Daily Papers

The remarkable advances in deep learning have led to the emergence of many off-the-shelf classifiers, e.g., large pre-trained models. However, since they are typically trained on clean data, they remain vulnerable to adversarial attacks. Despite this vulnerability, their superior performance and transferability make off-the-shelf classifiers still valuable in practice, demanding further work to provide adversarial robustness for them in a post-hoc manner. A recently proposed method, denoised smoothing, leverages a denoiser model in front of the classifier to obtain provable robustness without additional training. However, the denoiser often creates hallucination, i.e., images that have lost the semantics of their originally assigned class, leading to a drop in robustness. Furthermore, its noise-and-denoise procedure introduces a significant distribution shift from the original distribution, causing the denoised smoothing framework to achieve sub-optimal robustness. In this paper, we introduce Fine-Tuning with Confidence-Aware Denoised Image Selection (FT-CADIS), a novel fine-tuning scheme to enhance the certified robustness of off-the-shelf classifiers. FT-CADIS is inspired by the observation that the confidence of off-the-shelf classifiers can effectively identify hallucinated images during denoised smoothing. Based on this, we develop a confidence-aware training objective to handle such hallucinated images and improve the stability of fine-tuning from denoised images. In this way, the classifier can be fine-tuned using only images that are beneficial for adversarial robustness. We also find that such a fine-tuning can be done by updating a small fraction of parameters of the classifier. Extensive experiments demonstrate that FT-CADIS has established the state-of-the-art certified robustness among denoised smoothing methods across all ell_2-adversary radius in various benchmarks.

Diffusion language models are structurally well-suited for iterative error correction, as their non-causal denoising dynamics allow arbitrary positions in a sequence to be revised. However, standard masked diffusion language model (MDLM) training fails to reliably induce this behavior, as models often cannot identify unreliable tokens in a complete input, rendering confidence-guided refinement ineffective. We study corrective behavior in diffusion language models, defined as the ability to assign lower confidence to incorrect tokens and iteratively refine them while preserving correct content. We show that this capability is not induced by conventional masked diffusion objectives and propose a correction-oriented post-training principle that explicitly supervises visible incorrect tokens, enabling error-aware confidence and targeted refinement. To evaluate corrective behavior, we introduce the Code Revision Benchmark (CRB), a controllable and executable benchmark for assessing error localization and in-place correction. Experiments on code revision tasks and controlled settings demonstrate that models trained with our approach substantially outperform standard MDLMs in correction scenarios, while also improving pure completion performance. Our code is publicly available at https://github.com/zhangshuibai/CDLM.

Reliable confidence estimation is increasingly central to the trustworthy deployment of language models: a calibrated estimate of the probability that an output is correct decides what to ship, what to escalate, and what to retry. Existing confidence estimators, however, share one design premise: they only read the current inference process, either by introspecting on it, scoring its token probabilities, or resampling it. We argue that the current inference is not a sufficient basis for confidence. We propose XConf (eXperiential Confidence): estimating confidence together with the model's accumulated experience. The experience is stored as a record of the model's own graded past episodes, each holding the task, the model's reflection, its stated confidence, the outcome, and a lesson written once the grade arrived. Given a new task, XConf's Recall stage retrieves past episodes on similar tasks met with a similar stated confidence, and reads off their historical success rate; its Reflect stage shows the model this record, has it name its recurring failure mode, and restate a confidence now informed by its own track records. Our estimator is format-general, requiring no logit access or weight updates, and costs only one answer generation. Across nine benchmarks spanning reasoning, coding, multimodal QA, and interactive agents, and four models from three families, XConf beats or matches ten-sample self-consistency in discrimination (AUROC) on 23 of 24 comparisons, with much lower calibration error (ECE), at a tenth of the generation cost. Used for selective prediction, abstaining on the 10% least-confident episodes raises the delivered success rate by up to 8.7 points on agent tasks. We therefore see experiential confidence estimation as a new paradigm for future general-purpose confidence estimation.

Large language models (LLMs) often produce answers with high certainty even when they are incorrect, making reliable confidence estimation essential for deployment in real-world scenarios. Verbalized confidence, where models explicitly state their confidence in natural language, provides a flexible and user-facing uncertainty signal that can be applied even when token logits are unavailable. However, existing verbalized-confidence methods often optimize answer generation and confidence generation jointly, which can cause confidence-alignment objectives to interfere with answer accuracy. In this work, we propose a decoupled and order-aware framework for verbalized confidence calibration. Our method first generates an answer and then estimates confidence conditioned on the fixed question--answer pair, allowing confidence optimization without directly perturbing the answer-generation process. To align confidence with correctness likelihood, we construct a sampling-based surrogate from multiple model completions and optimize rank-based reinforcement learning objectives that encourage responses with higher estimated correctness likelihood to receive higher verbalized confidence. Experiments on reasoning and knowledge-intensive benchmarks show that our method improves calibration and failure prediction performance while largely preserving answer accuracy. These results demonstrate that verbalized confidence can be more reliably aligned by decoupling confidence estimation from answer generation and optimizing the relative ordering of confidence across responses.

Large language models (LLMs) often generate inaccurate or fabricated information and generally fail to indicate their confidence, which limits their broader applications. Previous work elicits confidence from LLMs by direct or self-consistency prompting, or constructing specific datasets for supervised finetuning. The prompting-based approaches have inferior performance, and the training-based approaches are limited to binary or inaccurate group-level confidence estimates. In this work, we present the advanced SaySelf, a training framework that teaches LLMs to express more accurate fine-grained confidence estimates. In addition, beyond the confidence scores, SaySelf initiates the process of directing LLMs to produce self-reflective rationales that clearly identify gaps in their parametric knowledge and explain their uncertainty. This is achieved by using an LLM to automatically summarize the uncertainties in specific knowledge via natural language. The summarization is based on the analysis of the inconsistency in multiple sampled reasoning chains, and the resulting data is utilized for supervised fine-tuning. Moreover, we utilize reinforcement learning with a meticulously crafted reward function to calibrate the confidence estimates, motivating LLMs to deliver accurate, high-confidence predictions and to penalize overconfidence in erroneous outputs. Experimental results in both in-distribution and out-of-distribution datasets demonstrate the effectiveness of SaySelf in reducing the confidence calibration error and maintaining the task performance. We show that the generated self-reflective rationales are reasonable and can further contribute to the calibration. The code is made public at https://github.com/xu1868/SaySelf.

While large language models (LLMs) have demonstrated remarkable performance across diverse tasks, they fundamentally lack self-awareness and frequently exhibit overconfidence, assigning high confidence scores to incorrect predictions. Accurate confidence estimation is therefore critical for enhancing the trustworthiness and reliability of LLM-generated outputs. However, existing approaches suffer from coarse-grained scoring mechanisms that fail to provide fine-grained, continuous confidence estimates throughout the generation process. To address these limitations, we introduce FineCE, a novel confidence estimation method that delivers accurate, fine-grained confidence scores during text generation. Specifically, we first develop a comprehensive pipeline for constructing training data that effectively captures the underlying probabilistic distribution of LLM responses, and then train a model to predict confidence scores for arbitrary text sequences in a supervised manner. Furthermore, we propose a Backward Confidence Integration (BCI) strategy that leverages information from the subsequent text to enhance confidence estimation for the current sequence during inference. We also introduce three strategies for identifying optimal positions to perform confidence estimation within the generation process. Extensive experiments on multiple benchmark datasets demonstrate that FineCE consistently outperforms existing classical confidence estimation methods. Our code and all baselines used in the paper are available on GitHub.

Long chains of thought (CoT) from current language models frequently contain logical gaps and unjustified leaps, limiting the gains from additional test-time compute. Improving reasoning quality directly would require process reward models, but the step-level annotations needed to train them are expensive and scarce. We find such a signal in how the model's confidence evolves during reasoning: premature confidence, the tendency to commit to an answer early and use the remaining tokens to rationalize it, strongly predicts flawed reasoning across tasks and model scales. We exploit this in progressive confidence shaping, a reinforcement learning objective that trains models to update their confidence as they reason rather than commit early -- rewarding gradual confidence growth and penalizing early commitment, with no external labels or reward models. The method improves accuracy and reasoning quality from 1.5B to 8B parameters across arithmetic (Countdown), math (DAPO, AIME), and science (ScienceQA): on Countdown, accuracy improves 3.2x (+42.0pp) and flawed reasoning drops 48pp; on AIME, Pass@64 improves 6.6pp. Consistent with this mechanism, the method also improves faithfulness: on a safety benchmark, our models more transparently surface misleading content in their reasoning traces rather than concealing it. Controlled experiments reveal that the problem and its remedy scale together: premature confidence grows with model size and task difficulty, and so do the gains from addressing it.

Large Language Models suffer from hallucination, generating plausible yet factually incorrect content. Current mitigation strategies focus on post-generation correction, which is computationally expensive and fails to prevent unreliable content generation. We propose a confidence-aware routing system that proactively assesses model uncertainty before generation and redirects queries based on estimated reliability. Our approach combines three complementary signals: semantic alignment between internal representations and reference embeddings, internal convergence analysis across model layers, and learned confidence estimation. The unified confidence score determines routing to four pathways: local generation for high confidence, retrieval-augmented generation for medium confidence, larger models for low confidence, and human review for very low confidence. Evaluation on knowledge-intensive QA benchmarks demonstrates significant improvements in hallucination detection (0.74 vs. 0.42 baseline) while reducing computational costs by 40% compared to post-hoc methods. The F1 score improves from 0.61 to 0.82 with low false positive rates (0.09). This paradigm shift from reactive correction to proactive assessment offers a computationally efficient approach to LLM reliability enhancement.

Reward models can significantly enhance the reasoning capabilities of large language models (LLMs), but they typically require extensive curated data and costly training. To mitigate these challenges, training-free approaches such as LLM-as-a-Judge leverage the intrinsic reasoning abilities of LLMs to evaluate responses, achieving promising results. Recent works have also indicated that model confidence can serve effectively as a reward metric, distinguishing between chain-of-thought (CoT) and non-CoT paths. However, the concept of using confidence as a reward has not been comprehensively studied. In this work, we systematically investigate Confidence-as-a-Reward (CRew), a simple yet powerful training-free method that utilizes token-level confidence in the model's final answers as a proxy for reward, especially suitable for close-ended tasks. Through extensive experiments on mathematical reasoning tasks, we demonstrate that CRew outperforms existing training-free reward approaches on the MATH500 and RewardMATH benchmarks, and even surpasses most trained reward models. We further identify a strong correlation between CRew scores and the actual reasoning performance of the model. Additionally, we find that CRew can effectively filter high-quality training data. Building upon these insights, we propose CRew-DPO, a training strategy that constructs preference data from confidence scores combined with correctness signals. Finetuning with CRew-DPO further enhances the model's judging capabilities and consistently outperforms existing self-training methods.

Model evolution and constant availability of data are two common phenomena in large-scale real-world machine learning applications, e.g. ads and recommendation systems. To adapt, the real-world system typically retrain with all available data and online learn with recently available data to update the models periodically with the goal of better serving performance. In this paper, we propose a novel framework, named Confidence Ranking, which designs the optimization objective as a ranking function with two different models. Our confidence ranking loss allows direct optimization of the logits output for different convex surrogate functions of metrics, e.g. AUC and Accuracy depending on the target task and dataset. Armed with our proposed methods, our experiments show that the introduction of confidence ranking loss can outperform all baselines on the CTR prediction tasks of public and industrial datasets. This framework has been deployed in the advertisement system of JD.com to serve the main traffic in the fine-rank stage.

Large reasoning models (LRMs) often suffer from overconfidence when expressing their uncertainty. Confidence-aware reinforcement learning (RL) offers a promising way to optimize calibration. However, it relies on on-policy rollouts and is thus constrained by the model's pre-RL confidence distribution, which we term confidence prior. In this work, we reveal that off-the-shelf LRMs exhibit a confidence prior heavily concentrated on a few high values, which persists throughout RL. Theoretically, we prove that this concentration suppresses policy gradient updates for rarely sampled confidence values and inflates the lower bound on expected Brier risk. To overcome this exploration bottleneck, we propose CalibSFT, a plug-and-play supervised fine-tuning stage that shapes a calibrated confidence prior with broad support before RL. For each question, CalibSFT constructs confidence targets combining its success rate with response-level correctness, which provably preserves proper-scoring optimality, and then balances training responses across the confidence spectrum to enable diverse confidence exploration during RL. To learn from incorrect responses without imitating their reasoning, CalibSFT introduces correctness-conditional supervision, guiding confidence across all responses while supervising reasoning only on correct ones. Across 16 mathematical and general reasoning benchmarks, incorporating CalibSFT reduces calibration errors and improves discrimination across five representative RL algorithms while preserving comparable accuracy. Furthermore, CalibSFT delivers practical benefits for downstream selective prediction and model routing. Our code is available at https://github.com/ml-stat-Sustech/verbalized-confidence-training.

Estimating uncertainty or confidence in the responses of a model can be significant in evaluating trust not only in the responses, but also in the model as a whole. In this paper, we explore the problem of estimating confidence for responses of large language models (LLMs) with simply black-box or query access to them. We propose a simple and extensible framework where, we engineer novel features and train a (interpretable) model (viz. logistic regression) on these features to estimate the confidence. We empirically demonstrate that our simple framework is effective in estimating confidence of flan-ul2, llama-13b and mistral-7b with it consistently outperforming existing black-box confidence estimation approaches on benchmark datasets such as TriviaQA, SQuAD, CoQA and Natural Questions by even over 10% (on AUROC) in some cases. Additionally, our interpretable approach provides insight into features that are predictive of confidence, leading to the interesting and useful discovery that our confidence models built for one LLM generalize zero-shot across others on a given dataset.

Large language models (LLMs) have demonstrated impressive performance on several tasks and are increasingly deployed in real-world applications. However, especially in high-stakes settings, it becomes vital to know when the output of an LLM may be unreliable. Depending on whether an answer is trustworthy, a system can then choose to route the question to another expert, or otherwise fall back on a safe default behavior. In this work, we study the extent to which LLMs can reliably indicate confidence in their answers, and how this notion of confidence can translate into downstream accuracy gains. We propose Self-REF, a lightweight training strategy to teach LLMs to express confidence in whether their answers are correct in a reliable manner. Self-REF introduces confidence tokens into the LLM, from which a confidence score can be extracted. Compared to conventional approaches such as verbalizing confidence and examining token probabilities, we demonstrate empirically that confidence tokens show significant improvements in downstream routing and rejection learning tasks.

Large language models (LLMs) often produce confident but incorrect answers in settings where abstention would be safer. Standard evaluation protocols, however, require a response and do not account for how confidence should guide decisions under different risk preferences. To address this gap, we introduce the Behavioral Alignment Score (BAS), a decision-theoretic metric for evaluating how well LLM confidence supports abstention-aware decision making. BAS is derived from an explicit answer-or-abstain utility model and aggregates realized utility across a continuum of risk thresholds, yielding a measure of decision-level reliability that depends on both the magnitude and ordering of confidence. We show theoretically that truthful confidence estimates uniquely maximize expected BAS utility, linking calibration to decision-optimal behavior. BAS is related to proper scoring rules such as log loss, but differs structurally: log loss penalizes underconfidence and overconfidence symmetrically, whereas BAS imposes an asymmetric penalty that strongly prioritizes avoiding overconfident errors. Using BAS alongside widely used metrics such as ECE and AURC, we then construct a benchmark of self-reported confidence reliability across multiple LLMs and tasks. Our results reveal substantial variation in decision-useful confidence, and while larger and more accurate models tend to achieve higher BAS, even frontier models remain prone to severe overconfidence. Importantly, models with similar ECE or AURC can exhibit very different BAS due to highly overconfident errors, highlighting limitations of standard metrics. We further show that simple interventions, such as top-k confidence elicitation and post-hoc calibration, can meaningfully improve confidence reliability. Overall, our work provides both a principled metric and a comprehensive benchmark for evaluating LLM confidence reliability.

While confidence estimation is a promising direction for mitigating hallucinations in Large Language Models (LLMs), current research dominantly focuses on single-turn settings. The dynamics of model confidence in multi-turn conversations, where context accumulates and ambiguity is progressively resolved, remain largely unexplored. Reliable confidence estimation in multi-turn settings is critical for many downstream applications, such as autonomous agents and human-in-the-loop systems. This work presents the first systematic study of confidence estimation in multi-turn interactions, establishing a formal evaluation framework grounded in two key desiderata: per-turn calibration and monotonicity of confidence as more information becomes available. To facilitate this, we introduce novel metrics, including a length-normalized Expected Calibration Error (InfoECE), and a new "Hinter-Guesser" paradigm for generating controlled evaluation datasets. Our experiments reveal that widely-used confidence techniques struggle with calibration and monotonicity in multi-turn dialogues. We propose P(Sufficient), a logit-based probe that achieves comparatively better performance, although the task remains far from solved. Our work provides a foundational methodology for developing more reliable and trustworthy conversational agents.

Large Reasoning Models (LRMs) perform strongly in complex reasoning tasks via Chain-of-Thought (CoT) prompting, but often suffer from verbose outputs caused by redundant content, increasing computational overhead, and degrading user experience. Existing compression methods either operate post-hoc pruning, risking disruption to reasoning coherence, or rely on sampling-based selection, which fails to intervene effectively during generation. In this work, we introduce a confidence-guided perspective to explain the emergence of redundant reflection in LRMs, identifying two key patterns: Confidence Deficit, where the model reconsiders correct steps due to low internal confidence, and Termination Delay, where reasoning continues even after reaching a confident answer. Based on this analysis, we propose ConCISE (Confidence-guided Compression In Step-by-step Efficient Reasoning), a framework that simplifies reasoning chains by reinforcing the model's confidence during inference, thus preventing the generation of redundant reflection steps. It integrates Confidence Injection to stabilize intermediate steps and Early Stopping to terminate reasoning when confidence is sufficient. Extensive experiments demonstrate that fine-tuning LRMs on ConCISE-generated data yields significantly shorter outputs, reducing length by up to approximately 50% under SimPO, while maintaining high task accuracy. ConCISE consistently outperforms existing baselines across multiple reasoning benchmarks.

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.

Language models (LMs) should provide reliable confidence estimates to help users detect mistakes in their outputs and defer to human experts when necessary. Asking a language model to assess its confidence ("Score your confidence from 0-1.") is a natural way of evaluating its uncertainty. However, models struggle to provide absolute assessments of confidence (i.e. judging confidence in answering a question independent of other questions) and the coarse-grained scores they produce are not useful for evaluating the correctness of their answers. We propose relative confidence estimation, where we match up questions against each other and ask the model to make relative judgments of confidence ("Which question are you more confident in answering correctly?"). Treating each question as a "player" in a series of matchups against other questions and the model's preferences as match outcomes, we can use rank aggregation methods like Elo rating and Bradley-Terry to translate the model's confidence preferences into confidence scores. We evaluate relative confidence estimation against absolute confidence estimation and self-consistency confidence methods on five state-of-the-art LMs -- GPT-4, GPT-4o, Gemini 1.5 Pro, Claude 3.5 Sonnet, and Llama 3.1 405B -- across 14 challenging STEM, social science, and commonsense reasoning question answering tasks. Our results demonstrate that relative confidence estimation consistently provides more reliable confidence scores than absolute confidence estimation, with average gains of 3.5% in selective classification AUC over direct absolute confidence estimation methods and 1.7% over self-consistency approaches across all models and datasets.

Large language models (LLMs) can increase users' perceived trust by verbalizing confidence in their outputs. However, prior work has shown that LLMs are often overconfident, making their stated confidence unreliable since it does not consistently align with factual accuracy. To better understand the sources of this verbalized confidence, we introduce TracVC (Tracing Verbalized Confidence), a method that builds on information retrieval and influence estimation to trace generated confidence expressions back to the training data. We evaluate TracVC on OLMo and Llama models in a question answering setting, proposing a new metric, content groundness, which measures the extent to which an LLM grounds its confidence in content-related training examples (relevant to the question and answer) versus in generic examples of confidence verbalization. Our analysis reveals that OLMo2-13B is frequently influenced by confidence-related data that is lexically unrelated to the query, suggesting that it may mimic superficial linguistic expressions of certainty rather than rely on genuine content grounding. These findings point to a fundamental limitation in current training regimes: LLMs may learn how to sound confident without learning when confidence is justified. Our analysis provides a foundation for improving LLMs' trustworthiness in expressing more reliable confidence.

Answer-level rewards cannot distinguish reasoning traces with equally correct outcomes. We study whether auxiliary trajectory preferences improve small-language-model self-improvement and transfer under limited supervision. We compare confidence-based (SC) and entropy-based metrics (UID-Conj.), which combines global entropy variation and local smoothness, through online reward augmentation and offline training on correct responses. Online experiments adapt Qwen3-1.7B on 30 AIME problems without reference answers; offline experiments use historical AIME problems. UID-Conj. improves the online macro-average across the adaptation benchmark and three transfer benchmarks by 2.08 percentage points over unmodified TTRL. The strongest evidence comes from offline weighted SFT: UID-Conj. exceeds uniform weighting on the same response pool by 1.93 points, with a paired prompt-bootstrap 95\% CI of [0.44, 3.44]. Benefits are task-dependent: SC rewards judged trace quality and instruction following, while UID-Conj. rewards yield stronger training outcomes in several settings. We find that auxiliary preferences can expose learning value among equally correct traces not captured during inference time, motivating their evaluation through downstream gains.

Large reasoning models often reach correct answers through flawed intermediate steps, creating a gap between final accuracy and reasoning reliability. Existing alignment strategies address this with external verifiers or massive sampling, limiting scalability. In this work, we introduce CASPO (Confidence-Aware Step-wise Preference Optimization), a framework that aligns token-level confidence with step-wise logical correctness through iterative Direct Preference Optimization, without training a separate reward model. During inference, we propose Confidence-aware Thought (CaT), which leverages this calibrated confidence to dynamically prune uncertain reasoning branches with negligible O(V) latency. Experiments across ten benchmarks and multiple model families show that CASPO consistently improves reasoning reliability and inference efficiency. CASPO scales to Qwen3-8B-Base and surpasses tree-search baselines on AIME'24 and AIME'25 without using reward-model data. We also release a step-wise dataset with confidence annotations to support fine-grained analysis of reasoning reliability. Code is available at https://github.com/Thecommonirin/CASPO.

Confidence estimates are often "detection-like" - driven by positive evidence in favour of a decision. This empirical observation has been interpreted as showing that human metacognition is limited by biases or heuristics. Here, we show that Bayesian confidence estimates also exhibit heightened sensitivity to decision-congruent evidence in higher-dimensional signal detection theoretic spaces, leading to detection-like confidence criteria. This effect is due to a nonlinearity induced by normalisation of confidence by a large number of unchosen alternatives. Our analysis suggests that detection-like confidence is rational when participants consider a greater number of hypotheses than assumed by the experimenter. Further, we show that a similar dimensionality-driven mechanism can give rise to and modulate the strength of the positive evidence biases in convolutional neural networks, linking our signal detection theoretic analysis to confidence behaviour in artificial systems.

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.

Generating accurate and calibrated confidence estimates is critical for deploying LLMs in high-stakes or user-facing applications, and remains an open challenge. Prior research has often framed confidence as a problem of eliciting a model's "self-knowledge", i.e., the ability of an LLM to judge whether its own answers are correct; this approach implicitly assumes that there is some privileged information about the answer's correctness that is accessible to the model itself. However, our experiments reveal that an LLM attempting to predict the correctness of its own outputs generally performs no better than an unrelated LLM. Moreover, we hypothesize that a key factor in building a "Correctness Model" (CM) is exposure to a target model's historical predictions. We propose multiple methods to inject this historical correctness information, creating a Generalized Correctness Model (GCM). We first show that GCMs can be trained on the correctness data from many LLMs and learn patterns for correctness prediction applicable across datasets and models. We then use CMs as a lens for studying the source of correctness prediction ability and its generalization, systematically controlling their training data and finding that answer phrasing is a strong predictor for correctness. We further explore alternative methods of injecting history without training an LLM, finding that including history as in-context examples can help improve correctness prediction, and post-hoc calibration can provide complementary reductions in calibration error. We evaluate GCMs based on Qwen3-8B across 5 model families and the MMLU and TriviaQA datasets, as well as on a downstream selective prediction task, finding that reliable LLM confidence estimation is a generalizable and model-agnostic skill learned by systematically encoding correctness history rather than a model-specific skill reliant on self-introspection.

End-to-end vision-based imitation learning has demonstrated promising results in autonomous driving by learning control commands directly from expert demonstrations. However, traditional approaches rely on either regressionbased models, which provide precise control but lack confidence estimation, or classification-based models, which offer confidence scores but suffer from reduced precision due to discretization. This limitation makes it challenging to quantify the reliability of predicted actions and apply corrections when necessary. In this work, we introduce a dual-head neural network architecture that integrates both regression and classification heads to improve decision reliability in imitation learning. The regression head predicts continuous driving actions, while the classification head estimates confidence, enabling a correction mechanism that adjusts actions in low-confidence scenarios, enhancing driving stability. We evaluate our approach in a closed-loop setting within the CARLA simulator, demonstrating its ability to detect uncertain actions, estimate confidence, and apply real-time corrections. Experimental results show that our method reduces lane deviation and improves trajectory accuracy by up to 50%, outperforming conventional regression-only models. These findings highlight the potential of classification-guided confidence estimation in enhancing the robustness of vision-based imitation learning for autonomous driving. The source code is available at https://github.com/ElaheDlv/Confidence_Aware_IL.

The conventional modus operandi for adapting pre-trained vision-language models (VLMs) during test-time involves tuning learnable prompts, ie, test-time prompt tuning. This paper introduces Test-Time Low-rank adaptation (TTL) as an alternative to prompt tuning for zero-shot generalization of large-scale VLMs. Taking inspiration from recent advancements in efficiently fine-tuning large language models, TTL offers a test-time parameter-efficient adaptation approach that updates the attention weights of the transformer encoder by maximizing prediction confidence. The self-supervised confidence maximization objective is specified using a weighted entropy loss that enforces consistency among predictions of augmented samples. TTL introduces only a small amount of trainable parameters for low-rank adapters in the model space while keeping the prompts and backbone frozen. Extensive experiments on a variety of natural distribution and cross-domain tasks show that TTL can outperform other techniques for test-time optimization of VLMs in strict zero-shot settings. Specifically, TTL outperforms test-time prompt tuning baselines with a significant improvement on average. Our code is available at at https://github.com/Razaimam45/TTL-Test-Time-Low-Rank-Adaptation.

Reliable deployment of large language models (LLMs) requires accurate uncertainty estimation. Existing methods are predominantly answer-first, producing confidence only after generating an answer, which measure the correctness of a specific response and limits practical usability. We study a confidence-first paradigm, where the model outputs its confidence before answering, interpreting this score as the model's probability of answering the question correctly under its current policy. We propose CoCA(Co-optimized Confidence and Answers), a GRPO reinforcement learning framework that jointly optimizes confidence calibration and answer accuracy via segmented credit assignment. By assigning separate rewards and group-relative advantages to confidence and answer segments, CoCA enables stable joint optimization and avoids reward hacking. Experiments across math, code, and factual QA benchmarks show improved calibration and uncertainty discrimination while preserving answer quality, thereby enabling a broader range of downstream applications.

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.

A critical component in the trustworthiness of LLMs is reliable uncertainty communication, yet LLMs often use assertive language when conveying false claims, leading to over-reliance and eroded trust. We present the first systematic study of faithful confidence calibration of LLMs, benchmarking models' ability to use linguistic expressions of uncertainty that faithfully reflect their intrinsic uncertainty, across a comprehensive array of models, datasets, and prompting strategies. Our results demonstrate that LLMs largely fail at this task, and that existing interventions are insufficient: standard prompt approaches provide only marginal gains, and existing, factuality-based calibration techniques can even harm faithful calibration. To address this critical gap, we introduce MetaFaith, a novel prompt-based calibration approach inspired by human metacognition. We show that MetaFaith robustly improves faithful calibration across diverse models and task domains, enabling up to 61% improvement in faithfulness and achieving an 83% win rate over original generations as judged by humans.

In recent years, multimodal large language models (MLLMs) have made significant progress but continue to face inherent challenges in multimodal reasoning, which requires multi-level (e.g., perception, reasoning) and multi-granular (e.g., multi-step reasoning chain) advanced inferencing. Prior work on estimating model confidence tends to focus on the overall response for training and calibration, but fails to assess confidence in each reasoning step, leading to undesirable hallucination snowballing. In this work, we present MMBoundary, a novel framework that advances the knowledge boundary awareness of MLLMs through reasoning step confidence calibration. To achieve this, we propose to incorporate complementary textual and cross-modal self-rewarding signals to estimate confidence at each step of the MLLM reasoning process. In addition to supervised fine-tuning MLLM on this set of self-rewarded confidence estimation signal for initial confidence expression warm-up, we introduce a reinforcement learning stage with multiple reward functions for further aligning model knowledge and calibrating confidence at each reasoning step, enhancing reasoning chain self-correction. Empirical results show that MMBoundary significantly outperforms existing methods across diverse domain datasets and metrics, achieving an average of 7.5% reduction in multimodal confidence calibration errors and up to 8.3% improvement in task performance.

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.

Large language models (LLMs) are increasingly used in applications requiring factual accuracy, yet their outputs often contain hallucinated responses. While fact-checking can mitigate these errors, existing methods typically retrieve external evidence indiscriminately, overlooking the model's internal knowledge and potentially introducing irrelevant noise. Moreover, current systems lack targeted mechanisms to resolve specific uncertainties in the model's reasoning. Inspired by how humans fact-check, we argue that LLMs should adaptively decide whether to rely on internal knowledge or initiate retrieval based on their confidence in a given claim. We introduce Probabilistic Certainty and Consistency (PCC), a framework that estimates factual confidence by jointly modeling an LLM's probabilistic certainty and reasoning consistency. These confidence signals enable an adaptive verification strategy: the model answers directly when confident, triggers targeted retrieval when uncertain or inconsistent, and escalates to deep search when ambiguity is high. Our confidence-guided routing mechanism ensures that retrieval is invoked only when necessary, improving both efficiency and reliability. Extensive experiments across three challenging benchmarks show that PCC achieves better uncertainty quantification than verbalized confidence and consistently outperforms strong LLM-based fact-checking baselines. Furthermore, we demonstrate that PCC generalizes well across various LLMs.

On-policy distillation (OPD) is an increasingly important paradigm for post-training language models. However, we identify a pervasive Scaling Law of Miscalibration: while OPD effectively improves task accuracy, it systematically traps models in severe overconfidence. We trace this failure to an information mismatch: teacher supervision is formed under privileged context available during training, whereas the deployed model must report confidence using only deployment-time information. We formalize this perspective theoretically, showing that teacher-conditioned success is generally not a valid target for deployment-time confidence and that helpful privileged context induces entropy collapse and a systematic optimism bias. To address this, we propose a calibration-aware OPD framework, CaOPD, that estimates empirical confidence from model rollouts, replaces self-reported confidence with this student-grounded target, and distills the revised response through the same self-distillation pipeline. Experiments across various models and domains show that CaOPD achieves Pareto-optimal calibration while maintaining competitive capability, generalizing robustly under out-of-distribution and continual learning. Our findings highlight that capability distillation does not imply calibrated confidence, and that confidence should be treated as an essential objective in post-training. Code: https://github.com/SalesforceAIResearch/CaOPD

Recent advancements in multimodal large language models (MLLMs) have shown exceptional potential in enabling mobile-using agents to autonomously execute human instructions. However, fully automated agents often try to execute tasks even when they are unable to resolve them, leading to the problem of over-execution. Previous studies solve it by training a interactive mobile-using agents to let agents request human interaction when agents can not complete user instructions. However, we find that these interactive agents tend to exhibit over-soliciting behavior, relying excessively on human intervention. To mitigate both over-execution and over-soliciting, we propose a universal confidence integration framework that enables confidence-driven proactive and robust interaction in MLLM-based mobile-using agents. The framework consists of two stages: interaction capability empowerment and confidence bias correction. In the interaction capability empowerment stage, agents learn through supervised fine-tuning to output both actions and confidence scores. In the confidence bias correction stage, agents learn to output more accurate confidence scores by combining semantic similarity retrieval with direct preference optimization. Experimental results show Mobile-Aptus achieves state-of-the-art performance on the four popular mobile-using agent benchmarks: OS-Kairos, AITZ, Meta-GUI, and AndroidControl. Mobile-Aptus consistently outperforms all baselines in offline benchmarks, with an average improvement over 17\% in task success rate. In real-world dynamic experiments, Mobile-Aptus surpasses the baseline by 26% in task success rate with only 0.64 intervention steps per instruction. The codes are available at https://github.com/Wuzheng02/Mobile-Aptus.

Autonomous Graphical User Interface (GUI) agents rely on accurate GUI grounding, which maps language instructions to on-screen coordinates, to execute user commands. However, current models, whether trained via supervised fine-tuning (SFT) or reinforcement fine-tuning (RFT), lack self-awareness of their capability boundaries, leading to overconfidence and unreliable predictions. We first systematically evaluate probabilistic and verbalized confidence in general and GUI-specific models, revealing a misalignment between confidence and actual accuracy, which is particularly critical in dynamic GUI automation tasks, where single errors can cause task failure. To address this, we propose HyperClick, a novel framework that enhances reliable GUI grounding through uncertainty calibration. HyperClick introduces a dual reward mechanism, combining a binary reward for correct actions with a truncated Gaussian-based spatial confidence modeling, calibrated using the Brier score. This approach jointly optimizes grounding accuracy and confidence reliability, fostering introspective self-criticism. Extensive experiments on seven challenge benchmarks show that HyperClick achieves state-of-the-art performance while providing well-calibrated confidence. By enabling explicit confidence calibration and introspective self-criticism, HyperClick reduces overconfidence and supports more reliable GUI automation.

We aim to improve the performance of regressing hand keypoints and segmenting pixel-level hand masks under new imaging conditions (e.g., outdoors) when we only have labeled images taken under very different conditions (e.g., indoors). In the real world, it is important that the model trained for both tasks works under various imaging conditions. However, their variation covered by existing labeled hand datasets is limited. Thus, it is necessary to adapt the model trained on the labeled images (source) to unlabeled images (target) with unseen imaging conditions. While self-training domain adaptation methods (i.e., learning from the unlabeled target images in a self-supervised manner) have been developed for both tasks, their training may degrade performance when the predictions on the target images are noisy. To avoid this, it is crucial to assign a low importance (confidence) weight to the noisy predictions during self-training. In this paper, we propose to utilize the divergence of two predictions to estimate the confidence of the target image for both tasks. These predictions are given from two separate networks, and their divergence helps identify the noisy predictions. To integrate our proposed confidence estimation into self-training, we propose a teacher-student framework where the two networks (teachers) provide supervision to a network (student) for self-training, and the teachers are learned from the student by knowledge distillation. Our experiments show its superiority over state-of-the-art methods in adaptation settings with different lighting, grasping objects, backgrounds, and camera viewpoints. Our method improves by 4% the multi-task score on HO3D compared to the latest adversarial adaptation method. We also validate our method on Ego4D, egocentric videos with rapid changes in imaging conditions outdoors.

As large language models (LLMs) are increasingly deployed in user-facing applications, building trust and maintaining safety by accurately quantifying a model's confidence in its prediction becomes even more important. However, finding effective ways to calibrate LLMs - especially when the only interface to the models is their generated text - remains a challenge. We propose APRICOT (auxiliary prediction of confidence targets): A method to set confidence targets and train an additional model that predicts an LLM's confidence based on its textual input and output alone. This approach has several advantages: It is conceptually simple, does not require access to the target model beyond its output, does not interfere with the language generation, and has a multitude of potential usages, for instance by verbalizing the predicted confidence or adjusting the given answer based on the confidence. We show how our approach performs competitively in terms of calibration error for white-box and black-box LLMs on closed-book question-answering to detect incorrect LLM answers.

In continual learning, many classifiers use softmax function to learn confidence. However, numerous studies have pointed out its inability to accurately determine confidence distributions for outliers, often referred to as epistemic uncertainty. This inherent limitation also curtails the accurate decisions for selecting what to forget and keep in previously trained confidence distributions over continual learning process. To address the issue, we revisit the effects of masking softmax function. While this method is both simple and prevalent in literature, its implication for retaining confidence distribution during continual learning, also known as stability, has been under-investigated. In this paper, we revisit the impact of softmax masking, and introduce a methodology to utilize its confidence preservation effects. In class- and task-incremental learning benchmarks with and without memory replay, our approach significantly increases stability while maintaining sufficiently large plasticity. In the end, our methodology shows better overall performance than state-of-the-art methods, particularly in the use with zero or small memory. This lays a simple and effective foundation of strongly stable replay-based continual learning.

We introduce a simple, yet novel entropy-based framework to drive token efficiency in large language models during reasoning tasks. Our approach uses Shannon entropy from token-level logprobs as a confidence signal to enable early stopping, achieving 25-50% computational savings while maintaining task accuracy. Crucially, we demonstrate that entropy-based confidence calibration represents an emergent property of advanced post-training optimization present in modern reasoning models but notably absent in standard instruction-tuned and pre-trained models (Llama 3.3 70B). We show that the entropy threshold to stop reasoning varies from model to model but can be calculated easily in one shot using only a few examples from existing reasoning datasets. Our results indicate that advanced reasoning models often know that they've gotten a correct answer early on, and that this emergent confidence awareness can be exploited to save tokens and reduce latency. The framework demonstrates consistent performance across reasoning-optimized model families with 25-50% computational cost reduction while preserving accuracy, revealing that confidence mechanisms represent a distinguishing characteristic of modern post-trained reasoning systems versus their predecessors.

Increasing test-time computation is a straightforward approach to enhancing the quality of responses in Large Language Models (LLMs). While Best-of-N sampling and Self-Consistency with majority voting are simple and effective, they require a fixed number of sampling responses for each query, regardless of its complexity. This could result in wasted computation for simpler questions and insufficient exploration for more challenging ones. In this work, we argue that model confidence of responses can be used for improving the efficiency of test-time scaling. Unfortunately, LLMs are known to be overconfident and provide unreliable confidence estimation. To address this limitation, we introduce Self-Calibration by distilling Self-Consistency-derived confidence into the model itself. This enables reliable confidence estimation at test time with one forward pass. We then design confidence-based efficient test-time scaling methods to handle queries of various difficulty, such as Early-Stopping for Best-of-N and Self-Consistency with calibrated confidence. Experiments on three LLMs across six datasets demonstrate the effectiveness of our approach. Specifically, applying confidence-based Early Stopping to Best-of-N improves MathQA accuracy from 81.0 to 83.6 with a sample budget of 16 responses, indicating the efficacy of confidence-based sampling strategy at inference time.

This paper presents a novel technique for accelerating inference in large, pre-trained language models (LLMs) by introducing early exits during inference. The computational demands of these models, used across a wide range of applications, can be substantial. By capitalizing on the inherent variability in token complexity, our approach enables selective acceleration of the inference process. Specifically, we propose the integration of early exit ''heads'' atop existing transformer layers, which facilitate conditional terminations based on a confidence metric. These heads are trained in a self-supervised manner using the model's own predictions as training data, thereby eliminating the need for additional annotated data. The confidence metric, established using a calibration set, ensures a desired level of accuracy while enabling early termination when confidence exceeds a predetermined threshold. Notably, our method preserves the original accuracy and reduces computational time on certain tasks, leveraging the existing knowledge of pre-trained LLMs without requiring extensive retraining. This lightweight, modular modification has the potential to greatly enhance the practical usability of LLMs, particularly in applications like real-time language processing in resource-constrained environments.

Large language models have made strong reasoning gains through supervised fine-tuning, reinforcement learning, and on-policy distillation, yet these post-training methods are usually evaluated only by final-answer accuracy. We study how they reshape confidence during reasoning. We introduce a three-stage calibration framework that evaluates confidence before, during, and after chain-of-thought generation, corresponding to difficulty estimation, early termination, and answer aggregation. Through a controlled comparison on mathematical reasoning benchmarks, we find that OPD provides the most useful pre-reasoning confidence, SFT gives the strongest online signal for early stopping, and RL produces the most reliable trace-level signal for aggregation. We further show that confidence reliability is position-dependent: RL confidence becomes informative after a path-commitment phase, while OPD confidence is useful early but can become inversely calibrated later. Based on this observation, we propose PosConf, a position-aware confidence strategy that uses confidence only from reliable relative-position intervals. PosConf improves RL answer aggregation by 6.1 points over majority voting and consistently improves OPD early stopping under tight token budgets, with gains up to 4.3 points by avoiding its later inverse-calibration region, showing that confidence in reasoning models should be used both stage-wise and position-awarely. Our code is available at https://github.com/EIT-NLP/Post-Training-Calibration.

Self-consistency decoding enhances LLMs' performance on reasoning tasks by sampling diverse reasoning paths and selecting the most frequent answer. However, it is computationally expensive, as sampling many of these (lengthy) paths is required to increase the chances that the correct answer emerges as the most frequent one. To address this, we introduce Confidence-Informed Self-Consistency (CISC). CISC performs a weighted majority vote based on confidence scores obtained directly from the model. By prioritizing high-confidence paths, it can identify the correct answer with a significantly smaller sample size. When tested on nine models and four datasets, CISC outperforms self-consistency in nearly all configurations, reducing the required number of reasoning paths by over 40% on average. In addition, we introduce the notion of within-question confidence evaluation, after showing that standard evaluation methods are poor predictors of success in distinguishing correct and incorrect answers to the same question. In fact, the most calibrated confidence method proved to be the least effective for CISC. Lastly, beyond these practical implications, our results and analyses show that LLMs can effectively judge the correctness of their own outputs, contributing to the ongoing debate on this topic.

The recent success of Large Language Models (LLMs) has catalyzed an increasing interest in their self-correction capabilities. This paper presents a comprehensive investigation into the intrinsic self-correction of LLMs, attempting to address the ongoing debate about its feasibility. Our research has identified an important latent factor - the "confidence" of LLMs - during the self-correction process. Overlooking this factor may cause the models to over-criticize themselves, resulting in unreliable conclusions regarding the efficacy of self-correction. We have experimentally observed that LLMs possess the capability to understand the "confidence" in their own responses. It motivates us to develop an "If-or-Else" (IoE) prompting framework, designed to guide LLMs in assessing their own "confidence", facilitating intrinsic self-corrections. We conduct extensive experiments and demonstrate that our IoE-based Prompt can achieve a consistent improvement regarding the accuracy of self-corrected responses over the initial answers. Our study not only sheds light on the underlying factors affecting self-correction in LLMs, but also introduces a practical framework that utilizes the IoE prompting principle to efficiently improve self-correction capabilities with "confidence". The code is available at https://github.com/MBZUAI-CLeaR/IoE-Prompting.git.

LLM-as-a-Judge (LLMaaJ) now underpins scalable evaluation, yet we lack a decisive test of a judge's qualification: can it recover a conversation's latent objective and know when that inference is trustworthy? LLMs degrade under irrelevant or long context; multi-turn jailbreaks further hide goals across turns. We introduce ObjexMT, a benchmark for objective extraction and metacognition. Given a multi-turn transcript, a model must return a one-sentence base objective and a self-reported confidence. Accuracy is computed via LLM-judge semantic similarity to gold objectives, converted to binary correctness by a single human-aligned threshold calibrated once on N = 100 items (tau^*=0.61). Metacognition is evaluated with ECE, Brier, Wrong-at-High-Conf, and risk-coverage. Across gpt-4.1, claude-sonnet-4, and Qwen3-235B-A22B-FP8 on SafeMTData_Attack600, SafeMTData_1K, MHJ, and CoSafe, claude-sonnet-4 attains the best objective-extraction accuracy (0.515) and calibration (ECE 0.296; Brier 0.324); gpt-4.1 and Qwen3-235B-A22B-FP8 tie at 0.441 but are overconfident (mean confidence approx0.88 vs. accuracy approx0.44; Wrong-at-0.90 approx48-52%). Performance varies by dataset (approx0.167-0.865). ObjexMT thus supplies an actionable test for LLM judges: when objectives are not explicit, judges often misinfer them with high confidence. We recommend exposing objectives when feasible and gating decisions by confidence otherwise. Code and data at https://github.com/hyunjun1121/ObjexMT_dataset.

Test-time scaling often uses an external verifier, such as compilers and test cases in coding or trained value functions in robotics applications, to obtain high-quality rollouts. Verifier-free test-time scaling (or VF-TTS) is gaining extensive attention as a mechanism to enhance Large Language Model (LLM) reasoning, primarily because we do not have access to such high-quality verifiers in many real-world applications. Among existing VF-TTS methods, confidence-based VF-TTS methods, which compute and rank rollouts solely by confidence, are particularly promising. Such methods introduce near-zero overhead for sample evaluation and require minimal access to internal model states, making the methods highly flexible across models and tasks. In this paper, we demonstrate a critical limitation of existing confidence-based VF-TTS methods by showing that such methods catastrophically break down on complex tasks. We observe a very interesting phenomenon: uniformly high confidence frequently indicates a failure to explore, favoring confidently wrong answers. To address this, our core insight is that robust cognitive search requires a specific confidence trajectory pattern: such methods perform exploratory branching at the beginning, as manifested by low initial confidence, and converge to a high final confidence solution. To implement this insight, we introduce consilience, a novel selection framework that explicitly evaluates the temporal asymmetry of confidence in reasoning. We operationalize this via a combinatorial metric that actively penalizes high initial confidence while strictly demanding final certainty. Extensive experiments covering both graduate-level mathematics problems and free-form code generation demonstrate that consilience effectively outperforms existing baselines, validating our novel perspective on completion confidence.

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.

Recent progress in large language models (LLMs) has enabled them to express their confidence in natural language, enhancing transparency and reliability. However, their confidence often exhibits overconfidence, the cause of which remains poorly understood. In this work, we conduct a detailed analysis of the dynamics underlying verbalized confidence and identify answer-independence as a key factor, defined as the model's failure to condition confidence on its own answer. To address this, we propose ADVICE (Answer-Dependent Verbalized Confidence Estimation), a fine-tuning framework that facilitates answer-grounded confidence estimation. Extensive experiments show that ADVICE substantially improves confidence calibration while preserving task performance. Further analyses confirm that ADVICE strengthens answer-groundedness, leading to more balanced and well-calibrated confidence distributions. Our findings shed light on the origin of overconfidence and establish a framework for more trustworthy confidence verbalization.

As Large Language Models (LLMs) are increasingly deployed in real-world settings, correctness alone is insufficient. Reliable deployment requires maintaining truthful beliefs under contextual perturbations. Existing evaluations largely rely on point-wise confidence like Self-Consistency, which can mask brittle belief. We show that even facts answered with perfect self-consistency can rapidly collapse under mild contextual interference. To address this gap, we propose Neighbor-Consistency Belief (NCB), a structural measure of belief robustness that evaluates response coherence across a conceptual neighborhood. To validate the efficiency of NCB, we introduce a new cognitive stress-testing protocol that probes outputs stability under contextual interference. Experiments across multiple LLMs show that the performance of high-NCB data is relatively more resistant to interference. Finally, we present Structure-Aware Training (SAT), which optimizes context-invariant belief structure and reduces long-tail knowledge brittleness by approximately 30%. Code will be available at https://github.com/zjunlp/belief.

Large Vision Language Models (LVLMs) achieve strong multimodal reasoning but frequently exhibit hallucinations and incorrect responses with high certainty, which hinders their usage in high-stakes domains. Existing verbalized confidence calibration methods, largely developed for text-only LLMs, typically optimize a single holistic confidence score using binary answer-level correctness. This design is mismatched to LVLMs: an incorrect prediction may arise from perceptual failures or from reasoning errors given correct perception, and a single confidence conflates these sources while visual uncertainty is often dominated by language priors. To address these issues, we propose VL-Calibration, a reinforcement learning framework that explicitly decouples confidence into visual and reasoning confidence. To supervise visual confidence without ground-truth perception labels, we introduce an intrinsic visual certainty estimation that combines (i) visual grounding measured by KL-divergence under image perturbations and (ii) internal certainty measured by token entropy. We further propose token-level advantage reweighting to focus optimization on tokens based on visual certainty, suppressing ungrounded hallucinations while preserving valid perception. Experiments on thirteen benchmarks show that VL-Calibration effectively improves calibration while boosting visual reasoning accuracy, and it generalizes to out-of-distribution benchmarks across model scales and architectures.

Reliable prediction by classifiers is crucial for their deployment in high security and dynamically changing situations. However, modern neural networks often exhibit overconfidence for misclassified predictions, highlighting the need for confidence estimation to detect errors. Despite the achievements obtained by existing methods on small-scale datasets, they all require training from scratch and there are no efficient and effective misclassification detection (MisD) methods, hindering practical application towards large-scale and ever-changing datasets. In this paper, we pave the way to exploit vision language model (VLM) leveraging text information to establish an efficient and general-purpose misclassification detection framework. By harnessing the power of VLM, we construct FSMisD, a Few-Shot prompt learning framework for MisD to refrain from training from scratch and therefore improve tuning efficiency. To enhance misclassification detection ability, we use adaptive pseudo sample generation and a novel negative loss to mitigate the issue of overconfidence by pushing category prompts away from pseudo features. We conduct comprehensive experiments with prompt learning methods and validate the generalization ability across various datasets with domain shift. Significant and consistent improvement demonstrates the effectiveness, efficiency and generalizability of our approach.

Large Language Models (LLMs) are widely used as automated judges, where practical value depends on both accuracy and trustworthy, risk-aware judgments. Existing approaches predominantly focus on accuracy, overlooking the necessity of well-calibrated confidence, which is vital for adaptive and reliable evaluation pipelines. In this work, we advocate a shift from accuracy-centric evaluation to confidence-driven, risk-aware LLM-as-a-Judge systems, emphasizing the necessity of well-calibrated confidence for trustworthy and adaptive evaluation. We systematically identify the Overconfidence Phenomenon in current LLM-as-a-Judges, where predicted confidence significantly overstates actual correctness, undermining reliability in practical deployment. To quantify this phenomenon, we introduce TH-Score, a novel metric measuring confidence-accuracy alignment. Furthermore, we propose LLM-as-a-Fuser, an ensemble framework that transforms LLMs into reliable, risk-aware evaluators. Extensive experiments demonstrate that our approach substantially improves calibration and enables adaptive, confidence-driven evaluation pipelines, achieving superior reliability and accuracy compared to existing baselines.

Learning exists in the context of data, yet notions of confidence typically focus on model predictions, not label quality. Confident learning (CL) is an alternative approach which focuses instead on label quality by characterizing and identifying label errors in datasets, based on the principles of pruning noisy data, counting with probabilistic thresholds to estimate noise, and ranking examples to train with confidence. Whereas numerous studies have developed these principles independently, here, we combine them, building on the assumption of a class-conditional noise process to directly estimate the joint distribution between noisy (given) labels and uncorrupted (unknown) labels. This results in a generalized CL which is provably consistent and experimentally performant. We present sufficient conditions where CL exactly finds label errors, and show CL performance exceeding seven recent competitive approaches for learning with noisy labels on the CIFAR dataset. Uniquely, the CL framework is not coupled to a specific data modality or model (e.g., we use CL to find several label errors in the presumed error-free MNIST dataset and improve sentiment classification on text data in Amazon Reviews). We also employ CL on ImageNet to quantify ontological class overlap (e.g., estimating 645 "missile" images are mislabeled as their parent class "projectile"), and moderately increase model accuracy (e.g., for ResNet) by cleaning data prior to training. These results are replicable using the open-source cleanlab release.

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 ability to judge whether a caption correctly describes an image is a critical part of vision-language understanding. However, state-of-the-art models often misinterpret the correctness of fine-grained details, leading to errors in outputs such as hallucinating objects in generated captions or poor compositional reasoning. In this work, we explore Token-Level Confidence, or TLC, as a simple yet surprisingly effective method to assess caption correctness. Specifically, we fine-tune a vision-language model on image captioning, input an image and proposed caption to the model, and aggregate either algebraic or learned token confidences over words or sequences to estimate image-caption consistency. Compared to sequence-level scores from pretrained models, TLC with algebraic confidence measures achieves a relative improvement in accuracy by 10% on verb understanding in SVO-Probes and outperforms prior state-of-the-art in image and group scores for compositional reasoning in Winoground by a relative 37% and 9%, respectively. When training data are available, a learned confidence estimator provides further improved performance, reducing object hallucination rates in MS COCO Captions by a relative 30% over the original model and setting a new state-of-the-art.

Medical vision-language models (VLMs) require confidence that reflects both answer correctness and patient-specific visual evidence. Recent GRPO-based methods optimize verbalized confidence together with answer generation. However, this joint optimization may interfere with answer learning and drive confidence toward near-binary values. Verbalized confidence also provides no explicit assessment of visual support. We therefore separate capability learning from confidence estimation and propose DualRead. DualRead builds on the insight that reliability can be read from the actor's internal states at critical moments in the answering process. It freezes the GRPO-trained actor and combines pre-answer solvability with a post-answer assessment of the generated answer and its visual support. To further assess whether confidence reflects visual grounding, we introduce Counterfactual Confidence Grounding AUC (CCG-AUC). It measures whether confidence decreases when real-image substitution changes the actor from correct to incorrect. Across two VLM backbones and both in- and out-of-distribution medical VQA benchmarks, DualRead improves correctness discrimination and calibration over verbalized confidence while preserving answer accuracy. CCG-AUC reveals whether confidence responds to answer-relevant visual evidence rather than primarily to non-visual cues.

Accurate confidence estimation is essential for trustworthy large language models (LLMs) systems, as it empowers the user to determine when to trust outputs and enables reliable deployment in safety-critical applications. Current confidence estimation methods for LLMs neglect the relevance between responses and contextual information, a crucial factor in output quality evaluation, particularly in scenarios where background knowledge is provided. To bridge this gap, we propose CRUX (Context-aware entropy Reduction and Unified consistency eXamination), the first framework that integrates context faithfulness and consistency for confidence estimation via two novel metrics. First, contextual entropy reduction represents data uncertainty with the information gain through contrastive sampling with and without context. Second, unified consistency examination captures potential model uncertainty through the global consistency of the generated answers with and without context. Experiments across three benchmark datasets (CoQA, SQuAD, QuAC) and two domain-specific datasets (BioASQ, EduQG) demonstrate CRUX's effectiveness, achieving the highest AUROC than existing baselines.

Self-training is a well-known approach for semi-supervised learning. It consists of iteratively assigning pseudo-labels to unlabeled data for which the model is confident and treating them as labeled examples. For neural networks, softmax prediction probabilities are often used as a confidence measure, although they are known to be overconfident, even for wrong predictions. This phenomenon is particularly intensified in the presence of sample selection bias, i.e., when data labeling is subject to some constraint. To address this issue, we propose a novel confidence measure, called T-similarity, built upon the prediction diversity of an ensemble of linear classifiers. We provide the theoretical analysis of our approach by studying stationary points and describing the relationship between the diversity of the individual members and their performance. We empirically demonstrate the benefit of our confidence measure for three different pseudo-labeling policies on classification datasets of various data modalities. The code is available at https://github.com/ambroiseodt/tsim.

Multimodal large language models (MLLMs) hold considerable promise for applications in healthcare. However, their deployment in safety-critical settings is hindered by two key limitations: (i) sensitivity to prompt design, and (ii) a tendency to generate incorrect responses with high confidence. As clinicians may rely on a model's stated confidence to gauge the reliability of its predictions, it is especially important that when a model expresses high confidence, it is also highly accurate. We introduce Prompt4Trust, the first reinforcement learning (RL) framework for prompt augmentation targeting confidence calibration in MLLMs. A lightweight LLM is trained to produce context-aware auxiliary prompts that guide a downstream task MLLM to generate responses in which the expressed confidence more accurately reflects predictive accuracy. Unlike conventional calibration techniques, Prompt4Trust specifically prioritizes aspects of calibration most critical for safe and trustworthy clinical decision-making. Beyond improvements driven by this clinically motivated calibration objective, our proposed method also improves task accuracy, achieving state-of-the-art medical visual question answering (VQA) performance on the PMC-VQA benchmark, which is composed of multiple-choice questions spanning diverse medical imaging modalities. Moreover, our framework trained with a small downstream task MLLM showed promising zero-shot generalization to larger MLLMs in our experiments, suggesting the potential for scalable calibration without the associated computational costs. This work demonstrates the potential of automated yet human-aligned prompt engineering for improving the the trustworthiness of MLLMs in safety critical settings. Our codebase can be found at https://github.com/xingbpshen/prompt4trust.

Metacognition is a critical component of intelligence that describes the ability to monitor and regulate one's own cognitive processes. Yet LLMs exhibit systemic deficiencies in key metacognitive faculties: they hallucinate with high confidence, fail to recognize knowledge boundaries, and misrepresent their internal uncertainty--undermining trustworthiness and reliability. Since monitoring task performance and adapting behavior accordingly are central to metacognition, we posit that models capable of accurately judging their own performance are better positioned to improve it. We operationalize this idea via two novel mechanisms: reinforcement learning with metacognitive feedback (RLMF), a paradigm to refine completion rankings during preference optimization based on the quality of a model's self-judgments of performance, and metacognitive data selection, which uses similar self-judgments to identify high-value training examples, outperforming naive active learning. We apply these innovations to the problem of faithful calibration (FC), a task that is itself fundamentally metacognitive: the goal is to align expressed with intrinsic uncertainty, difficult even for frontier LLMs. We adopt a two-stage, decoupled approach, first using these methods to calibrate the faithfulness of models' self-reported confidence scores, then mapping to natural, context-adaptable linguistic uncertainty via targeted output editing. Extensive experiments show RLMF achieves generalizable, state-of-the-art FC on diverse tasks while preserving accuracy. Further, RLMF surpasses standard RL by up to 63% while enhancing models' ability to assess and express their own capability limits. This positions RLMF as a promising paradigm to enhance LLM metacognition toward improved abilities and alignment, and suggests metacognitive performance as an effective RL signal to overcome limits of prior intrinsic feedback methods.

Confidence in LLMs is a useful indicator of model uncertainty and answer reliability. Existing work mainly focused on single-turn scenarios, while research on confidence in complex multi-turn interactions is limited. In this paper, we investigate whether LLM-based search agents have the ability to communicate their own confidence through verbalized confidence scores after long sequences of actions, a significantly more challenging task compared to outputting confidence in a single interaction. Experimenting on open-source agentic models, we first find that models exhibit much higher task accuracy at high confidence while having near-zero accuracy when confidence is low. Based on this observation, we propose Test-Time Scaling (TTS) methods that use confidence scores to determine answer quality, encourage the model to try again until reaching a satisfactory confidence level. Results show that our proposed methods significantly reduce token consumption while demonstrating competitive performance compared to baseline fixed budget TTS methods.

Quality estimation is omnipresent in machine translation, for both evaluation and generation. Unfortunately, quality estimation models are often opaque and computationally expensive, making them impractical to be part of large-scale pipelines. In this work, we tackle two connected challenges: (1) reducing the cost of quality estimation at scale, and (2) developing an inexpensive uncertainty estimation method for quality estimation. To address the latter, we introduce Instant Confidence COMET, an uncertainty-aware quality estimation model that matches the performance of previous approaches at a fraction of their costs. We extend this to Early-Exit COMET, a quality estimation model that can compute quality scores and associated confidences already at early model layers, allowing us to early-exit computations and reduce evaluation costs. We also apply our model to machine translation reranking. We combine Early-Exit COMET with an upper confidence bound bandit algorithm to find the best candidate from a large pool without having to run the full evaluation model on all candidates. In both cases (evaluation and reranking) our methods reduce the required compute by 50% with very little degradation in performance.

Linguistic cues such as "I believe" and "probably" offer an intuitive interface for communicating confidence, yet a generalisable, principled calibration framework for linguistic confidence expressions remains underexplored. In particular, co-occurring linguistic cues, contextual variation, and subjective audience interpretation pose unique challenges. We therefore model linguistic confidence as a distribution over plausible perceived probability values that a statement is correct, capturing interpretation variability that scalar representations discard. Within this distributional framework, we introduce faithfulness as a complementary evaluation dimension and present Faithfulness Divergence (FD), an information-theoretic metric quantifying the surprise induced in audience beliefs upon truth revelation. Building on these foundations, we present Retrieval-Augmented Linguistic Calibration (RALC), a lightweight post-hoc pipeline that propagates calibrated confidence signals back into natural language via retrieval-augmented rewriting. Across three QA benchmarks and five LLM families, RALC improves in-domain faithfulness and calibration up to 66% and 58%, respectively, outperforming black-box and grey-box calibration baselines.

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

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

Generalizing Multimodal Large Language Models (MLLMs) to novel video domains is essential for real-world deployment but remains challenging due to the scarcity of labeled data. While In-Context Learning (ICL) offers a training-free adaptation path, standard methods rely on large annotated pools, which are often impractical in specialized environments like industrial or surgical settings since they require the experts' annotations. To bridge this gap, we introduce VIOLA (Video In-cOntext Learning with minimal Annotation), a label-efficient framework that synergizes minimal expert supervision with abundant unlabeled data. First, to maximize the efficiency of a strict annotation budget, we propose density-uncertainty-weighted sampling. Unlike standard diversity or uncertainty strategies that risk selecting visual outliers, our method leverages density estimation to identify samples that are simultaneously diverse, representative, and informative. Second, to utilize the remaining unlabeled data without noise propagation, we construct a hybrid pool and introduce confidence-aware retrieval and confidence-aware prompting. These mechanisms explicitly model label reliability, retrieving demonstrations based on a composite score of similarity and confidence while enabling the MLLM to adaptively distinguish between verified ground truths and noisy pseudo-labels. Extensive experiments across nine diverse benchmarks using four MLLMs demonstrate that our framework significantly outperforms various baselines in low-resource settings, achieving robust adaptation with minimal annotation costs.

Small instruct-tuned LLMs produce degenerate verbal confidence under minimal elicitation: ceiling rates above 95%, near-chance Type-2 AUROC, and Invalid validity profiles. We test whether confidence-conditioned supervised fine-tuning (CSFT) with self-consistency-derived targets can close the gap between internal information and verbal readout. A pre-registered Phase 0 protocol on Gemma 3 4B-it with a modal filter restricting training to items with correct modal answers produced a negative result: AUROC2 dropped from 0.554 to 0.509 due to label-entropy collapse in the training targets. An exploratory rescue removed the filter, training on all 2,000 calibration items. This produced a binary verbal correctness discriminator with AUROC2 = 0.774 on held-out TriviaQA, compressing a 10-sample self-consistency signal (AUROC2 = 0.999) into a single-pass readout exceeding logit entropy (0.701). The shuffled-target control showed no improvement (0.501). On MMLU, accuracy improved from 54.2% to 77.4% with the shuffled model at baseline (56.1%), supporting a target-dependent interpretation. The result is exploratory, binary rather than continuously calibrated, and observed at a single scale. It identifies two design lessons: confidence training requires label entropy, and correct targets regularise output format.

We investigate whether language models internally track the value of their current trajectory, defined as the likelihood that their ongoing strategy will achieve their goals. Using synthetic, in-context reinforcement learning data, we construct a "value" axis for Qwen3-8B. We find that activations along this axis distinguish between high vs. low verbalized confidence, rollouts without and with backtracking, and correct vs. corrupted code. Steering towards high value causally suppresses self-correction and reduces explanatory verbosity, while steering towards low value induces backtracking and exploration. We demonstrate that direct preference optimization (DPO) can increase the internal value of rewarded behaviors (e.g. use a certain word), causing the model to act more confidently after exhibiting them. Finally, we apply the value axis to study in-the-wild settings. For example, we find that Qwen assigns low value to politically sensitive chat queries after post-training and that supervised fine-tuning increases internal confidence within the training domain. Our results suggest that language models linearly encode an estimate of expected goal success that modulates their confidence in pursuing a direction.

As language models improve and become increasingly deployed to solve a variety of tasks, trustworthiness becomes essential. Calibration is a good proxy for trust: well-calibrated confidence estimates help inform the risk versus reward tradeoff when trusting a specific model output. Unfortunately, even as models improve, they remain poorly calibrated, often biasing towards overconfidence. Additionally, calibration can be gamed: a policy that always predicts the base rate is perfectly calibrated, but completely uninformative. To resolve this, we develop a new metric, expected utility renormalized by the oracle (EURO), that balances calibration and informativeness. We also propose a general-purpose activation-based confidence, utility, and trust estimation protocol (ACUTE) to appropriately adjudicate uncertainty. The ACUTE protocol provides flexible, sample-efficient, and compute-efficient confidence estimators for 3 tasks including multiple choice question answering, tool-calling, and scientific document summarization across 6 models from 4 model families. ACUTE outperforms strong baselines on EURO, while maintaining low calibration error. Taken together, our work shows that equipping LLMs with the ACUTE protocol can improve calibration, utility, and trustworthiness in numerous settings.

Neural Radiance Fields (NeRF) exhibit remarkable performance for Novel View Synthesis (NVS) given a set of 2D images. However, NeRF training requires accurate camera pose for each input view, typically obtained by Structure-from-Motion (SfM) pipelines. Recent works have attempted to relax this constraint, but they still often rely on decent initial poses which they can refine. Here we aim at removing the requirement for pose initialization. We present Incremental CONfidence (ICON), an optimization procedure for training NeRFs from 2D video frames. ICON only assumes smooth camera motion to estimate initial guess for poses. Further, ICON introduces ``confidence": an adaptive measure of model quality used to dynamically reweight gradients. ICON relies on high-confidence poses to learn NeRF, and high-confidence 3D structure (as encoded by NeRF) to learn poses. We show that ICON, without prior pose initialization, achieves superior performance in both CO3D and HO3D versus methods which use SfM pose.

Large Language Models (LLMs) are often augmented with external information as contexts, but this external information can sometimes be inaccurate or even intentionally misleading. We argue that robust LLMs should demonstrate situated faithfulness, dynamically calibrating their trust in external information based on their confidence in the internal knowledge and the external context. To benchmark this capability, we evaluate LLMs across several QA datasets, including a newly created dataset called RedditQA featuring in-the-wild incorrect contexts sourced from Reddit posts. We show that when provided with both correct and incorrect contexts, both open-source and proprietary models tend to overly rely on external information, regardless of its factual accuracy. To enhance situated faithfulness, we propose two approaches: Self-Guided Confidence Reasoning (SCR) and Rule-Based Confidence Reasoning (RCR). SCR enables models to self-access the confidence of external information relative to their own internal knowledge to produce the most accurate answer. RCR, in contrast, extracts explicit confidence signals from the LLM and determines the final answer using predefined rules. Our results show that for LLMs with strong reasoning capabilities, such as GPT-4o and GPT-4o mini, SCR outperforms RCR, achieving improvements of up to 24.2% over a direct input augmentation baseline. Conversely, for a smaller model like Llama-3-8B, RCR outperforms SCR. Fine-tuning SCR with our proposed Confidence Reasoning Direct Preference Optimization (CR-DPO) method improves performance on both seen and unseen datasets, yielding an average improvement of 8.9% on Llama-3-8B. In addition to quantitative results, we offer insights into the relative strengths of SCR and RCR. Our findings highlight promising avenues for improving situated faithfulness in LLMs. The data and code are released.

Large Language Models (LLMs) have shown remarkable capabilities across various tasks, but their deployment in high-stake domains requires consistent performance across multiple interaction rounds. This paper introduces a comprehensive framework for evaluating and improving LLM response consistency, making three key contributions. First, we propose a novel Position-Weighted Consistency (PWC) score that captures both the importance of early-stage stability and recovery patterns in multi-turn interactions. Second, we present a carefully curated benchmark dataset spanning diverse domains and difficulty levels, specifically designed to evaluate LLM consistency under various challenging follow-up scenarios. Third, we introduce Confidence-Aware Response Generation (CARG), a framework that significantly improves response stability by incorporating model confidence signals into the generation process. Empirical results demonstrate that CARG significantly improves response stability without sacrificing accuracy, underscoring its potential for reliable LLM deployment in critical applications.

Video temporal grounding supports applications such as video search, content review, and automated editing by localizing events described in natural language. Yet existing generative models typically output timestamps without explicit interval-level confidence scores to guide candidate selection. We separate candidate generation from acceptance by scoring individual intervals within the original decoding pass. A lightweight confidence head reads pooled decoder states, providing an explicit score trained for interval selection. Offline verifier scores supervise the head on fixed candidate sequences, and temporal-overlap labels adapt it to current rollouts during reinforcement learning. GT-anchored candidate-pool supervision and set-level optimization train the generator. The resulting scores support ranking, threshold-based selection, and rejection without invoking an external verifier at inference. On a fixed OMTG-Bench candidate pool, confidence raises query-macro Recall@0.5 from 9.95% to 14.42% over generation order at a 10% global return budget, and from 26.48% to 31.12% at a 25% budget. The continuous scores let downstream applications adjust return budgets or acceptance thresholds to match their precision-recall preferences, without regenerating candidate intervals.

Large Language Models (LLMs) have acquired ubiquitous attention for their performances across diverse domains. Our study here searches through LLMs' cognitive abilities and confidence dynamics. We dive deep into understanding the alignment between their self-assessed confidence and actual performance. We exploit these models with diverse sets of questionnaires and real-world scenarios and extract how LLMs exhibit confidence in their responses. Our findings reveal intriguing instances where models demonstrate high confidence even when they answer incorrectly. This is reminiscent of the Dunning-Kruger effect observed in human psychology. In contrast, there are cases where models exhibit low confidence with correct answers revealing potential underestimation biases. Our results underscore the need for a deeper understanding of their cognitive processes. By examining the nuances of LLMs' self-assessment mechanism, this investigation provides noteworthy revelations that serve to advance the functionalities and broaden the potential applications of these formidable language models.

Retrieval-Augmented Generation (RAG) mitigates hallucinations in Large Language Models (LLMs) by integrating external knowledge. However, conflicts between parametric knowledge and retrieved context pose challenges, particularly when retrieved information is unreliable or the model's internal knowledge is outdated. In such cases, LLMs struggle to determine whether to rely more on their own parameters or the conflicted context. To address this, we propose **CK-PLUG**, a plug-and-play method for controlling LLMs' reliance on parametric and contextual knowledge. We introduce a novel knowledge consistency metric, Confidence Gain, which detects knowledge conflicts by measuring entropy shifts in token probability distributions after context insertion. CK-PLUG then enables fine-grained control over knowledge preference by adjusting the probability distribution of tokens with negative confidence gain through a single tuning parameter. Experiments demonstrate CK-PLUG's ability to significantly regulate knowledge reliance in counterfactual RAG scenarios while maintaining generation fluency and knowledge accuracy. For instance, on Llama3-8B, memory recall (MR) of RAG response can be adjusted within a broad range (9.9%-71.9%), compared to the baseline of 42.1%. Moreover, CK-PLUG supports adaptive control based on the model's confidence in both internal and external knowledge, achieving consistent performance improvements across various general RAG tasks. Our code is available at: https://github.com/byronBBL/CK-PLUG{this https URL}.

Large language models (LLMs) frequently hallucinate due to misaligned self-awareness, generating erroneous outputs when addressing queries beyond their knowledge boundaries. While existing approaches mitigate hallucinations via uncertainty estimation or query rejection, they suffer from computational inefficiency or sacrificed helpfulness. To address these issues, we propose the Explicit Knowledge Boundary Modeling (EKBM) framework, integrating fast and slow reasoning systems to harmonize reliability and usability. The framework first employs a fast-thinking model to generate confidence-labeled responses, enabling immediate use of high-confidence outputs. For uncertain predictions, a slow refinement model conducts targeted reasoning to improve accuracy. To align model behavior with our proposed object, we propose a hybrid training pipeline, enhancing self-awareness without degrading task performance. Evaluations on dialogue state tracking tasks demonstrate that EKBM achieves superior model reliability over uncertainty-based baselines. Further analysis reveals that refinement substantially boosts accuracy while maintaining low computational overhead. Our work establishes a scalable paradigm for advancing LLM reliability and balancing accuracy and practical utility in error-sensitive applications.

Large Vision-Language Models (LVLMs) integrate visual perception with language generation, enabling responses that span image understanding and complex reasoning. However, LVLMs do not just inherit the text-level hallucinations; they also hallucinate against the image, producing fluent responses ungrounded in what they see. This makes LVLM response scoring inherently harder, and our diagnostics show that existing confidence-based metrics adopted from LLMs are insufficient for LVLMs. Specifically, removing the input image barely changes confidence-based selection, suggesting that output-space confidence primarily captures textual plausibility rather than agreement with the image. To address this gap, we propose LookBack, a training-free LVLM response scoring method that augments token likelihood with visual lookback score, a lightweight measure of how strongly each response token refers to image tokens. Across four benchmarks and three models, LookBack consistently improves Best-of-N selection over existing baselines with negligible additional overhead.

Uncertainty estimation is a significant issue for current large language models (LLMs) that are generally poorly calibrated and over-confident, especially with reinforcement learning from human feedback (RLHF). Unlike humans, whose decisions and confidences not only stem from intrinsic beliefs but can also be adjusted through daily observations, existing calibration methods for LLMs focus on estimating or eliciting individual confidence without taking full advantage of the "Collective Wisdom": the interaction among multiple LLMs that can collectively improve both accuracy and calibration. In this work, we propose Collaborative Calibration, a post-hoc training-free calibration strategy that leverages the collaborative and expressive capabilities of multiple tool-augmented LLM agents in a simulated group deliberation process. We demonstrate the effectiveness of Collaborative Calibration on generative QA tasks across various domains, showing its potential in harnessing the rationalization of collectively calibrated confidence assessments and improving the reliability of model predictions.

Reinforcement Learning with Verifiable Rewards (RLVR) has become the leading paradigm for enhancing reasoning in Large Language Models (LLMs). However, standard RLVR algorithms suffer from a well-documented pathology: while they improve Pass@1 accuracy through sharpened sampling, they simultaneously narrow the model's reasoning boundary and reduce generation diversity. We identify a root cause that existing methods overlook: the uniform penalization of errors. Current approaches -- whether data-filtering methods that select prompts by difficulty, or advantage normalization schemes -- treat all incorrect rollouts within a group identically. We show that this uniformity allows overconfident errors (incorrect reasoning paths that the RL process has spuriously reinforced) to persist and monopolize probability mass, ultimately suppressing valid exploratory trajectories. To address this, we propose the Asymmetric Confidence-aware Error Penalty (ACE). ACE introduces a per-rollout confidence shift metric, c_i = log(pi_theta(y_i|x) / pi_ref(y_i|x)), to dynamically modulate negative advantages. Theoretically, we demonstrate that ACE's gradient can be decomposed into the gradient of a selective regularizer restricted to overconfident errors, plus a well-characterized residual that partially moderates the regularizer's strength. We conduct extensive experiments fine-tuning Qwen2.5-Math-7B, Qwen3-8B-Base, and Llama-3.1-8B-Instruct on the DAPO-Math-17K dataset using GRPO and DAPO within the VERL framework. Evaluated on MATH-500 and AIME 2025, ACE composes seamlessly with existing methods and consistently improves the full Pass@k spectrum across all three model families and benchmarks.

Tool-using agents that act in the world need to be both useful and safe. Well-calibrated model confidences can be used to weigh the risk versus reward of potential actions, but prior work shows that many models are poorly calibrated. Inspired by interpretability literature exploring the internals of models, we propose a novel class of model-internal confidence estimators (MICE) to better assess confidence when calling tools. MICE first decodes from each intermediate layer of the language model using logitLens and then computes similarity scores between each layer's generation and the final output. These features are fed into a learned probabilistic classifier to assess confidence in the decoded output. On the simulated trial and error (STE) tool-calling dataset using Llama3 models, we find that MICE beats or matches the baselines on smoothed expected calibration error. Using MICE confidences to determine whether to call a tool significantly improves over strong baselines on a new metric, expected tool-calling utility. Further experiments show that MICE is sample-efficient, can generalize zero-shot to unseen APIs, and results in higher tool-calling utility in scenarios with varying risk levels. Our code is open source, available at https://github.com/microsoft/mice_for_cats.

Multi-agent debates have been introduced to improve the accuracy of Large Language Models (LLMs) by having multiple agents discuss solutions to a problem over several rounds of debate. However, models often generate incorrect yet confident-sounding responses, which can mislead others. This issue arises partly because agents do not consider how confident their peers are. To address this, we propose DebUnc, a debate framework that uses uncertainty metrics to assess agent confidence. Confidence is then conveyed through a modified attention mechanism that adjusts token weights, or through textual prompts. Evaluations across benchmarks show that attention-based methods are particularly effective and that performance continues to improve as uncertainty estimation becomes more reliable. The code is available at https://github.com/lukeyoffe/debunc.

We study the tradeoff between computational effort and classification accuracy in a cascade of deep neural networks. During inference, the user sets the acceptable accuracy degradation which then automatically determines confidence thresholds for the intermediate classifiers. As soon as the confidence threshold is met, inference terminates immediately without having to compute the output of the complete network. Confidence levels are derived directly from the softmax outputs of intermediate classifiers, as we do not train special decision functions. We show that using a softmax output as a confidence measure in a cascade of deep neural networks leads to a reduction of 15%-50% in the number of MAC operations while degrading the classification accuracy by roughly 1%. Our method can be easily incorporated into pre-trained non-cascaded architectures, as we exemplify on ResNet. Our main contribution is a method that dynamically adjusts the tradeoff between accuracy and computation without retraining the model.

Large language models (LLMs) tend to verbalize confidence scores that are largely detached from their actual accuracy, yet the geometric relationship governing this behavior remain poorly understood. In this work, we present a mechanistic interpretability analysis of verbalized confidence, using linear probes and contrastive activation addition (CAA) steering to show that calibration and verbalized confidence signals are encoded linearly but are orthogonal to one another -- a finding consistent across three open-weight models and four datasets. Interestingly, when models are prompted to simultaneously reason through a problem and verbalize a confidence score, the reasoning process disrupts the verbalized confidence direction, exacerbating miscalibration. We term this the "Reasoning Contamination Effect." Leveraging this insight, we introduce a two-stage adaptive steering pipeline that reads the model's internal accuracy estimate and steers verbalized output to match it, substantially improving calibration alignment across all evaluated models.

Large language models (LLMs) have demonstrated impressive capabilities across various tasks, but their performance is highly sensitive to the prompts utilized. This variability poses challenges for accurate assessment and user satisfaction. Current research frequently overlooks instance-level prompt variations and their implications on subjective evaluations. To address these shortcomings, we introduce ProSA, a framework designed to evaluate and comprehend prompt sensitivity in LLMs. ProSA incorporates a novel sensitivity metric, PromptSensiScore, and leverages decoding confidence to elucidate underlying mechanisms. Our extensive study, spanning multiple tasks, uncovers that prompt sensitivity fluctuates across datasets and models, with larger models exhibiting enhanced robustness. We observe that few-shot examples can alleviate this sensitivity issue, and subjective evaluations are also susceptible to prompt sensitivities, particularly in complex, reasoning-oriented tasks. Furthermore, our findings indicate that higher model confidence correlates with increased prompt robustness. We believe this work will serve as a helpful tool in studying prompt sensitivity of LLMs. The project is released at: https://github.com/open-compass/ProSA .

Human feedback has become the de facto standard for evaluating the performance of Large Language Models, and is increasingly being used as a training objective. However, it is not clear which properties of a generated output this single `preference' score captures. We hypothesise that preference scores are subjective and open to undesirable biases. We critically analyse the use of human feedback for both training and evaluation, to verify whether it fully captures a range of crucial error criteria. We find that while preference scores have fairly good coverage, they under-represent important aspects like factuality. We further hypothesise that both preference scores and error annotation may be affected by confounders, and leverage instruction-tuned models to generate outputs that vary along two possible confounding dimensions: assertiveness and complexity. We find that the assertiveness of an output skews the perceived rate of factuality errors, indicating that human annotations are not a fully reliable evaluation metric or training objective. Finally, we offer preliminary evidence that using human feedback as a training objective disproportionately increases the assertiveness of model outputs. We encourage future work to carefully consider whether preference scores are well aligned with the desired objective.

Self-awareness, i.e., the ability to assess and correct one's own generation, is a fundamental aspect of human intelligence, making its replication in large language models (LLMs) an important yet challenging task. Previous works tackle this by employing extensive reinforcement learning or rather relying on large external verifiers. In this work, we propose Refine via Intrinsic Self-Verification (ReVISE), an efficient and effective framework that enables LLMs to self-correct their outputs through self-verification. The core idea of ReVISE is to enable LLMs to verify their reasoning processes and continually rethink reasoning trajectories based on its verification. We introduce a structured curriculum based upon online preference learning to implement this efficiently. Specifically, as ReVISE involves two challenging tasks (i.e., self-verification and reasoning correction), we tackle each task sequentially using curriculum learning, collecting both failed and successful reasoning paths to construct preference pairs for efficient training. During inference, our approach enjoys natural test-time scaling by integrating self-verification and correction capabilities, further enhanced by our proposed confidence-aware decoding mechanism. Our experiments on various reasoning tasks demonstrate that ReVISE achieves efficient self-correction and significantly improves reasoning performance.

We present a novel approach for attacking black-box large language models (LLMs) by exploiting their ability to express confidence in natural language. Existing black-box attacks require either access to continuous model outputs like logits or confidence scores (which are rarely available in practice), or rely on proxy signals from other models. Instead, we demonstrate how to prompt LLMs to express their internal confidence in a way that is sufficiently calibrated to enable effective adversarial optimization. We apply our general method to three attack scenarios: adversarial examples for vision-LLMs, jailbreaks and prompt injections. Our attacks successfully generate malicious inputs against systems that only expose textual outputs, thereby dramatically expanding the attack surface for deployed LLMs. We further find that better and larger models exhibit superior calibration when expressing confidence, creating a concerning security paradox where model capability improvements directly enhance vulnerability. Our code is available at this [link](https://github.com/zj-jayzhang/black_box_llm_optimization).

Realistic graphs contain both (1) rich self-features of nodes and (2) informative structures of neighborhoods, jointly handled by a Graph Neural Network (GNN) in the typical setup. We propose to decouple the two modalities by Mixture of weak and strong experts (Mowst), where the weak expert is a light-weight Multi-layer Perceptron (MLP), and the strong expert is an off-the-shelf GNN. To adapt the experts' collaboration to different target nodes, we propose a "confidence" mechanism based on the dispersion of the weak expert's prediction logits. The strong expert is conditionally activated in the low-confidence region when either the node's classification relies on neighborhood information, or the weak expert has low model quality. We reveal interesting training dynamics by analyzing the influence of the confidence function on loss: our training algorithm encourages the specialization of each expert by effectively generating soft splitting of the graph. In addition, our "confidence" design imposes a desirable bias toward the strong expert to benefit from GNN's better generalization capability. Mowst is easy to optimize and achieves strong expressive power, with a computation cost comparable to a single GNN. Empirically, Mowst on 4 backbone GNN architectures show significant accuracy improvement on 6 standard node classification benchmarks, including both homophilous and heterophilous graphs (https://github.com/facebookresearch/mowst-gnn).

The hallucination of non-existent facts by LLMs is an important problem given its widespread adoption across various applications. Previous research addresses this problem by analyzing the internal parameterized knowledge boundaries to estimate confidence. However, these studies focus on the single-problem setting and have not explored the more challenging multi-problem setting, which requires accurately answering multiple questions simultaneously. We introduce a novel method for the multi-problem setting, Multiple Answers and Confidence Stepwise Tuning (MAC-Tuning), that separates the learning of answer prediction and confidence estimation during fine-tuning on instruction data. Extensive experiments demonstrate that our method outperforms baselines by up to 25\% in average precision.

Reinforcement learning (RL) has become a standard paradigm for refining large language models (LLMs) beyond pre-training and instruction tuning. A prominent line of work is RL with verifiable rewards (RLVR), which leverages automatically verifiable outcomes (e.g., correctness or executability) to generate reward signals. While efficient, this framework faces two key limitations: First, its binary feedback is too sparse to capture the quality of the reasoning process. Second, its coarse-grained rewards potentially lead to vanishing gradients. Inspired by observations from human learning, we introduce a RL technique that integrates verifiable outcomes with the model's own confidence estimates. This joint design enriches the reward signal, providing finer-grained feedback and implicitly supervising the reasoning process. Experimental results demonstrate that our proposed method enhances RL performance across multiple datasets and reduces token consumption during inference, while incurring negligible additional training cost. Moreover, it can be used as a plug-in module to enhance other state-of-the-art RL methods.

A key advance in learning generative models is the use of amortized inference distributions that are jointly trained with the models. We find that existing training objectives for variational autoencoders can lead to inaccurate amortized inference distributions and, in some cases, improving the objective provably degrades the inference quality. In addition, it has been observed that variational autoencoders tend to ignore the latent variables when combined with a decoding distribution that is too flexible. We again identify the cause in existing training criteria and propose a new class of objectives (InfoVAE) that mitigate these problems. We show that our model can significantly improve the quality of the variational posterior and can make effective use of the latent features regardless of the flexibility of the decoding distribution. Through extensive qualitative and quantitative analyses, we demonstrate that our models outperform competing approaches on multiple performance metrics.

Multimodal machine learning has achieved remarkable progress in a wide range of scenarios. However, the reliability of multimodal learning remains largely unexplored. In this paper, through extensive empirical studies, we identify current multimodal classification methods suffer from unreliable predictive confidence that tend to rely on partial modalities when estimating confidence. Specifically, we find that the confidence estimated by current models could even increase when some modalities are corrupted. To address the issue, we introduce an intuitive principle for multimodal learning, i.e., the confidence should not increase when one modality is removed. Accordingly, we propose a novel regularization technique, i.e., Calibrating Multimodal Learning (CML) regularization, to calibrate the predictive confidence of previous methods. This technique could be flexibly equipped by existing models and improve the performance in terms of confidence calibration, classification accuracy, and model robustness.

Large language models (LLMs) have demonstrated remarkable capabilities across a wide range of tasks in various domains. Despite their impressive performance, they can be unreliable due to factual errors in their generations. Assessing their confidence and calibrating them across different tasks can help mitigate risks and enable LLMs to produce better generations. There has been a lot of recent research aiming to address this, but there has been no comprehensive overview to organize it and outline the main lessons learned. The present survey aims to bridge this gap. In particular, we outline the challenges and we summarize recent technical advancements for LLM confidence estimation and calibration. We further discuss their applications and suggest promising directions for future work.

Recent feed-forward geometry foundation models have demonstrated impressive generalization by recovering depth and poses in a single forward pass. However, these models are typically constrained by a global coordinate frame assumption. This dependency becomes a significant bottleneck for long-context and streaming reconstruction, as it forces the network to maintain an arbitrary temporal origin and handle translation magnitudes that grow unbounded over time. Our solution, which we call R^3, employs relative regression. We employ a lightweight MLP to predict confidence-weighted relative constraints. These confidences serve as a unified anchor: weighting losses during training and guiding pose aggregation during inference. R^3 supports both full-context offline reconstruction and causal, bounded-memory streaming. Our evaluation in both offline and streaming settings validates the effectiveness of our relative mechanism. Project page: https://kevinxu02.github.io/r3-site

Given the broad capabilities of large language models, it should be possible to work towards a general-purpose, text-based assistant that is aligned with human values, meaning that it is helpful, honest, and harmless. As an initial foray in this direction we study simple baseline techniques and evaluations, such as prompting. We find that the benefits from modest interventions increase with model size, generalize to a variety of alignment evaluations, and do not compromise the performance of large models. Next we investigate scaling trends for several training objectives relevant to alignment, comparing imitation learning, binary discrimination, and ranked preference modeling. We find that ranked preference modeling performs much better than imitation learning, and often scales more favorably with model size. In contrast, binary discrimination typically performs and scales very similarly to imitation learning. Finally we study a `preference model pre-training' stage of training, with the goal of improving sample efficiency when finetuning on human preferences.

Autoregressive generation in large language models (LLMs) conventionally decodes from the final layer, assuming that deeper representations yield more reliable next-token predictions. We revisit this assumption by revealing a recurring Guess-Refine-Perturb dynamic: early layers form coarse guesses, intermediate layers refine reasoning-relevant semantics, and final layers can perturb these refined predictions toward generic or alignment-preferred tokens. We introduce Confident Decoding, a training-free decoding strategy that dynamically selects the most reliable near-final layer through entropy-guided conservative backward search. We further provide a theoretical formulation of layer selection as an optimal stopping problem, showing that under bounded projection noise and dominant late-stage alignment perturbation, our search rule filters perturbation while bounding the loss relative to the oracle refinement layer. Experiments across dense and Mixture-of-Experts LLMs demonstrate consistent gains on challenging reasoning benchmarks, including GPQA-Diamond, Omni-MATH, and HLE, with zero memory overhead and less than 2% latency increase. These results suggest dynamically bypassing final-layer perturbations can unlock stronger reasoning behavior from aligned LLMs.

For large language models (LLMs) to be trusted by humans they need to be well-calibrated in the sense that they can accurately assess and communicate how likely it is that their predictions are correct. Recent work has focused on the quality of internal LLM confidence assessments, but the question remains of how well LLMs can communicate this internal model confidence to human users. This paper explores the disparity between external human confidence in an LLM's responses and the internal confidence of the model. Through experiments involving multiple-choice questions, we systematically examine human users' ability to discern the reliability of LLM outputs. Our study focuses on two key areas: (1) assessing users' perception of true LLM confidence and (2) investigating the impact of tailored explanations on this perception. The research highlights that default explanations from LLMs often lead to user overestimation of both the model's confidence and its' accuracy. By modifying the explanations to more accurately reflect the LLM's internal confidence, we observe a significant shift in user perception, aligning it more closely with the model's actual confidence levels. This adjustment in explanatory approach demonstrates potential for enhancing user trust and accuracy in assessing LLM outputs. The findings underscore the importance of transparent communication of confidence levels in LLMs, particularly in high-stakes applications where understanding the reliability of AI-generated information is essential.

Real-world machine learning deployments are characterized by mismatches between the source (training) and target (test) distributions that may cause performance drops. In this work, we investigate methods for predicting the target domain accuracy using only labeled source data and unlabeled target data. We propose Average Thresholded Confidence (ATC), a practical method that learns a threshold on the model's confidence, predicting accuracy as the fraction of unlabeled examples for which model confidence exceeds that threshold. ATC outperforms previous methods across several model architectures, types of distribution shifts (e.g., due to synthetic corruptions, dataset reproduction, or novel subpopulations), and datasets (Wilds, ImageNet, Breeds, CIFAR, and MNIST). In our experiments, ATC estimates target performance 2-4times more accurately than prior methods. We also explore the theoretical foundations of the problem, proving that, in general, identifying the accuracy is just as hard as identifying the optimal predictor and thus, the efficacy of any method rests upon (perhaps unstated) assumptions on the nature of the shift. Finally, analyzing our method on some toy distributions, we provide insights concerning when it works. Code is available at https://github.com/saurabhgarg1996/ATC_code/.

The regression of 3D Human Pose and Shape (HPS) from an image is becoming increasingly accurate. This makes the results useful for downstream tasks like human action recognition or 3D graphics. Yet, no regressor is perfect, and accuracy can be affected by ambiguous image evidence or by poses and appearance that are unseen during training. Most current HPS regressors, however, do not report the confidence of their outputs, meaning that downstream tasks cannot differentiate accurate estimates from inaccurate ones. To address this, we develop POCO, a novel framework for training HPS regressors to estimate not only a 3D human body, but also their confidence, in a single feed-forward pass. Specifically, POCO estimates both the 3D body pose and a per-sample variance. The key idea is to introduce a Dual Conditioning Strategy (DCS) for regressing uncertainty that is highly correlated to pose reconstruction quality. The POCO framework can be applied to any HPS regressor and here we evaluate it by modifying HMR, PARE, and CLIFF. In all cases, training the network to reason about uncertainty helps it learn to more accurately estimate 3D pose. While this was not our goal, the improvement is modest but consistent. Our main motivation is to provide uncertainty estimates for downstream tasks; we demonstrate this in two ways: (1) We use the confidence estimates to bootstrap HPS training. Given unlabelled image data, we take the confident estimates of a POCO-trained regressor as pseudo ground truth. Retraining with this automatically-curated data improves accuracy. (2) We exploit uncertainty in video pose estimation by automatically identifying uncertain frames (e.g. due to occlusion) and inpainting these from confident frames. Code and models will be available for research at https://poco.is.tue.mpg.de.

Large language models can detect their own errors and sometimes correct them without external feedback, but the underlying mechanisms remain unknown. We investigate this through the lens of second-order models of confidence from decision neuroscience. In a first-order system, confidence derives from the generation signal itself and is therefore maximal for the chosen response, precluding error detection. Second-order models posit a partially independent evaluative signal that can disagree with the committed response, providing the basis for error detection. Kumaran et al. (2026) showed that LLMs cache a confidence representation at a token immediately following the answer (i.e. post-answer newline: PANL) -- that causally drives verbal confidence and dissociates from log-probabilities. Here we test whether this PANL signal extends beyond confidence to support error detection and self-correction. Here we test whether this signal supports error detection and self-correction, deriving predictions from the second-order framework. Using a verify-then-correct paradigm, we show that: (i) verbal confidence predicts error detection far beyond token log-probabilities, ruling out a first-order account; (ii) PANL activations predict error detection beyond verbal confidence itself; and (iii) PANL predicts which errors the model can correct -- where all behavioural signals fail. Causal interventions confirm that PANL signals rescue error detection behavior when answer information is corrupted. All findings replicate across models (Gemma 3 27B and Qwen 2.5 7B) and tasks (TriviaQA and MNLI). These results reveal that LLMs naturally implement a second-order confidence architecture whose internal evaluative signal encodes not only whether an answer is likely wrong but whether the model has the knowledge to fix it.

Accurately assessing model confidence is essential for deploying large language models (LLMs) in mission-critical factual domains. While retrieval-augmented generation (RAG) is widely adopted to improve grounding, confidence calibration in RAG settings remains poorly understood. We conduct a systematic study across four benchmarks, revealing that LLMs exhibit poor calibration performance due to noisy retrieved contexts. Specifically, contradictory or irrelevant evidence tends to inflate the model's false certainty, leading to severe overconfidence. To address this, we propose NAACL Rules (Noise-AwAre Confidence CaLibration Rules) to provide a principled foundation for resolving overconfidence under noise. We further design NAACL, a noise-aware calibration framework that synthesizes supervision from about 2K HotpotQA examples guided by these rules. By performing supervised fine-tuning (SFT) with this data, NAACL equips models with intrinsic noise awareness without relying on stronger teacher models. Empirical results show that NAACL yields substantial gains, improving ECE scores by 10.9% in-domain and 8.0% out-of-domain. By bridging the gap between retrieval noise and verbal calibration, NAACL paves the way for both accurate and epistemically reliable LLMs.

Major cloud providers have employed advanced AI-based solutions like large language models to aid humans in identifying the root causes of cloud incidents. Despite the growing prevalence of AI-driven assistants in the root cause analysis process, their effectiveness in assisting on-call engineers is constrained by low accuracy due to the intrinsic difficulty of the task, a propensity for LLM-based approaches to hallucinate, and difficulties in distinguishing these well-disguised hallucinations. To address this challenge, we propose to perform confidence estimation for the predictions to help on-call engineers make decisions on whether to adopt the model prediction. Considering the black-box nature of many LLM-based root cause predictors, fine-tuning or temperature-scaling-based approaches are inapplicable. We therefore design an innovative confidence estimation framework based on prompting retrieval-augmented large language models (LLMs) that demand a minimal amount of information from the root cause predictor. This approach consists of two scoring phases: the LLM-based confidence estimator first evaluates its confidence in making judgments in the face of the current incident that reflects its ``grounded-ness" level in reference data, then rates the root cause prediction based on historical references. An optimization step combines these two scores for a final confidence assignment. We show that our method is able to produce calibrated confidence estimates for predicted root causes, validate the usefulness of retrieved historical data and the prompting strategy as well as the generalizability across different root cause prediction models. Our study takes an important move towards reliably and effectively embedding LLMs into cloud incident management systems.

Large language models excel at reasoning but lack key aspects of introspection, including anticipating their own success and the computation required to achieve it. Humans use real-time introspection to decide how much effort to invest, when to make multiple attempts, when to stop, and when to signal success or failure. Without this, LLMs struggle to make intelligent meta-cognition decisions. Test-time scaling methods like Best-of-N drive up cost and latency by using a fixed budget of samples regardless of the marginal benefit of each one at any point in generation, and the absence of confidence signals can mislead people, prevent appropriate escalation to better tools, and undermine trustworthiness. Learned verifiers or reward models can provide confidence estimates, but do not enable adaptive inference and add substantial cost by requiring extra models or forward passes. We present ZIP-RC, which equips models with zero-overhead introspective predictions of reward and cost. At every token, ZIP-RC reuses reserved or unused logits in the same forward pass as next-token prediction to output a joint distribution over final reward and remaining length -- no extra models, architecture change, or inference overhead. This full joint distribution is used to compute a sampling utility which is the linear combination of the expected maximum reward, total compute, and latency of set of samples if generated to completion. During inference, we maximize this utility with meta-actions that determine which prefix of tokens to continue or initiate sampling from. On mixed-difficulty mathematical benchmarks, ZIP-RC improves accuracy by up to 12% over majority voting at equal or lower average cost, and traces smooth Pareto frontiers between quality, compute, and latency. By providing real-time reward-cost introspection, ZIP-RC enables adaptive, efficient reasoning.

Wild Test-Time Adaptation (WTTA) is proposed to adapt a source model to unseen domains under extreme data scarcity and multiple shifts. Previous approaches mainly focused on sample selection strategies, while overlooking the fundamental problem on underlying optimization. Initially, we critically analyze the widely-adopted entropy minimization framework in WTTA and uncover its significant limitations in noisy optimization dynamics that substantially hinder adaptation efficiency. Through our analysis, we identify region confidence as a superior alternative to traditional entropy, however, its direct optimization remains computationally prohibitive for real-time applications. In this paper, we introduce a novel region-integrated method ReCAP that bypasses the lengthy process. Specifically, we propose a probabilistic region modeling scheme that flexibly captures semantic changes in embedding space. Subsequently, we develop a finite-to-infinite asymptotic approximation that transforms the intractable region confidence into a tractable and upper-bounded proxy. These innovations significantly unlock the overlooked potential dynamics in local region in a concise solution. Our extensive experiments demonstrate the consistent superiority of ReCAP over existing methods across various datasets and wild scenarios.

Retrieval Augmented Generation (RAG) complements the knowledge of Large Language Models (LLMs) by leveraging external information to enhance response accuracy for queries. This approach is widely applied in several fields by taking its advantage of injecting the most up-to-date information, and researchers are focusing on understanding and improving this aspect to unlock the full potential of RAG in such high-stakes applications. However, despite the potential of RAG to address these needs, the mechanisms behind the confidence levels of its outputs remain underexplored, although the confidence of information is very critical in some domains, such as finance, healthcare, and medicine. Our study focuses the impact of RAG on confidence within the medical domain under various configurations and models. We evaluate confidence by treating the model's predicted probability as its output and calculating Expected Calibration Error (ECE) and Adaptive Calibration Error (ACE) scores based on the probabilities and accuracy. In addition, we analyze whether the order of retrieved documents within prompts calibrates the confidence. Our findings reveal large variation in confidence and accuracy depending on the model, settings, and the format of input prompts. These results underscore the necessity of optimizing configurations based on the specific model and conditions.

One paradigm of language model (LM) fine-tuning relies on creating large training datasets, under the assumption that high quantity and diversity will enable models to generalize to novel tasks after post-training. In practice, gathering large sets of data is inefficient, and training on them is prohibitively expensive; worse, there is no guarantee that the resulting model will handle complex scenarios or generalize better. Moreover, existing techniques rarely assess whether a training sample provides novel information or is redundant with the knowledge already acquired by the model, resulting in unnecessary costs. In this work, we explore a new test-time self-improvement method to create more effective and generalizable agentic LMs on-the-fly. The proposed algorithm can be summarized in three steps: (i) first it identifies the samples that model struggles with (self-awareness), (ii) then generates similar examples from detected uncertain samples (self-data augmentation), and (iii) uses these newly generated samples at test-time fine-tuning (self-improvement). We study two variants of this approach: Test-Time Self-Improvement (TT-SI), where the same model generates additional training examples from its own uncertain cases and then learns from them, and contrast this approach with Test-Time Distillation (TT-D), where a stronger model generates similar examples for uncertain cases, enabling student to adapt using distilled supervision. Empirical evaluations across different agent benchmarks demonstrate that TT-SI improves the performance with +5.48% absolute accuracy gain on average across all benchmarks and surpasses other standard learning methods, yet using 68x less training samples. Our findings highlight the promise of TT-SI, demonstrating the potential of self-improvement algorithms at test-time as a new paradigm for building more capable agents toward self-evolution.

Despite their vast capabilities, Large Language Models (LLMs) often struggle with generating reliable outputs, frequently producing high-confidence inaccuracies known as hallucinations. Addressing this challenge, our research introduces InternalInspector, a novel framework designed to enhance confidence estimation in LLMs by leveraging contrastive learning on internal states including attention states, feed-forward states, and activation states of all layers. Unlike existing methods that primarily focus on the final activation state, InternalInspector conducts a comprehensive analysis across all internal states of every layer to accurately identify both correct and incorrect prediction processes. By benchmarking InternalInspector against existing confidence estimation methods across various natural language understanding and generation tasks, including factual question answering, commonsense reasoning, and reading comprehension, InternalInspector achieves significantly higher accuracy in aligning the estimated confidence scores with the correctness of the LLM's predictions and lower calibration error. Furthermore, InternalInspector excels at HaluEval, a hallucination detection benchmark, outperforming other internal-based confidence estimation methods in this task.

We consider the problem of ranking n experts based on their performances on d tasks. We make a monotonicity assumption stating that for each pair of experts, one outperforms the other on all tasks. We consider the sequential setting where in each round, the learner has access to noisy evaluations of actively chosen pair of expert-task, given the information available up to the actual round. Given a confidence parameter delta in (0, 1), we provide strategies allowing to recover the correct ranking of experts and develop a bound on the total number of queries made by our algorithm that hold with probability at least 1 -- delta. We show that our strategy is adaptive to the complexity of the problem (our bounds are instance dependent), and develop matching lower bounds up to a poly-logarithmic factor. Finally, we adapt our strategy to the relaxed problem of best expert identification and provide numerical simulation consistent with our theoretical results.

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.

When answering questions, LLMs can convey not only an answer, but a level of confidence about the answer being correct. This includes explicit confidence markers (e.g. giving a numeric score) as well as implicit markers, like an authoritative tone or elaborating with additional knowledge. For LLMs to be trustworthy knowledge sources, the confidence they convey should match their actual expertise; however, most current models tend towards overconfidence. To calibrate both implicit and explicit confidence markers, we introduce a pragmatic, listener-aware finetuning method (LACIE) that models the listener, considering not only whether an answer is right, but whether it will be accepted by a listener. We cast calibration as preference optimization, creating data via a two-agent game, where a speaker model's outputs are judged by a simulated listener. We then finetune three LLMs (Mistral-7B, Llama3-8B, Llama3-70B) with LACIE, and show that the resulting models are better calibrated w.r.t. a simulated listener. Crucially, these trends transfer to human listeners, helping them correctly predict model correctness: we conduct a human evaluation where annotators accept or reject an LLM's answers, finding that training with LACIE results in 47% fewer incorrect answers being accepted while maintaining the same level of acceptance for correct answers. Furthermore, LACIE generalizes to another dataset, resulting in a large increase in truthfulness on TruthfulQA when trained on TriviaQA. Our analysis indicates that LACIE leads to a better confidence separation between correct and incorrect examples. Qualitatively, we find that a LACIE-trained model hedges more and implicitly signals certainty when it is correct by using an authoritative tone or including details. Finally, LACIE finetuning leads to an emergent increase in model abstention (e.g. saying "I don't know") for answers that are likely wrong.

Vision-language models (VLMs) often underperform on evidence intensive tasks because decisive visual evidence are small, localized, and easy to overlook, leading to failures in evidence readout even when high-level reasoning is intact. Prior inference-time visual interventions can improve grounding without retraining, but they are largely open-loop and lack a mechanism to verify whether highlighted evidence is actually used. We study answer-span prediction entropy as a model-internal feedback signal and show that naive entropy minimization is ambiguous, since low entropy may arise from evidence-grounded confidence or shortcut collapse. To resolve this ambiguity, we introduce low-entropy anchors and an entropy-shaping objective that reduces answer uncertainty while preserving baseline high-confidence tokens. We instantiate this principle in SPOT-E, a plug-and-play test-time method that produces question-conditioned spotlights, optimized per instance via light-weight tuning based on Group Relative Policy Optimization (GRPO). Across all benchmarks and different VLM families, SPOT-E yields consistent gains and improved robustness under visual corruptions. Code is publicly available at: https://github.com/YinBo0927/SPOT-E

Diffusion language models decode text by iteratively denoising masked token sequences, making the choice of which positions to decode a central inference-time decision. Most training-free decoding strategies use model confidence for position selection, assuming that high-confidence positions are ready to be decoded. In this work, we revisit this assumption by studying when confidence misleads fully non-autoregressive (fully non-AR) decoding. EOT tokens can receive high confidence and cause incomplete generation; inserting a suffix anchor can mitigate this issue but introduces local overconfidence near the anchor, causing anchor-adjacent tokens to be decoded too early. To address these issues, we propose Suffix-Anchored Confidence Modulation, a simple training-free method that inserts a short suffix anchor to encourage response completion and modulates confidence near the anchor according to decoding progress. This preserves the response-completion benefit of suffix anchoring while reducing premature decoding of anchor-adjacent tokens. Across text-only reasoning, vision-language reasoning, and code-generation benchmarks, our method consistently improves confidence-based fully non-AR decoding, outperforms explicit EOT suppression, and preserves the parallel decoding advantage of fully non-AR generation.

Masked language modeling is a widely used method for learning language representations, where the model predicts a randomly masked word in each input. However, this approach typically considers only a single correct answer during training, ignoring the variety of plausible alternatives that humans might choose. This issue becomes more pronounced when the input text is short, as the possible word distribution tends to have higher entropy, potentially causing the model to become overconfident in its predictions. To mitigate this, we propose a novel confidence regularizer that adaptively adjusts the regularization strength based on the input length. Experiments on the GLUE and SQuAD benchmarks show that our method improves both accuracy and expected calibration error

Chain-of-thought (CoT) prompting is a common technique for improving the reasoning abilities of large language models (LLMs). However, extended reasoning is often unnecessary and substantially increases token usage. As such, a key question becomes how to optimally allocate compute to when reasoning is actually needed. We study this through confidence-gated CoT, where a model produces a direct answer and a confidence estimate to decide whether to invoke CoT. We present an evaluation framework together with the first systematic study of confidence signals for this decision. We evaluate four representative confidence measures and compare them with random gating and an oracle upper bound. Experiments across two model families and diverse reasoning tasks show that existing training-free confidence measures can reduce redundant reasoning. However, we also find that the utility of individual confidence measures is inconsistent across settings. Through our evaluation framework and analysis, our study provides practical guidance toward developing and evaluating models that selectively use CoT.

A trustworthy real-world prediction system should produce well-calibrated confidence scores; that is, its confidence in an answer should be indicative of the likelihood that the answer is correct, enabling deferral to an expert in cases of low-confidence predictions. Recent studies have shown that unsupervised pre-training produces large language models (LMs) whose conditional probabilities are remarkably well-calibrated. However, the most widely-used LMs are fine-tuned with reinforcement learning from human feedback (RLHF-LMs), and some studies have suggested that RLHF-LMs produce conditional probabilities that are very poorly calibrated. In light of this perceived weakness, we conduct a broad evaluation of methods for extracting confidence scores from RLHF-LMs. For RLHF-LMs such as ChatGPT, GPT-4, and Claude, we find that verbalized confidences emitted as output tokens are typically better-calibrated than the model's conditional probabilities on the TriviaQA, SciQ, and TruthfulQA benchmarks, often reducing the expected calibration error by a relative 50%.

A correctly reconstructed distant point appears uncertain even when a frozen 3D model processes equivalent inputs because its output frame rotates fractionally. This exposes a weakness of trainingfree perturbation uncertainty: when outputs contain an unobserved symmetry, run-to-run variation potentially reflects symmetry rather than error. Existing alternatives have trade-offs: built-in confidence is outperformed in most evaluated conditions, while trained evidential heads require modelspecific supervision. For point maps, this research derives a closed-form, error-independent variance term that grows with scene extent and potentially overwhelms the desired signal. Simulation reproduces the effect; all 30 real VGGT view-sets tested exhibit its predicted |x_p|^2 signature. ReVar3R robustly registers predictions to a common similarity frame before computing per-point variance, without retraining or modifying the frozen model. Optional calibration and fusion use a held-out split. Across VGGT, π3, and MASt3R on six datasets, the same estimator on every backbone lowers AUSE below built-in confidence in 15 of 18 conditions. The staged evaluation yields 11 of 18 wins for the label-free core, 12/18 for label-free equal-weight fusion, 14/18 with held-out weights, and 15/18 when the built-in signal is included. Against a trained evidential head, the result is a trade-off: the head calibrates magnitude better and leads in its training domain, whereas ReVar3R transfers across backbones without adaptation. Its ranking improves point filtering, but it does not detect stable systematic bias, aid novel-view synthesis, or transfer calibration across domains.

Honesty alignment-the ability of large language models (LLMs) to recognize their knowledge boundaries and express calibrated confidence-is essential for trustworthy deployment. Existing methods either rely on training-free confidence estimation (e.g., token probabilities, self-consistency) or training-based calibration with correctness annotations. While effective, achieving universal honesty alignment with training-based calibration requires costly, large-scale labeling. To support annotation-efficient training, we introduce Elicitation-Then-Calibration (EliCal), a two-stage framework that first elicits internal confidence using inexpensive self-consistency supervision, then calibrates this confidence with a small set of correctness annotations. To support a large-scale study, we release HonestyBench, a benchmark covering ten free-form QA datasets with 560k training and 70k evaluation instances annotated with correctness and self-consistency signals. Experiments show that EliCal achieves near-optimal alignment with only 1k correctness annotations (0.18% of full supervision) and better alignment performance on unseen MMLU tasks than the calibration-only baseline, offering a scalable solution toward universal honesty alignment in LLMs.

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.

Driver observation models are rarely deployed under perfect conditions. In practice, illumination, camera placement and type differ from the ones present during training and unforeseen behaviours may occur at any time. While observing the human behind the steering wheel leads to more intuitive human-vehicle-interaction and safer driving, it requires recognition algorithms which do not only predict the correct driver state, but also determine their prediction quality through realistic and interpretable confidence measures. Reliable uncertainty estimates are crucial for building trust and are a serious obstacle for deploying activity recognition networks in real driving systems. In this work, we for the first time examine how well the confidence values of modern driver observation models indeed match the probability of the correct outcome and show that raw neural network-based approaches tend to significantly overestimate their prediction quality. To correct this misalignment between the confidence values and the actual uncertainty, we consider two strategies. First, we enhance two activity recognition models often used for driver observation with temperature scaling-an off-the-shelf method for confidence calibration in image classification. Then, we introduce Calibrated Action Recognition with Input Guidance (CARING)-a novel approach leveraging an additional neural network to learn scaling the confidences depending on the video representation. Extensive experiments on the Drive&Act dataset demonstrate that both strategies drastically improve the quality of model confidences, while our CARING model out-performs both, the original architectures and their temperature scaling enhancement, leading to best uncertainty estimates.

Large language models (LLMs) are increasingly used in decision-making contexts, but when they present answers without signaling low confidence, users may unknowingly act on erroneous outputs. Prior work shows that LLMs maintain internal uncertainty signals, yet their expressed confidence is often miscalibrated and poorly discriminates between correct and incorrect answers. We investigate whether supervised fine-tuning can improve models' ability to communicate uncertainty and whether such improvements generalize across tasks and domains. We fine-tune LLMs on datasets spanning general knowledge, mathematics, and open-ended trivia, and evaluate two metacognitive tasks: (1) single-question confidence estimation, where the model assigns a numeric certainty to its answer, and (2) pairwise confidence comparison, where the model selects which of two answers it is more likely to answer correctly. We assess generalization to unseen domains, including medical and legal reasoning. Results show that fine-tuning improves calibration (alignment between stated confidence and accuracy) and discrimination (higher confidence for correct vs. incorrect responses) within and across domains. However, gains are task-specific: training on single-question calibration does not transfer to pairwise comparison, and vice versa. Multitask fine-tuning yields broader gains, lowering calibration error and strengthening discrimination in out-of-domain evaluations. This suggests that uncertainty communication in LLMs is trainable but requires multitask training to generalize effectively.