior knowledge obtained through pretraining and the uncertainty reduction achieved by reasoning and acting. Our empirical validation shows that it outperforms various existing frameworks and achieves nearly perfect scores on a few benchmarks.

Ensuring safe, comfortable, and efficient planning is crucial for autonomous driving systems. While end-to-end models trained on large datasets perform well in standard driving scenarios, they struggle with complex low-frequency events. Recent Large Language Models (LLMs) and Vision Language Models (VLMs) advancements offer enhanced reasoning but suffer from computational inefficiency. Inspired by the dual-process cognitive model "Thinking, Fast and Slow", we propose FASIONAD -- a novel dual-system framework that synergizes a fast end-to-end planner with a VLM-based reasoning module. The fast system leverages end-to-end learning to achieve real-time trajectory generation in common scenarios, while the slow system activates through uncertainty estimation to perform contextual analysis and complex scenario resolution. Our architecture introduces three key innovations: (1) A dynamic switching mechanism enabling slow system intervention based on real-time uncertainty assessment; (2) An information bottleneck with high-level plan feedback that optimizes the slow system's guidance capability; (3) A bidirectional knowledge exchange where visual prompts enhance the slow system's reasoning while its feedback refines the fast planner's decision-making. To strengthen VLM reasoning, we develop a question-answering mechanism coupled with reward-instruct training strategy. In open-loop experiments, FASIONAD achieves a 6.7% reduction in average L2 trajectory error and 28.1% lower collision rate.

Reasoning and strategic behavior in social interactions is a hallmark of intelligence. This form of reasoning is significantly more sophisticated than isolated planning or reasoning tasks in static settings (e.g., math problem solving). In this paper, we present Strategic Planning, Interaction, and Negotiation (SPIN-Bench), a new multi-domain evaluation designed to measure the intelligence of strategic planning and social reasoning. While many existing benchmarks focus on narrow planning or single-agent reasoning, SPIN-Bench combines classical PDDL tasks, competitive board games, cooperative card games, and multi-agent negotiation scenarios in one unified framework. The framework includes both a benchmark as well as an arena to simulate and evaluate the variety of social settings to test reasoning and strategic behavior of AI agents. We formulate the benchmark SPIN-Bench by systematically varying action spaces, state complexity, and the number of interacting agents to simulate a variety of social settings where success depends on not only methodical and step-wise decision making, but also conceptual inference of other (adversarial or cooperative) participants. Our experiments reveal that while contemporary LLMs handle basic fact retrieval and short-range planning reasonably well, they encounter significant performance bottlenecks in tasks requiring deep multi-hop reasoning over large state spaces and socially adept coordination under uncertainty. We envision SPIN-Bench as a catalyst for future research on robust multi-agent planning, social reasoning, and human--AI teaming.

This paper presents a case study on the design, administration, post-processing, and evaluation of surveys on large language models (LLMs). It comprises two components: (1) A statistical method for eliciting beliefs encoded in LLMs. We introduce statistical measures and evaluation metrics that quantify the probability of an LLM "making a choice", the associated uncertainty, and the consistency of that choice. (2) We apply this method to study what moral beliefs are encoded in different LLMs, especially in ambiguous cases where the right choice is not obvious. We design a large-scale survey comprising 680 high-ambiguity moral scenarios (e.g., "Should I tell a white lie?") and 687 low-ambiguity moral scenarios (e.g., "Should I stop for a pedestrian on the road?"). Each scenario includes a description, two possible actions, and auxiliary labels indicating violated rules (e.g., "do not kill"). We administer the survey to 28 open- and closed-source LLMs. We find that (a) in unambiguous scenarios, most models "choose" actions that align with commonsense. In ambiguous cases, most models express uncertainty. (b) Some models are uncertain about choosing the commonsense action because their responses are sensitive to the question-wording. (c) Some models reflect clear preferences in ambiguous scenarios. Specifically, closed-source models tend to agree with each other.

Despite increasingly fluent, relevant, and coherent language generation, major gaps remain between how humans and machines use language. We argue that a key dimension that is missing from our understanding of language models (LMs) is the model's ability to interpret and generate expressions of uncertainty. Whether it be the weatherperson announcing a chance of rain or a doctor giving a diagnosis, information is often not black-and-white and expressions of uncertainty provide nuance to support human-decision making. The increasing deployment of LMs in the wild motivates us to investigate whether LMs are capable of interpreting expressions of uncertainty and how LMs' behaviors change when learning to emit their own expressions of uncertainty. When injecting expressions of uncertainty into prompts (e.g., "I think the answer is..."), we discover that GPT3's generations vary upwards of 80% in accuracy based on the expression used. We analyze the linguistic characteristics of these expressions and find a drop in accuracy when naturalistic expressions of certainty are present. We find similar effects when teaching models to emit their own expressions of uncertainty, where model calibration suffers when teaching models to emit certainty rather than uncertainty. Together, these results highlight the challenges of building LMs that interpret and generate trustworthy expressions of uncertainty.

Reasoning is a fundamental aspect of human intelligence that plays a crucial role in activities such as problem solving, decision making, and critical thinking. In recent years, large language models (LLMs) have made significant progress in natural language processing, and there is observation that these models may exhibit reasoning abilities when they are sufficiently large. However, it is not yet clear to what extent LLMs are capable of reasoning. This paper provides a comprehensive overview of the current state of knowledge on reasoning in LLMs, including techniques for improving and eliciting reasoning in these models, methods and benchmarks for evaluating reasoning abilities, findings and implications of previous research in this field, and suggestions on future directions. Our aim is to provide a detailed and up-to-date review of this topic and stimulate meaningful discussion and future work.

We explore uncertainty quantification in large language models (LLMs), with the goal to identify when uncertainty in responses given a query is large. We simultaneously consider both epistemic and aleatoric uncertainties, where the former comes from the lack of knowledge about the ground truth (such as about facts or the language), and the latter comes from irreducible randomness (such as multiple possible answers). In particular, we derive an information-theoretic metric that allows to reliably detect when only epistemic uncertainty is large, in which case the output of the model is unreliable. This condition can be computed based solely on the output of the model obtained simply by some special iterative prompting based on the previous responses. Such quantification, for instance, allows to detect hallucinations (cases when epistemic uncertainty is high) in both single- and multi-answer responses. This is in contrast to many standard uncertainty quantification strategies (such as thresholding the log-likelihood of a response) where hallucinations in the multi-answer case cannot be detected. We conduct a series of experiments which demonstrate the advantage of our formulation. Further, our investigations shed some light on how the probabilities assigned to a given output by an LLM can be amplified by iterative prompting, which might be of independent interest.

While Large Language Models (LLMs) demonstrate impressive capabilities, they still struggle with generating factually incorrect content (i.e., hallucinations). A promising approach to mitigate this issue is enabling models to express uncertainty when unsure. Previous research on uncertainty modeling has primarily focused on short-form QA, but realworld applications often require much longer responses. In this work, we introduce the task of Long-form Generation with Uncertainty(LoGU). We identify two key challenges: Uncertainty Suppression, where models hesitate to express uncertainty, and Uncertainty Misalignment, where models convey uncertainty inaccurately. To tackle these challenges, we propose a refinement-based data collection framework and a two-stage training pipeline. Our framework adopts a divide-and-conquer strategy, refining uncertainty based on atomic claims. The collected data are then used in training through supervised fine-tuning (SFT) and direct preference optimization (DPO) to enhance uncertainty expression. Extensive experiments on three long-form instruction following datasets show that our method significantly improves accuracy, reduces hallucinations, and maintains the comprehensiveness of responses.

We present a state-of-the-art model for fine-grained probability estimation of propositions conditioned on context. Recent advances in large language models (LLMs) have significantly enhanced their reasoning capabilities, particularly on well-defined tasks with complete information. However, LLMs continue to struggle with making accurate and well-calibrated probabilistic predictions under uncertainty or partial information. While incorporating uncertainty into model predictions often boosts performance, obtaining reliable estimates of that uncertainty remains understudied. In particular, LLM probability estimates tend to be coarse and biased towards more frequent numbers. Through a combination of human and synthetic data creation and assessment, scaling to larger models, and better supervision, we propose a set of strong and precise probability estimation models. We conduct systematic evaluations across tasks that rely on conditional probability estimation and show that our approach consistently outperforms existing fine-tuned and prompting-based methods by a large margin.

Widely deployed large language models (LLMs) can produce convincing yet incorrect outputs, potentially misleading users who may rely on them as if they were correct. To reduce such overreliance, there have been calls for LLMs to communicate their uncertainty to end users. However, there has been little empirical work examining how users perceive and act upon LLMs' expressions of uncertainty. We explore this question through a large-scale, pre-registered, human-subject experiment (N=404) in which participants answer medical questions with or without access to responses from a fictional LLM-infused search engine. Using both behavioral and self-reported measures, we examine how different natural language expressions of uncertainty impact participants' reliance, trust, and overall task performance. We find that first-person expressions (e.g., "I'm not sure, but...") decrease participants' confidence in the system and tendency to agree with the system's answers, while increasing participants' accuracy. An exploratory analysis suggests that this increase can be attributed to reduced (but not fully eliminated) overreliance on incorrect answers. While we observe similar effects for uncertainty expressed from a general perspective (e.g., "It's not clear, but..."), these effects are weaker and not statistically significant. Our findings suggest that using natural language expressions of uncertainty may be an effective approach for reducing overreliance on LLMs, but that the precise language used matters. This highlights the importance of user testing before deploying LLMs at scale.

We consider the problem of performing Bayesian inference in probabilistic models where observations are accompanied by uncertainty, referred to as "uncertain evidence." We explore how to interpret uncertain evidence, and by extension the importance of proper interpretation as it pertains to inference about latent variables. We consider a recently-proposed method "distributional evidence" as well as revisit two older methods: Jeffrey's rule and virtual evidence. We devise guidelines on how to account for uncertain evidence and we provide new insights, particularly regarding consistency. To showcase the impact of different interpretations of the same uncertain evidence, we carry out experiments in which one interpretation is defined as "correct." We then compare inference results from each different interpretation illustrating the importance of careful consideration of uncertain evidence.

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.

Large language models have demonstrated remarkable proficiency in long and complex reasoning tasks. However, they frequently exhibit a problematic reliance on familiar reasoning patterns, a phenomenon we term reasoning rigidity. Despite explicit instructions from users, these models often override clearly stated conditions and default to habitual reasoning trajectories, leading to incorrect conclusions. This behavior presents significant challenges, particularly in domains such as mathematics and logic puzzle, where precise adherence to specified constraints is critical. To systematically investigate reasoning rigidity, a behavior largely unexplored in prior work, we introduce a expert-curated diagnostic set, . Our dataset includes specially modified variants of existing mathematical benchmarks, namely AIME and MATH500, as well as well-known puzzles deliberately redesigned to require deviation from familiar reasoning strategies. Using this dataset, we identify recurring contamination patterns that occur when models default to ingrained reasoning. Specifically, we categorize this contamination into three distinctive modes: (i) Interpretation Overload, (ii) Input Distrust, and (iii) Partial Instruction Attention, each causing models to ignore or distort provided instructions. We publicly release our diagnostic set to facilitate future research on mitigating reasoning rigidity in language models.

Recent advances in Large Reasoning Models (LRMs) have shown impressive capabilities in mathematical and logical reasoning. However, current LRMs rarely admit ignorance or respond with "I don't know". Instead, they often produce incorrect answers while showing undue confidence, raising concerns about their factual reliability. In this work, we identify two pathological reasoning patterns characterized by overthinking that contribute to the overconfident and incorrect answers: last-minute guessing and second-thought spiraling. To address these issues, we propose BARREL-a novel framework that promotes concise and boundary-aware factual reasoning. Our experiments show that BARREL-training increases the reliability of DeepSeek-R1-Distill-Llama-8B from 39.33% to 61.48%, while still achieving accuracy comparable to models finetuned on reasoning data generated by R1. These results demonstrate that our pilot study is inspiring to build more reliable and factual System 2 LRMs.

Uncertainty quantification (UQ) is a critical aspect of artificial intelligence (AI) systems, particularly in high-risk domains such as healthcare, autonomous systems, and financial technology, where decision-making processes must account for uncertainty. This review explores the evolution of uncertainty quantification techniques in AI, distinguishing between aleatoric and epistemic uncertainties, and discusses the mathematical foundations and methods used to quantify these uncertainties. We provide an overview of advanced techniques, including probabilistic methods, ensemble learning, sampling-based approaches, and generative models, while also highlighting hybrid approaches that integrate domain-specific knowledge. Furthermore, we examine the diverse applications of UQ across various fields, emphasizing its impact on decision-making, predictive accuracy, and system robustness. The review also addresses key challenges such as scalability, efficiency, and integration with explainable AI, and outlines future directions for research in this rapidly developing area. Through this comprehensive survey, we aim to provide a deeper understanding of UQ's role in enhancing the reliability, safety, and trustworthiness of AI systems.

Reasoning, as an essential ability for complex problem-solving, can provide back-end support for various real-world applications, such as medical diagnosis, negotiation, etc. This paper provides a comprehensive survey of cutting-edge research on reasoning with language model prompting. We introduce research works with comparisons and summaries and provide systematic resources to help beginners. We also discuss the potential reasons for emerging such reasoning abilities and highlight future research directions. Resources are available at https://github.com/zjunlp/Prompt4ReasoningPapers (updated periodically).

Reasoning is a fundamental cognitive process that enables logical inference, problem-solving, and decision-making. With the rapid advancement of large language models (LLMs), reasoning has emerged as a key capability that distinguishes advanced AI systems from conventional models that empower chatbots. In this survey, we categorize existing methods along two orthogonal dimensions: (1) Regimes, which define the stage at which reasoning is achieved (either at inference time or through dedicated training); and (2) Architectures, which determine the components involved in the reasoning process, distinguishing between standalone LLMs and agentic compound systems that incorporate external tools, and multi-agent collaborations. Within each dimension, we analyze two key perspectives: (1) Input level, which focuses on techniques that construct high-quality prompts that the LLM condition on; and (2) Output level, which methods that refine multiple sampled candidates to enhance reasoning quality. This categorization provides a systematic understanding of the evolving landscape of LLM reasoning, highlighting emerging trends such as the shift from inference-scaling to learning-to-reason (e.g., DeepSeek-R1), and the transition to agentic workflows (e.g., OpenAI Deep Research, Manus Agent). Additionally, we cover a broad spectrum of learning algorithms, from supervised fine-tuning to reinforcement learning such as PPO and GRPO, and the training of reasoners and verifiers. We also examine key designs of agentic workflows, from established patterns like generator-evaluator and LLM debate to recent innovations. ...

While Large Language Models (LLMs) have demonstrated remarkable potential in natural language generation and instruction following, a persistent challenge lies in their susceptibility to "hallucinations", which erodes trust in their outputs. Although Uncertainty Quantification (UQ) presents a promising solution, its accurate implementation within the context of LLMs remains a significant hurdle. To address this critical roadblock, our research originates from a fundamental heuristic insight: tokens within auto-regressive LLM-generated text do not equally reflect the underlying meaning. Some tokens carry greater relevance and representativeness than others, owing to the phenomenon of "linguistic redundancy", wherein a select few keywords suffice to convey the essence of lengthy sentences. Regrettably, existing methodologies treat all tokens with equal importance when estimating uncertainty, disregarding these inherent generative inequalities. Our analysis reveals a significant issue with state-of-the-art: numerous tokens (and sentences) of limited semantic significance receive equal or even excessive weighting during uncertainty estimation. To rectify this bias, we propose to jointly Shifting Attention to more Relevant (SAR) components, at both the token- and the sentence-levels for accurate uncertainty estimation. We conduct extensive experiments involving a range of popular "off-the-shelf" LLMs, including instruction-tuned LLMs such as Vicuna, WizardLM, and LLaMA-2-chat, as well as pretrained LLMs like OPT and LLaMA, with model sizes extending up to 33B parameters. We carry out evaluation across various free-form question-answering tasks, encompassing domains such as reading comprehension, science Q&A, and medical Q&A. Our experimental results demonstrate the superior performance of SAR in addressing the challenges of uncertainty estimation within the realm of LLMs.

Recent advances in handling long sequences have facilitated the exploration of long-context in-context learning (ICL). While much of the existing research emphasizes performance improvements driven by additional in-context examples, the influence on the trustworthiness of generated responses remains underexplored. This paper addresses this gap by investigating how increased examples influence predictive uncertainty, an essential aspect in trustworthiness. We begin by systematically quantifying the uncertainty of ICL with varying shot counts, analyzing the impact of example quantity. Through uncertainty decomposition, we introduce a novel perspective on performance enhancement, with a focus on epistemic uncertainty (EU). Our results reveal that additional examples reduce total uncertainty in both simple and complex tasks by injecting task-specific knowledge, thereby diminishing EU and enhancing performance. For complex tasks, these advantages emerge only after addressing the increased noise and uncertainty associated with longer inputs. Finally, we explore the evolution of internal confidence across layers, unveiling the mechanisms driving the reduction in uncertainty.

The recent performance leap of Large Language Models (LLMs) opens up new opportunities across numerous industrial applications and domains. However, erroneous generations, such as false predictions, misinformation, and hallucination made by LLMs, have also raised severe concerns for the trustworthiness of LLMs', especially in safety-, security- and reliability-sensitive scenarios, potentially hindering real-world adoptions. While uncertainty estimation has shown its potential for interpreting the prediction risks made by general machine learning (ML) models, little is known about whether and to what extent it can help explore an LLM's capabilities and counteract its undesired behavior. To bridge the gap, in this paper, we initiate an exploratory study on the risk assessment of LLMs from the lens of uncertainty. In particular, we experiment with twelve uncertainty estimation methods and four LLMs on four prominent natural language processing (NLP) tasks to investigate to what extent uncertainty estimation techniques could help characterize the prediction risks of LLMs. Our findings validate the effectiveness of uncertainty estimation for revealing LLMs' uncertain/non-factual predictions. In addition to general NLP tasks, we extensively conduct experiments with four LLMs for code generation on two datasets. We find that uncertainty estimation can potentially uncover buggy programs generated by LLMs. Insights from our study shed light on future design and development for reliable LLMs, facilitating further research toward enhancing the trustworthiness of LLMs.

Abstract reasoning is a key ability for an intelligent system. Large language models achieve above-chance performance on abstract reasoning tasks, but exhibit many imperfections. However, human abstract reasoning is also imperfect, and depends on our knowledge and beliefs about the content of the reasoning problem. For example, humans reason much more reliably about logical rules that are grounded in everyday situations than arbitrary rules about abstract attributes. The training experiences of language models similarly endow them with prior expectations that reflect human knowledge and beliefs. We therefore hypothesized that language models would show human-like content effects on abstract reasoning problems. We explored this hypothesis across three logical reasoning tasks: natural language inference, judging the logical validity of syllogisms, and the Wason selection task (Wason, 1968). We find that state of the art large language models (with 7 or 70 billion parameters; Hoffman et al., 2022) reflect many of the same patterns observed in humans across these tasks -- like humans, models reason more effectively about believable situations than unrealistic or abstract ones. Our findings have implications for understanding both these cognitive effects, and the factors that contribute to language model performance.

Predictions made by deep learning models are prone to data perturbations, adversarial attacks, and out-of-distribution inputs. To build a trusted AI system, it is therefore critical to accurately quantify the prediction uncertainties. While current efforts focus on improving uncertainty quantification accuracy and efficiency, there is a need to identify uncertainty sources and take actions to mitigate their effects on predictions. Therefore, we propose to develop explainable and actionable Bayesian deep learning methods to not only perform accurate uncertainty quantification but also explain the uncertainties, identify their sources, and propose strategies to mitigate the uncertainty impacts. Specifically, we introduce a gradient-based uncertainty attribution method to identify the most problematic regions of the input that contribute to the prediction uncertainty. Compared to existing methods, the proposed UA-Backprop has competitive accuracy, relaxed assumptions, and high efficiency. Moreover, we propose an uncertainty mitigation strategy that leverages the attribution results as attention to further improve the model performance. Both qualitative and quantitative evaluations are conducted to demonstrate the effectiveness of our proposed methods.

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.

Large Language Models deployed as question answering tools require robust calibration to avoid overconfidence. We systematically evaluate how reasoning capabilities and budget affect confidence assessment accuracy, using the ClimateX dataset (Lacombe et al., 2023) and expanding it to human and planetary health. Our key finding challenges the "test-time scaling" paradigm: while recent reasoning LLMs achieve 48.7% accuracy in assessing expert confidence, increasing reasoning budgets consistently impairs rather than improves calibration. Extended reasoning leads to systematic overconfidence that worsens with longer thinking budgets, producing diminishing and negative returns beyond modest computational investments. Conversely, search-augmented generation dramatically outperforms pure reasoning, achieving 89.3% accuracy by retrieving relevant evidence. Our results suggest that information access, rather than reasoning depth or inference budget, may be the critical bottleneck for improved confidence calibration of knowledge-intensive tasks.