Daily Papers

Confidence-based voting aggregates parallel LLM rollouts by weighting each with internal signals such as token log probabilities, and has been actively studied for single-turn reasoning. However, modern LLMs increasingly act as multi-turn search agents that retrieve and condition on external documents. In this paper, we show that confidence-based voting transfers poorly to this multi-turn setting, and identify the underlying failure reason as copy inflation: when retrieved documents are appended to an agent's context, tokens copied from those documents receive systematically inflated log probabilities. This flattens confidence scores within each question and weakens the resulting weighted vote. To address this issue, we propose Retrieval-Grounded Voting (RGV), which scores each rollout by the lexical overlap between its final answer and the documents it retrieved. By computing the signal outside the contaminated context, RGV sidesteps both token log probabilities and additional LLM calls. Across four search-agent benchmarks and five LLMs, RGV consistently outperforms confidence-based voting, with gains of up to +5.4% accuracy and +35% on minority-correct questions, where the correct answer appears in only 1-2 of 8 rollouts.

The challenge in sourcing attribution for forgery faces has gained widespread attention due to the rapid development of generative techniques. While many recent works have taken essential steps on GAN-generated faces, more threatening attacks related to identity swapping or expression transferring are still overlooked. And the forgery traces hidden in unknown attacks from the open-world unlabeled faces still remain under-explored. To push the related frontier research, we introduce a new benchmark called Open-World DeepFake Attribution (OW-DFA), which aims to evaluate attribution performance against various types of fake faces under open-world scenarios. Meanwhile, we propose a novel framework named Contrastive Pseudo Learning (CPL) for the OW-DFA task through 1) introducing a Global-Local Voting module to guide the feature alignment of forged faces with different manipulated regions, 2) designing a Confidence-based Soft Pseudo-label strategy to mitigate the pseudo-noise caused by similar methods in unlabeled set. In addition, we extend the CPL framework with a multi-stage paradigm that leverages pre-train technique and iterative learning to further enhance traceability performance. Extensive experiments verify the superiority of our proposed method on the OW-DFA and also demonstrate the interpretability of deepfake attribution task and its impact on improving the security of deepfake detection area.

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.

Recent progress in large language models (LLMs) like GPT-4 and PaLM-2 has brought significant advancements in addressing math reasoning problems. In particular, OpenAI's latest version of GPT-4, known as GPT-4 Code Interpreter, shows remarkable performance on challenging math datasets. In this paper, we explore the effect of code on enhancing LLMs' reasoning capability by introducing different constraints on the Code Usage Frequency of GPT-4 Code Interpreter. We found that its success can be largely attributed to its powerful skills in generating and executing code, evaluating the output of code execution, and rectifying its solution when receiving unreasonable outputs. Based on this insight, we propose a novel and effective prompting method, explicit code-based self-verification~(CSV), to further boost the mathematical reasoning potential of GPT-4 Code Interpreter. This method employs a zero-shot prompt on GPT-4 Code Interpreter to encourage it to use code to self-verify its answers. In instances where the verification state registers as ``False'', the model shall automatically amend its solution, analogous to our approach of rectifying errors during a mathematics examination. Furthermore, we recognize that the states of the verification result indicate the confidence of a solution, which can improve the effectiveness of majority voting. With GPT-4 Code Interpreter and CSV, we achieve an impressive zero-shot accuracy on MATH dataset (53.9\% to 84.3\%).

Large Reasoning Models have demonstrated remarkable performance with the advancement of test-time scaling techniques, which enhances prediction accuracy by generating multiple candidate responses and selecting the most reliable answer. While prior work has analyzed that internal model signals like confidence scores can partly indicate response correctness and exhibit a distributional correlation with accuracy, such distributional information has not been fully utilized to guide answer selection. Motivated by this, we propose DistriVoting, which incorporates distributional priors as another signal alongside confidence during voting. Specifically, our method (1) first decomposes the mixed confidence distribution into positive and negative components using Gaussian Mixture Models, (2) then applies a reject filter based on positive/negative samples from them to mitigate overlap between the two distributions. Besides, to further alleviate the overlap from the perspective of distribution itself, we propose SelfStepConf, which uses step-level confidence to dynamically adjust inference process, increasing the separation between the two distributions to improve the reliability of confidences in voting. Experiments across 16 models and 5 benchmarks demonstrate that our method significantly outperforms state-of-the-art approaches.

A standard technique for scaling inference-time reasoning is Self-Consistency, whereby multiple candidate answers are sampled from an LLM and the most common answer is selected. More recently, it has been shown that weighted majority voting (e.g. Confidence-Informed Self Consistency (CISC)), which assigns a confidence value to each candidate answer and chooses the answer with the largest accumulated score, tends to be more accurate on a wide range of popular benchmarks. In practice, weighted majority voting necessitates calling a critic LLM on each candidate's reasoning trace to produce the answer's confidence score. This secondary series of LLM calls greatly increases the overhead and cost of weighted majority voting, despite its potential performance benefits. To reduce this expense, we propose VecCISC, a lightweight, adaptive framework that uses a measure of semantic similarity to filter reasoning traces that are semantically equivalent to others, degenerate, or hallucinated, thus decreasing the number of candidate answers that must be evaluated by the critic. To ensure adequate experimental thoroughness, we evaluate VecCISC on five challenging, widely-adopted datasets spanning the domains of mathematics, chemistry, biology, commonsense reasoning, and the humanities. Our results demonstrate that VecCISC reduces the total token usage by 47%, while maintaining or exceeding the accuracy of CISC.

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.

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.

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.

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.

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.

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.

Generative Large Language Models (LLMs) have demonstrated remarkable performance across a wide range of tasks. Recent research has introduced Multi-Agent Debate (MAD) systems, which leverage multiple LLMs to simulate human debate and thereby improve task performance. However, while some LLMs may possess superior knowledge or reasoning capabilities for specific tasks, they often struggle to clearly communicate this advantage during debates, in part due to a lack of confidence expression. Moreover, inappropriate confidence expression can cause agents in MAD systems to either stubbornly maintain incorrect beliefs or converge prematurely on suboptimal answers, ultimately reducing debate effectiveness and overall system performance. To address these challenges, we propose incorporating confidence expression into MAD systems to allow LLMs to explicitly communicate their confidence levels. To validate this approach, we develop ConfMAD, a MAD framework that integrates confidence expression throughout the debate process. Experimental results demonstrate the effectiveness of our method, and we further analyze how confidence influences debate dynamics, offering insights into the design of confidence-aware MAD systems.

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.

The massive population election simulation aims to model the preferences of specific groups in particular election scenarios. It has garnered significant attention for its potential to forecast real-world social trends. Traditional agent-based modeling (ABM) methods are constrained by their ability to incorporate complex individual background information and provide interactive prediction results. In this paper, we introduce ElectionSim, an innovative election simulation framework based on large language models, designed to support accurate voter simulations and customized distributions, together with an interactive platform to dialogue with simulated voters. We present a million-level voter pool sampled from social media platforms to support accurate individual simulation. We also introduce PPE, a poll-based presidential election benchmark to assess the performance of our framework under the U.S. presidential election scenario. Through extensive experiments and analyses, we demonstrate the effectiveness and robustness of our framework in U.S. presidential election simulations.

Modern large language models (LLMs) have exhibited cooperative synergy on complex task-solving, and collective decision-making (CDM) is a pivotal component in LLM-based multi-agent collaboration frameworks. Our survey on 52 recent such systems uncovers a severe lack of diversity, with a heavy reliance on dictatorial and plurality voting for CDM. Through the lens of social choice theory, we scrutinize widely-adopted CDM methods and identify their limitations. To enrich current landscape of LLM-based CDM, we present GEDI, an electoral CDM module that incorporates various ordinal preferential voting mechanisms. Our empirical case study across three benchmarks shows that the integration of certain CDM methods can markedly improve the reasoning capabilities and robustness of some leading LLMs, all without requiring intricate system designs. Additionally, we find that some CDM mechanisms generate positive synergies even with as few as three agents. The voting-based methods also demonstrate robustness against single points of failure, as well as diversity in terms of hit-rate@k and subject-wise impacts.

Multi-agent debate (MAD) is widely used to improve large language model (LLM) performance through test-time scaling, yet recent work shows that vanilla MAD often underperforms simple majority vote despite higher computational cost. Studies show that, under homogeneous agents and uniform belief updates, debate preserves expected correctness and therefore cannot reliably improve outcomes. Drawing on findings from human deliberation and collective decision-making, we identify two key mechanisms missing from vanilla MAD: (i) diversity of initial viewpoints and (ii) explicit, calibrated confidence communication. We propose two lightweight interventions. First, a diversity-aware initialisation that selects a more diverse pool of candidate answers, increasing the likelihood that a correct hypothesis is present at the start of debate. Second, a confidence-modulated debate protocol in which agents express calibrated confidence and condition their updates on others' confidence. We show theoretically that diversity-aware initialisation improves the prior probability of MAD success without changing the underlying update dynamics, while confidence-modulated updates enable debate to systematically drift to the correct hypothesis. Empirically, across six reasoning-oriented QA benchmarks, our methods consistently outperform vanilla MAD and majority vote. Our results connect human deliberation with LLM-based debate and demonstrate that simple, principled modifications can substantially enhance debate effectiveness.

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.

The development of state-of-the-art systems in different applied areas of machine learning (ML) is driven by benchmarks, which have shaped the paradigm of evaluating generalisation capabilities from multiple perspectives. Although the paradigm is shifting towards more fine-grained evaluation across diverse tasks, the delicate question of how to aggregate the performances has received particular interest in the community. In general, benchmarks follow the unspoken utilitarian principles, where the systems are ranked based on their mean average score over task-specific metrics. Such aggregation procedure has been viewed as a sub-optimal evaluation protocol, which may have created the illusion of progress. This paper proposes Vote'n'Rank, a framework for ranking systems in multi-task benchmarks under the principles of the social choice theory. We demonstrate that our approach can be efficiently utilised to draw new insights on benchmarking in several ML sub-fields and identify the best-performing systems in research and development case studies. The Vote'n'Rank's procedures are more robust than the mean average while being able to handle missing performance scores and determine conditions under which the system becomes the winner.

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.

The mathematical study of voting, social choice theory, has traditionally only been applicable to choices among a few predetermined alternatives, but not to open-ended decisions such as collectively selecting a textual statement. We introduce generative social choice, a design methodology for open-ended democratic processes that combines the rigor of social choice theory with the capability of large language models to generate text and extrapolate preferences. Our framework divides the design of AI-augmented democratic processes into two components: first, proving that the process satisfies representation guarantees when given access to oracle queries; second, empirically validating that these queries can be approximately implemented using a large language model. We apply this framework to the problem of summarizing free-form opinions into a proportionally representative slate of opinion statements; specifically, we develop a democratic process with representation guarantees and use this process to portray the opinions of participants in a survey about abortion policy. In a trial with 100 representative US residents, we find that 84 out of 100 participants feel "excellently" or "exceptionally" represented by the slate of five statements we extracted.

Multi-Agent Debate~(MAD) has emerged as a promising paradigm for improving the performance of large language models through collaborative reasoning. Despite recent advances, the key factors driving MAD's effectiveness remain unclear. In this work, we disentangle MAD into two key components--Majority Voting and inter-agent Debate--and assess their respective contributions. Through extensive experiments across seven NLP benchmarks, we find that Majority Voting alone accounts for most of the performance gains typically attributed to MAD. To explain this, we propose a theoretical framework that models debate as a stochastic process. We prove that it induces a martingale over agents' belief trajectories, implying that debate alone does not improve expected correctness. Guided by these insights, we demonstrate that targeted interventions, by biasing the belief update toward correction, can meaningfully enhance debate effectiveness. Overall, our findings suggest that while MAD has potential, simple ensembling methods remain strong and more reliable alternatives in many practical settings. Code is released in https://github.com/deeplearning-wisc/debate-or-vote.

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.

Can LLMs accurately adjust their confidence when facing opposition? Building on previous studies measuring calibration on static fact-based question-answering tasks, we evaluate Large Language Models (LLMs) in a dynamic, adversarial debate setting, uniquely combining two realistic factors: (a) a multi-turn format requiring models to update beliefs as new information emerges, and (b) a zero-sum structure to control for task-related uncertainty, since mutual high-confidence claims imply systematic overconfidence. We organized 60 three-round policy debates among ten state-of-the-art LLMs, with models privately rating their confidence (0-100) in winning after each round. We observed five concerning patterns: (1) Systematic overconfidence: models began debates with average initial confidence of 72.9% vs. a rational 50% baseline. (2) Confidence escalation: rather than reducing confidence as debates progressed, debaters increased their win probabilities, averaging 83% by the final round. (3) Mutual overestimation: in 61.7% of debates, both sides simultaneously claimed >=75% probability of victory, a logical impossibility. (4) Persistent self-debate bias: models debating identical copies increased confidence from 64.1% to 75.2%; even when explicitly informed their chance of winning was exactly 50%, confidence still rose (from 50.0% to 57.1%). (5) Misaligned private reasoning: models' private scratchpad thoughts sometimes differed from their public confidence ratings, raising concerns about faithfulness of chain-of-thought reasoning. These results suggest LLMs lack the ability to accurately self-assess or update their beliefs in dynamic, multi-turn tasks; a major concern as LLMs are now increasingly deployed without careful review in assistant and agentic roles. Code for our experiments is available at https://github.com/pradyuprasad/llms_overconfidence

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.

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.

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.

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.

Large Language Models (LLMs) can produce surprisingly sophisticated estimates of their own uncertainty. However, it remains unclear to what extent this expressed confidence is tied to the reasoning, knowledge, or decision making of the model. To test this, we introduce RiskEval: a framework designed to evaluate whether models adjust their abstention policies in response to varying error penalties. Our evaluation of several frontier models reveals a critical dissociation: models are neither cost-aware when articulating their verbal confidence, nor strategically responsive when deciding whether to engage or abstain under high-penalty conditions. Even when extreme penalties render frequent abstention the mathematically optimal strategy, models almost never abstain, resulting in utility collapse. This indicates that calibrated verbal confidence scores may not be sufficient to create trustworthy and interpretable AI systems, as current models lack the strategic agency to convert uncertainty signals into optimal and risk-sensitive decisions.

FOLD-RM is an explainable machine learning classification algorithm that uses training data to create a set of classification rules. In this paper we introduce CON-FOLD which extends FOLD-RM in several ways. CON-FOLD assigns probability-based confidence scores to rules learned for a classification task. This allows users to know how confident they should be in a prediction made by the model. We present a confidence-based pruning algorithm that uses the unique structure of FOLD-RM rules to efficiently prune rules and prevent overfitting. Furthermore, CON-FOLD enables the user to provide pre-existing knowledge in the form of logic program rules that are either (fixed) background knowledge or (modifiable) initial rule candidates. The paper describes our method in detail and reports on practical experiments. We demonstrate the performance of the algorithm on benchmark datasets from the UCI Machine Learning Repository. For that, we introduce a new metric, Inverse Brier Score, to evaluate the accuracy of the produced confidence scores. Finally we apply this extension to a real world example that requires explainability: marking of student responses to a short answer question from the Australian Physics Olympiad.

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.

Generations from large language models (LLMs) can be improved by sampling and scoring multiple solutions to select a final answer. Current "sample and select" methods such as self-consistency (SC) rely on majority voting to score answers. However, when tasks have many distinct and valid answers, selection by voting requires a large number of samples. This makes SC prohibitively expensive for interactive tasks that involve generating multiple actions (answers) sequentially. After establishing that majority voting fails to provide consistent gains on such tasks, we demonstrate how to increase success rates by softening the scoring criterion. We introduce Soft Self-Consistency (SOFT-SC), which replaces SC's discontinuous scoring with a continuous score computed from model likelihoods, allowing for selection even when actions are sparsely distributed. SOFT-SC improves both performance and efficiency on long-horizon interactive tasks, requiring half as many samples as SC for comparable or better performance. For a fixed number of samples, SOFT-SC leads to a 1.3% increase over SC in absolute success rate on writing bash programs, a 6.6% increase on online shopping (WebShop), and a 4.7% increase for an interactive household game (ALFWorld). Finally, we show that SOFT-SC can be applied to both open-source and black-box models.

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.

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

Large 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.

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).

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.

AI systems are fallible, and humans can make mistakes in deciding whether to trust AI over their own judgment. Thus, improving human-AI collaboration requires understanding when, why, and how humans decide to rely on AI. We study two distinct reliance decisions: the delegation choice -- deciding when to let AI act autonomously without knowing its output, and the adoption choice -- evaluating AI suggestions and deciding how to use them. Both of these decoupled reliance patterns shape collaboration, but prior work rarely studies them together in realistic settings with the same users. We address this gap by studying collaborative human--AI teams competing in a question-answering game in which humans can choose when and how to work with AI agents to win. Our 24 matches pair 23 expert humans with 16 AI agents, capturing 387 delegation and 1440 adoption decisions. While human--AI collaboration performs better than either AI or humans alone, humans make suboptimal collaboration decisions, both under-relying on correct AI suggestions (3.9% of opportunities missed) and over-relying when AI misleads them (1.7%). Both parties contribute wrong answers: reported model confidence is near chance when humans and AI disagree, while confirmation bias drives higher under-reliance (64.5%) when an AI suggestion agrees with humans' initial incorrect answer. To close this gap, we recommend calibrated confidence, evidence-grounded explanations, and mechanisms that help users refine trust.

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.

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%.

Zero-shot LLMs are now also used for textual classification tasks, e.g., sentiment/emotion detection of a given input as a sentence/article. However, their performance can be suboptimal in such data annotation tasks. We introduce a novel technique Perceived Confidence Scoring (PCS) that evaluates LLM's confidence for its classification of an input by leveraging Metamorphic Relations (MRs). The MRs generate semantically equivalent yet textually mutated versions of the input. Following the principles of Metamorphic Testing (MT), the mutated versions are expected to have annotation labels similar to the input. By analyzing the consistency of LLM responses across these variations, PCS computes a confidence score based on the frequency of predicted labels. PCS can be used both for single LLM and multiple LLM settings (e.g., majority voting). We introduce an algorithm Perceived Differential Evolution (PDE) that determines the optimal weights assigned to the MRs and the LLMs for a classification task. Empirical evaluation shows PCS significantly improves zero-shot accuracy for Llama-3-8B-Instruct (4.96%) and Mistral-7B-Instruct-v0.3 (10.52%), with Gemma-2-9b-it showing a 9.39% gain. When combining all three models, PCS significantly outperforms majority voting by 7.75%.

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.

LLM agents act in external environments where each action changes the state that later decisions condition on, and where a single wrong step can waste interaction budget or trigger irreversible side effects long before the final failure is observed. Reliable deployment therefore requires step-level confidence estimation: a calibrated probability that each proposed action is productive, available before the action is executed. Existing LLM confidence estimators are designed to score a response from the given prompt, but agent confidence also depends on execution consequences: whether similar actions in similar situations actually advanced the task after the environment responded. We introduce the \method (\methodshort), a self-evolving critic framework in which an LLM critic accumulates evidence from its own past judgments and their observed consequences. After each trajectory, a hindsight LLM that sees the full execution feedback votes on whether each step was productive. The resulting pseudo-labels populate a memory bank from which related productive and unproductive experiences are retrieved into the critic's prompt whenever a similar step recurs. \methodshort requires no training and uses no ground truth step labels. Across three agent benchmarks and three critic backbones, \methodshort attains the best calibration (ECE and Brier) and ranking (AUC) in every dataset--critic combination, reducing ECE by up to 54% relative to the strongest training-free baseline.

Self-consistency (SC) is a widely used test-time inference technique for improving performance in chain-of-thought reasoning. It involves generating multiple responses, or samples from a large language model (LLM) and selecting the most frequent answer. This procedure can naturally be viewed as a majority vote or empirical mode estimation. Despite its effectiveness, SC is prohibitively expensive at scale when naively applied to datasets, and it lacks a unified theoretical treatment of sample efficiency and scaling behavior. In this paper, we provide the first comprehensive analysis of SC's scaling behavior and its variants, drawing on mode estimation and voting theory. We derive and empirically validate power law scaling for self-consistency across datasets, and analyze the sample efficiency for fixed-allocation and dynamic-allocation sampling schemes. From these insights, we introduce Blend-ASC, a novel variant of self-consistency that dynamically allocates samples to questions during inference, achieving state-of-the-art sample efficiency. Our approach uses 6.8x fewer samples than vanilla SC on average, outperforming both fixed- and dynamic-allocation SC baselines, thereby demonstrating the superiority of our approach in terms of efficiency. In contrast to existing variants, Blend-ASC is hyperparameter-free and can fit an arbitrary sample budget, ensuring it can be easily applied to any self-consistency application.

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.

Federated learning allows collaborative workers to solve a machine learning problem while preserving data privacy. Recent studies have tackled various challenges in federated learning, but the joint optimization of communication overhead, learning reliability, and deployment efficiency is still an open problem. To this end, we propose a new scheme named federated learning via plurality vote (FedVote). In each communication round of FedVote, workers transmit binary or ternary weights to the server with low communication overhead. The model parameters are aggregated via weighted voting to enhance the resilience against Byzantine attacks. When deployed for inference, the model with binary or ternary weights is resource-friendly to edge devices. We show that our proposed method can reduce quantization error and converges faster compared with the methods directly quantizing the model updates.

LLM inference often generates a batch of candidates for a prompt and selects one via strategies like majority voting or Best-of- N (BoN). For difficult tasks, this single-shot selection often underperforms. Consequently, evaluations commonly report Pass@k: the agent may submit up to k responses, and only the best of them is used when computing regret. Motivated by this, we study inference scaling in the more general Pass@k inference setting, and prove that neither majority voting nor BoN exhibits the desirable scaling with k and the sampling budget N. Combining the advantages of majority voting and BoN, we propose a new inference strategy called Best-of-Majority (BoM), with a pivotal step that restricts the candidates to the responses with high frequency in the N samples before selecting the top-k rewards. We prove that when the sampling budget is N=tildeOmega(C^*), the regret of BoM is O(epsilon_{opt}+epsilon_{mathrm{RM}^2C^*/k}), where C^* is the coverage coefficient, epsilon_{RM} is the estimation error of the reward model, and epsilon_{opt} is the estimation error of reward at the optimal response. We further establish a matching lower bound, certifying that our algorithm is minimax optimal. Beyond optimality, BoM has a key advantage: unlike majority voting and BoN, its performance does not degrade when increasing N. Experimental results of inference on math problems show BoM outperforming both majority voting and BoN.

The adoption of Large Language Models (LLMs) as automated evaluators (LLM-as-a-judge) has revealed critical inconsistencies in current evaluation frameworks. We identify two fundamental types of inconsistencies: (1) Score-Comparison Inconsistency, where lower-rated responses outperform higher-scored ones in pairwise comparisons, and (2) Pairwise Transitivity Inconsistency, manifested through circular preference chains (A>B>C>A) and equivalence contradictions (A=B=C\neq A). We argue that these issues come from information loss in discrete rating systems and ambiguous tie judgments during pairwise evaluation. We propose TrustJudge, a probabilistic framework that addresses these limitations through two key innovations: 1) distribution-sensitive scoring that computes continuous expectations from discrete rating probabilities, preserving information entropy for more precise scoring, and 2) likelihood-aware aggregation that resolves transitivity violations using bidirectional preference probabilities or perplexity. We also formalize the theoretical limitations of current LLM-as-a-judge frameworks and demonstrate how TrustJudge's components overcome them. When evaluated with Llama-3.1-70B-Instruct as judge using our dataset, TrustJudge reduces Score-Comparison inconsistency by 8.43% (from 23.32% to 14.89%) and Pairwise Transitivity inconsistency by 10.82% (from 15.22% to 4.40%), while maintaining higher evaluation accuracy. Our work provides the first systematic analysis of evaluation framework inconsistencies in LLM-as-a-judge paradigms, offering both theoretical insights and practical solutions for reliable automated assessment. The framework demonstrates consistent improvements across various model architectures and scales, enabling more trustworthy LLM evaluation without requiring additional training or human annotations. The codes can be found at https://github.com/TrustJudge/TrustJudge.

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.

Majority voting over multiple LLM attempts improves mathematical reasoning, but correlated errors limit the effective sample size. A natural fix is to assign different reasoning strategies to different voters. The approach, Diverse Prompt Mixer, is tested on the AIMO 3 competition: 3 models, 23+ experiments, 50 IMO-level problems, one H100 80 GB, 5-hour limit. Every prompt-level intervention fails. High-temperature sampling already decorrelates errors; weaker strategies reduce accuracy more than they reduce correlation. Across an 8-point capability gap at equal N=8 and every optimization tested, model capability dominates. The gap between the best majority-vote score (42/50) and pass@20 (~45.5) is selection loss, not prompt loss. A verifier-based selector could close it. Prompt engineering cannot.

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.

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.

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.

Test-time reinforcement learning generates multiple candidate answers via repeated rollouts and performs online updates using pseudo-labels constructed by majority voting. To reduce overhead and improve exploration, prior work introduces tree structured rollouts, which share reasoning prefixes and branch at key nodes to improve sampling efficiency. However, this paradigm still faces two challenges: (1) high entropy branching can trigger rollout collapse, where the branching budget concentrates on a few trajectories with consecutive high-entropy segments, rapidly reducing the number of effective branches; (2) early pseudo-labels are noisy and biased, which can induce self-reinforcing overfitting, causing the policy to sharpen prematurely and suppress exploration. To address these issues, we propose Entropy Confidence Hybrid Group Relative Policy Optimization (ECHO). During rollout, ECHO jointly leverages local entropy and group level confidence to adaptively control branch width, and further introduces online confidence-based pruning to terminate persistently low confidence branches, avoiding high entropy traps and mitigating collapse. During policy updates, ECHO employs confidence adaptive clipping and an entropy confidence hybrid advantage shaping approach to enhance training robustness and mitigate early stage bias. Experiments demonstrate that ECHO achieves consistent gains on multiple mathematical and visual reasoning benchmarks, and generalizes more effectively under a limited rollout budget.

Semi-supervised semantic segmentation has long turned on one question, which pseudo-labels to trust, and a generation of selection rules, dynamic thresholds, per-class curricula, soft confidence weights, answered it for the noisy, under-confident ResNet teachers of their day. Self-supervised foundation encoders change the regime: with a DINOv2 teacher, confidence saturates, so the filtering that helped a weak teacher can hurt a strong one. We propose CW-BASS v2, a saturation-aware pseudo-label selection method that reads the teacher's confidence regime rather than committing to one rule. It pairs held-out calibration, an unbiased per-class noise estimate, with a self-adaptive confidence floor that provably bounds retention away from 1, and combines them in a one-pass gate: measure the reliability of the teacher's confident set, pi_kept = Pr[correct | c >= tau], on a held-out slice, and filter strictly when it meets the confidence demanded (pi_kept >= tau), falling back to the adaptive floor otherwise. The boundary is the pre-existing operating threshold, not a value tuned to mIoU, and across six DINOv2 teachers it makes the correct strict-vs-floor call blind. CW-BASS v2 thus recovers the UniMatch V2 operating point on the saturated benchmarks by selecting strict (Pascal VOC 1/8 87.4 against its reported 87.9; Cityscapes within 0.5), and improves on it where the confident set is unreliable (pi_kept ~ 89%, ADE20K), where the floor edges ahead (+1.5 mIoU, single seed). The gate is principled because the failure it avoids is measured, not assumed: on a reliable, saturated teacher the confidence distribution's dynamic range collapses (98% of Pascal pixels >= 0.95), so an adaptive cutoff floods the retention mask and self-training decays into confirmation bias.

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 high agreement with human raters across a variety of tasks, demonstrating potential to ease the challenges of human data collection. In computational social science (CSS), researchers are increasingly leveraging LLM annotations to complement slow and expensive human annotations. Still, guidelines for collecting and using LLM annotations, without compromising the validity of downstream conclusions, remain limited. We introduce Confidence-Driven Inference: a method that combines LLM annotations and LLM confidence indicators to strategically select which human annotations should be collected, with the goal of producing accurate statistical estimates and provably valid confidence intervals while reducing the number of human annotations needed. Our approach comes with safeguards against LLM annotations of poor quality, guaranteeing that the conclusions will be both valid and no less accurate than if we only relied on human annotations. We demonstrate the effectiveness of Confidence-Driven Inference over baselines in statistical estimation tasks across three CSS settings--text politeness, stance, and bias--reducing the needed number of human annotations by over 25% in each. Although we use CSS settings for demonstration, Confidence-Driven Inference can be used to estimate most standard quantities across a broad range of NLP problems.

Scaling educational assessment with large language models requires not just accuracy, but the ability to recognize when predictions are trustworthy. Instruction-tuned models tend to be overconfident, and their reliability deteriorates as curricula evolve, making fully autonomous deployment unsafe in high-stakes settings. We introduce CHiL(L)Grader, the first automated grading framework that incorporates calibrated confidence estimation into a human-in-the-loop workflow. Using post-hoc temperature scaling, confidence-based selective prediction, and continual learning, CHiL(L)Grader automates only high-confidence predictions while routing uncertain cases to human graders, and adapts to evolving rubrics and unseen questions. Across three short-answer grading datasets, CHiL(L)Grader automatically scores 35-65% of responses at expert-level quality (QWK >= 0.80). A QWK gap of 0.347 between accepted and rejected predictions confirms the effectiveness of the confidence-based routing. Each correction cycle strengthens the model's grading capability as it learns from teacher feedback. These results show that uncertainty quantification is key for reliable AI-assisted grading.

Diffusion Large Language Models (dLLMs) represent a new paradigm beyond autoregressive modeling, offering competitive performance while naturally enabling a flexible decoding process. Specifically, dLLMs can generate tokens at arbitrary positions in parallel, endowing them with significant potential for parallel test-time scaling, which was previously constrained by severe inefficiency in autoregressive modeling. In this work, we introduce dVoting, a fast voting technique that boosts reasoning capability without training, with only an acceptable extra computational overhead. dVoting is motivated by the observation that, across multiple samples for the same prompt, token predictions remain largely consistent, whereas performance is determined by a small subset of tokens exhibiting cross-sample variability. Leveraging the arbitrary-position generation capability of dLLMs, dVoting performs iterative refinement by sampling, identifying uncertain tokens via consistency analysis, regenerating them through voting, and repeating this process until convergence. Extensive evaluations demonstrate that dVoting consistently improves performance across various benchmarks. It achieves gains of 6.22%-7.66% on GSM8K, 4.40%-7.20% on MATH500, 3.16%-14.84% on ARC-C, and 4.83%-5.74% on MMLU. Our code is available at https://github.com/fscdc/dVoting

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 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.

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.

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.

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.

Out-of-distribution (OOD) detection aims to identify OOD inputs from unknown classes, which is important for the reliable deployment of machine learning models in the open world. Various scoring functions are proposed to distinguish it from in-distribution (ID) data. However, existing methods generally focus on excavating the discriminative information from a single input, which implicitly limits its representation dimension. In this work, we introduce a novel perspective, i.e., employing different common corruptions on the input space, to expand that. We reveal an interesting phenomenon termed confidence mutation, where the confidence of OOD data can decrease significantly under the corruptions, while the ID data shows a higher confidence expectation considering the resistance of semantic features. Based on that, we formalize a new scoring method, namely, Confidence aVerage (CoVer), which can capture the dynamic differences by simply averaging the scores obtained from different corrupted inputs and the original ones, making the OOD and ID distributions more separable in detection tasks. Extensive experiments and analyses have been conducted to understand and verify the effectiveness of CoVer. The code is publicly available at: https://github.com/tmlr-group/CoVer.

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.

In legal decisions, split votes (SV) occur when judges cannot reach a unanimous decision, posing a difficulty for lawyers who must navigate diverse legal arguments and opinions. In high-stakes domains, understanding the alignment of perceived difficulty between humans and AI systems is crucial to build trust. However, existing NLP calibration methods focus on a classifier's awareness of predictive performance, measured against the human majority class, overlooking inherent human label variation (HLV). This paper explores split votes as naturally observable human disagreement and value pluralism. We collect judges' vote distributions from the European Court of Human Rights (ECHR), and present SV-ECHR, a case outcome classification (COC) dataset with SV information. We build a taxonomy of disagreement with SV-specific subcategories. We further assess the alignment of perceived difficulty between models and humans, as well as confidence- and human-calibration of COC models. We observe limited alignment with the judge vote distribution. To our knowledge, this is the first systematic exploration of calibration to human judgements in legal NLP. Our study underscores the necessity for further research on measuring and enhancing model calibration considering HLV in legal decision tasks.

Reinforcement learning (RL) has significantly enhanced the reasoning capabilities of large language models (LLMs), but its reliance on expensive human-labeled data or complex reward models severely limits scalability. While existing self-feedback methods aim to address this problem, they are constrained by the capabilities of a single model, which can lead to overconfidence in incorrect answers, reward hacking, and even training collapse. To this end, we propose Reinforcement Learning from Coevolutionary Collective Feedback (RLCCF), a novel RL framework that enables multi-model collaborative evolution without external supervision. Specifically, RLCCF optimizes the ability of a model collective by maximizing its Collective Consistency (CC), which jointly trains a diverse ensemble of LLMs and provides reward signals by voting on collective outputs. Moreover, each model's vote is weighted by its Self-Consistency (SC) score, ensuring that more confident models contribute more to the collective decision. Benefiting from the diverse output distributions and complementary abilities of multiple LLMs, RLCCF enables the model collective to continuously enhance its reasoning ability through coevolution. Experiments on four mainstream open-source LLMs across four mathematical reasoning benchmarks demonstrate that our framework yields significant performance gains, achieving an average relative improvement of 16.72\% in accuracy. Notably, RLCCF not only improves the performance of individual models but also enhances the group's majority-voting accuracy by 4.51\%, demonstrating its ability to extend the collective capability boundary of the model collective.

Confidence calibration -- the problem of predicting probability estimates representative of the true correctness likelihood -- is important for classification models in many applications. We discover that modern neural networks, unlike those from a decade ago, are poorly calibrated. Through extensive experiments, we observe that depth, width, weight decay, and Batch Normalization are important factors influencing calibration. We evaluate the performance of various post-processing calibration methods on state-of-the-art architectures with image and document classification datasets. Our analysis and experiments not only offer insights into neural network learning, but also provide a simple and straightforward recipe for practical settings: on most datasets, temperature scaling -- a single-parameter variant of Platt Scaling -- is surprisingly effective at calibrating predictions.

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.

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.

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.

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 (LLMs) have demonstrated impressive performance across various tasks, with different models excelling in distinct domains and specific abilities. Effectively combining the predictions of multiple LLMs is crucial for enhancing system robustness and performance. However, existing ensemble methods often rely on simple techniques like voting or logits ensembling, which overlook the varying confidence and reliability of models in different contexts. In this work, we propose LENS (Learning ENsemble confidence from Neural States), a novel approach that learns to estimate model confidence by analyzing internal representations. For each LLM, we train a lightweight linear confidence predictor that leverages layer-wise hidden states and normalized probabilities as inputs. This allows for more nuanced weighting of model predictions based on their context-dependent reliability. Our method does not require modifying the model parameters and requires negligible additional computation. Experimental results on multiple-choice and boolean question-answering tasks demonstrate that LENS outperforms traditional ensemble methods by a substantial margin. Our findings suggest that internal representations provide valuable signals for determining model confidence and can be effectively leveraged for ensemble learning.

We present a novel framework that improves the reliability of LLM judges by selectively augmenting LLM with auxiliary evaluation dimensions. Existing LLM judges often miss crucial evaluation dimensions because they fail to recognize the implicit standards underlying human assessments. To address this challenge, we propose the Auto-Prompt Ensemble (APE), an adaptive framework that automatically learns evaluation dimensions from its failure cases. APE incorporates a confidence-based ensemble mechanism to decide when to adopt the judgments from additional evaluation dimensions through a novel confidence estimation approach called Collective Confidence. Extensive experiments demonstrate that APE improves the reliability of LLM Judge across diverse standard benchmarks. For instance, APE enhances GPT-4o agreement rate on Reward Bench from 87.2% to 90.5% in the zero-shot setting. Overall, APE provides a principled approach for LLM Judge to leverage test-time computation, and bridge the evaluation gap between human and LLM judges.

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.

To maintain user trust, large language models (LLMs) should signal low confidence on examples where they are incorrect, instead of misleading the user. The standard approach of estimating confidence is to use the softmax probabilities of these models, but as of November 2023, state-of-the-art LLMs such as GPT-4 and Claude-v1.3 do not provide access to these probabilities. We first study eliciting confidence linguistically -- asking an LLM for its confidence in its answer -- which performs reasonably (80.5% AUC on GPT-4 averaged across 12 question-answering datasets -- 7% above a random baseline) but leaves room for improvement. We then explore using a surrogate confidence model -- using a model where we do have probabilities to evaluate the original model's confidence in a given question. Surprisingly, even though these probabilities come from a different and often weaker model, this method leads to higher AUC than linguistic confidences on 9 out of 12 datasets. Our best method composing linguistic confidences and surrogate model probabilities gives state-of-the-art confidence estimates on all 12 datasets (84.6% average AUC on GPT-4).

Generative AI has made remarkable strides to revolutionize fields such as image and video generation. These advancements are driven by innovative algorithms, architecture, and data. However, the rapid proliferation of generative models has highlighted a critical gap: the absence of trustworthy evaluation metrics. Current automatic assessments such as FID, CLIP, FVD, etc often fail to capture the nuanced quality and user satisfaction associated with generative outputs. This paper proposes an open platform GenAI-Arena to evaluate different image and video generative models, where users can actively participate in evaluating these models. By leveraging collective user feedback and votes, GenAI-Arena aims to provide a more democratic and accurate measure of model performance. It covers three arenas for text-to-image generation, text-to-video generation, and image editing respectively. Currently, we cover a total of 27 open-source generative models. GenAI-Arena has been operating for four months, amassing over 6000 votes from the community. We describe our platform, analyze the data, and explain the statistical methods for ranking the models. To further promote the research in building model-based evaluation metrics, we release a cleaned version of our preference data for the three tasks, namely GenAI-Bench. We prompt the existing multi-modal models like Gemini, GPT-4o to mimic human voting. We compute the correlation between model voting with human voting to understand their judging abilities. Our results show existing multimodal models are still lagging in assessing the generated visual content, even the best model GPT-4o only achieves a Pearson correlation of 0.22 in the quality subscore, and behaves like random guessing in others.

Basic human values represent a set of values such as security, independence, success, kindness, and pleasure, which we deem important to our lives. Each of us holds different values with different degrees of significance. Existing studies show that values of a person can be identified from their social network usage. However, the value priority of a person may change over time due to different factors such as life experiences, influence, social structure and technology. Existing studies do not conduct any analysis regarding the change of users' value from the social influence, i.e., group persuasion, form the social media usage. In our research, first, we predict users' value score by the influence of friends from their social media usage. We propose a Bounded Confidence Model (BCM) based value dynamics model from 275 different ego networks in Facebook that predicts how social influence may persuade a person to change their value over time. Then, to predict better, we use particle swarm optimization based hyperparameter tuning technique. We observe that these optimized hyperparameters produce accurate future value score. We also run our approach with different machine learning based methods and find support vector regression (SVR) outperforms other regressor models. By using SVR with the best hyperparameters of BCM model, we find the lowest Mean Squared Error (MSE) score 0.00347.

Objective estimators of multimedia quality are often judged by comparing estimates with subjective "truth data," most often via Pearson correlation coefficient (PCC) or mean-squared error (MSE). But subjective test results contain noise, so striving for a PCC of 1.0 or an MSE of 0.0 is neither realistic nor repeatable. Numerous efforts have been made to acknowledge and appropriately accommodate subjective test noise in objective-subjective comparisons, typically resulting in new analysis frameworks and figures-of-merit. We take a different approach. By making only basic assumptions, we derive bounds on PCC and MSE that can be expected for a subjective test. Consistent with intuition, these bounds are functions of subjective vote variance. When a subjective test includes vote variance information, the calculation of the bounds is easy, and in this case we say the resulting bounds are "fully data-driven." We provide two options for calculating bounds in cases where vote variance information is not available. One option is to use vote variance information from other subjective tests that do provide such information, and the second option is to use a model for subjective votes. Thus we introduce a binomial-based model for subjective votes (BinoVotes) that naturally leads to a mean opinion score (MOS) model, named BinoMOS, with multiple unique desirable properties. BinoMOS reproduces the discrete nature of MOS values and its dependence on the number of votes per file. This modeling provides vote variance information required by the PCC and MSE bounds and we compare this modeling with data from 18 subjective tests. The modeling yields PCC and MSE bounds that agree very well with those found from the data directly. These results allow one to set expectations for the PCC and MSE that might be achieved for any subjective test, even those where vote variance information is not available.

Diagnosing 802.11 packet captures requires expert protocol knowledge, is slow, inconsistent across engineers, and unscalable. LLM-based approaches sound plausible but fabricate protocol events absent from captures (especially truncated traces), produce uncalibrated confidence scores, and suffer evaluation bias when golden references are co-produced by the model under test. We introduce PROBE (Protocol Reasoning Over evidence-Based Ensembles), a multi-stage pipeline addressing all three failures. It integrates (i) deterministic PCAP-to-text normalization with frame-level verifiability, (ii) multi-run, multi-candidate ensembles with optional cross-model second opinion and progressive obfuscation, (iii) a verdict-aware evidence framework treating absence of failure evidence as contributing evidence, and (iv) a fully deterministic composite reliability score from evidence validity, run-to-run stability, and cross-model agreement without LLM self-assessment. On 87 enterprise Wi-Fi captures (104 capture-reviewer pairs), single-pass LLM analysis raises weighted evidence F1 from 0.871 (expert baseline) to 0.912 but misses critical frames in 35% of cases. Naive ensemble voting drops below baseline (0.842) as majority voting amplifies conservative verdicts: 50% of confirmed failures are misclassified as 'no issue' or 'insufficient evidence.' Adding evidence-grounded reconciliation achieves 0.957 F1, a 96% auto-accept rate, and a worst-case floor above 0.70. LLM self-reported confidence clusters at 0.95 regardless of difficulty (71% report exactly 0.95), confirming it is uninformative. We also introduce a model-agnostic evaluation framework using per-field assertion matching, eliminating circular bias from model-co-produced golden references.

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.

Language models are increasingly used in Brazil, but most evaluation remains English-centric. This paper presents Alvorada-Bench, a 4,515-question, text-only benchmark drawn from five Brazilian university entrance examinations. Evaluating twenty models under zero-shot, role-playing, and chain-of-thought prompting, producing 270,900 responses with structured self-reports of confidence, perceived difficulty, and Bloom level. The top models exceed 94% accuracy overall, but accuracy declines on Mathematics and on the engineering oriented IME and ITA exams, indicating persistent weaknesses in multi-step reasoning. Confidence is well calibrated and correlates with perceived difficulty, revealing that models can accurately assess their own certainty capabilities. A cost accuracy analysis shows that high accuracy is achievable at under $2 per 1K tokens. On ENEM 2024 the top model (O3) achieved perfect scores in Languages subject questions while even the weakest system (GPT-4.1 Nano) only underperforms humans in Mathematics. Through exams that distill decades of Brazilian educational priorities and assess millions of students yearly, Alvorada-Bench establishes whether language models can navigate the intersection of language, culture, and reasoning that defines academic readiness in Brazil.

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.

In data poisoning attacks, an adversary tries to change a model's prediction by adding, modifying, or removing samples in the training data. Recently, ensemble-based approaches for obtaining provable defenses against data poisoning have been proposed where predictions are done by taking a majority vote across multiple base models. In this work, we show that merely considering the majority vote in ensemble defenses is wasteful as it does not effectively utilize available information in the logits layers of the base models. Instead, we propose Run-Off Election (ROE), a novel aggregation method based on a two-round election across the base models: In the first round, models vote for their preferred class and then a second, Run-Off election is held between the top two classes in the first round. Based on this approach, we propose DPA+ROE and FA+ROE defense methods based on Deep Partition Aggregation (DPA) and Finite Aggregation (FA) approaches from prior work. We evaluate our methods on MNIST, CIFAR-10, and GTSRB and obtain improvements in certified accuracy by up to 3%-4%. Also, by applying ROE on a boosted version of DPA, we gain improvements around 12%-27% comparing to the current state-of-the-art, establishing a new state-of-the-art in (pointwise) certified robustness against data poisoning. In many cases, our approach outperforms the state-of-the-art, even when using 32 times less computational power.

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.

Diffusion large language models promise parallel token generation, yet inference remains bottlenecked by deciding which masked tokens can be safely committed together. Fast-dLLM addressed this with KV caching and confidence-guided parallel decoding, but its decoding theory uses a homogeneous high-confidence assumption that effectively reduces each candidate set to its weakest selected token. We argue that this leaves speed on the table because real decoding steps exhibit heterogeneous confidence profiles. We propose Fast-dLLM++, a training-free extension that introduces Fréchet profile decoding: selecting parallel commit sets from the full sorted confidence profile rather than a single worst-case confidence. The resulting rule is a heterogeneous-confidence generalization of Fast-dLLM's factor selector and it recovers the previous rule exactly in the equal-confidence case and adds a provable heterogeneity bonus when the selected tokens have uneven confidences. Fast-dLLM++ leaves the model, diffusion process, and cache implementation entirely unchanged, making it a drop-in replacement for existing Fast-dLLM decoding. Experiments on GSM8K, MATH, HumanEval, and MBPP with the LLaDA-8B model show that the theoretical improvement translates directly into empirical gains: profile-aware selection improves the accuracy--throughput frontier by exploiting safe parallelism that weakest-token rules miss, achieving up to 37\% higher throughput at comparable accuracy. Our code release is at https://github.com/Ringo-Star/FastdLLM_plusplus.

Cascades are a classical strategy to enable inference cost to vary adaptively across samples, wherein a sequence of classifiers are invoked in turn. A deferral rule determines whether to invoke the next classifier in the sequence, or to terminate prediction. One simple deferral rule employs the confidence of the current classifier, e.g., based on the maximum predicted softmax probability. Despite being oblivious to the structure of the cascade -- e.g., not modelling the errors of downstream models -- such confidence-based deferral often works remarkably well in practice. In this paper, we seek to better understand the conditions under which confidence-based deferral may fail, and when alternate deferral strategies can perform better. We first present a theoretical characterisation of the optimal deferral rule, which precisely characterises settings under which confidence-based deferral may suffer. We then study post-hoc deferral mechanisms, and demonstrate they can significantly improve upon confidence-based deferral in settings where (i) downstream models are specialists that only work well on a subset of inputs, (ii) samples are subject to label noise, and (iii) there is distribution shift between the train and test set.

This study presents PARROT (Persuasion and Agreement Robustness Rating of Output Truth), a robustness focused framework designed to measure the degradation in accuracy that occurs under social pressure exerted on users through authority and persuasion in large language models (LLMs) the phenomenon of sycophancy (excessive conformity). PARROT (i) isolates causal effects by comparing the neutral version of the same question with an authoritatively false version using a double-blind evaluation, (ii) quantifies confidence shifts toward the correct and imposed false responses using log-likelihood-based calibration tracking, and (iii) systematically classifies failure modes (e.g., robust correct, sycophantic agreement, reinforced error, stubborn error, self-correction, etc.) using an eight-state behavioral taxonomy. We evaluated 22 models using 1,302 MMLU-style multiple-choice questions across 13 domains and domain-specific authority templates. Findings show marked heterogeneity: advanced models (e.g., GPT-5, GPT-4.1, Claude Sonnet 4.5) exhibit low "follow rates" (leq 11%, GPT-5: 4\%) and minimal accuracy loss, while older/smaller models show severe epistemic collapse (GPT-4: 80\%, Qwen 2.5-1.5B: 94\%). The danger is not limited to response changes; weak models reduce confidence in the correct response while increasing confidence in the imposed incorrect response. While international law and global knowledge at the domain level exhibit high fragility, elementary mathematics is relatively resilient. Consequently, we argue that the goal of "resistance to overfitting pressure" should be addressed as a primary objective alongside accuracy, harm avoidance, and privacy for safe deployment in the real world.

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

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.

Conjoint analysis, an application of factorial experimental design, is a popular tool in social science research for studying multidimensional preferences. In such experiments in the political analysis context, respondents are asked to choose between two hypothetical political candidates with randomly selected features, which can include partisanship, policy positions, gender and race. We consider the problem of identifying optimal candidate profiles. Because the number of unique feature combinations far exceeds the total number of observations in a typical conjoint experiment, it is impossible to determine the optimal profile exactly. To address this identification challenge, we derive an optimal stochastic intervention that represents a probability distribution of various attributes aimed at achieving the most favorable average outcome. We first consider an environment where one political party optimizes their candidate selection. We then move to the more realistic case where two political parties optimize their own candidate selection simultaneously and in opposition to each other. We apply the proposed methodology to an existing candidate choice conjoint experiment concerning vote choice for US president. We find that, in contrast to the non-adversarial approach, expected outcomes in the adversarial regime fall within range of historical electoral outcomes, with optimal strategies suggested by the method more likely to match the actual observed candidates compared to strategies derived from a non-adversarial approach. These findings indicate that incorporating adversarial dynamics into conjoint analysis may yield unique insight into social science data from experiments.

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.

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.

Given a large pool of unlabelled data and a smaller amount of labels, prediction-powered inference (PPI) leverages machine learning predictions to increase the statistical efficiency of confidence interval procedures based solely on labelled data, while preserving fixed-time validity. In this paper, we extend the PPI framework to the sequential setting, where labelled and unlabelled datasets grow over time. Exploiting Ville's inequality and the method of mixtures, we propose prediction-powered confidence sequence procedures that are asymptotically valid uniformly over time and naturally accommodate prior knowledge on the quality of the predictions to further boost efficiency. We carefully illustrate the design choices behind our method and demonstrate its effectiveness in real and synthetic examples.

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

Large Language Models (LLMs) have 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.

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.

As LLMs evolve on a daily basis, there is an urgent need for a trustworthy evaluation method that can provide robust evaluation results in a timely fashion. Currently, as static benchmarks are prone to contamination concerns, users tend to trust human voting platforms, such as Chatbot Arena. However, human annotations require extensive manual efforts. To provide an automatic, robust, and trustworthy evaluation framework, we innovatively propose the Auto-Arena of LLMs, which automates the entire evaluation process with LLM agents. Firstly, an examiner LLM devises queries. Then, a pair of candidate LLMs engage in a multi-round peer-battle around the query, during which the LLM's true performance gaps become visible. Finally, a committee of LLM judges collectively discuss and determine the winner, which alleviates bias and promotes fairness. In our extensive experiment on the 17 newest LLMs, Auto-Arena shows the highest correlation with human preferences, providing a promising alternative to human evaluation platforms.

Multi-Agent Debate has emerged as a promising framework for improving the reasoning quality of large language models through iterative inter-agent communication. However, broadcasting all agent messages at every round introduces noise and redundancy that can degrade debate quality and waste computational resources. Current approaches rely on uncertainty estimation to filter low-confidence responses before broadcasting, but this approach is unreliable due to miscalibrated confidence scores and sensitivity to threshold selection. To address this, we propose Diversity-Aware Retention (DAR), a lightweight debate framework that, at each debate round, selects the subset of agent responses that maximally disagree with each other and with the majority vote before broadcasting. Through an explicit index-based retention mechanism, DAR preserves the original messages without modification, ensuring that retained disagreements remain authentic. Experiments on diverse reasoning and question answering benchmarks demonstrate that our selective message propagation consistently improves debate performance, particularly as the number of agents scales, where noise accumulation is most severe. Our results highlight that what agents hear is as important as what agents say in multi-agent reasoning systems. Code is publicly available at https://github.com/DA2I2-SLM/DAR.

Visual Emotion Comprehension (VEC) aims to infer sentiment polarities or emotion categories from affective cues embedded in images. In recent years, Multimodal Large Language Models (MLLMs) have established a popular paradigm in VEC, leveraging their generalizability to unify VEC tasks defined under diverse emotion taxonomies. While this paradigm achieves notable success, it typically formulates VEC as a deterministic task, requiring the model to output a single, definitive emotion label for each image. Such a formulation insufficiently accounts for the inherent subjectivity of emotion perception, overlooking alternative interpretations that may be equally plausible to different viewers. To address this limitation, we propose equipping MLLMs with capabilities to verbalize their confidence in emotion predictions. This additional signal provides users with an estimate of both the plausibility of alternative interpretations and the MLLMs' self-assessed competence, thereby enhancing reliability in practice. Building on this insight, we introduce a three-stage training framework that progressively endows with structured reasoning, teaches to verbalize confidence, and calibrates confidence expression, culminating in EmoCaliber, a confidence-aware MLLM for VEC. Through fair and comprehensive evaluations on the unified benchmark VECBench, EmoCaliber demonstrates overall superiority against existing methods in both emotion prediction and confidence estimation. These results validate the effectiveness of our approach and mark a feasible step toward more reliable VEC systems. Project page: https://github.com/wdqqdw/EmoCaliber.

Recent advances such as self-consistency and test-time reinforcement learning (TTRL) improve the reliability of large language models (LLMs) without additional supervision, yet their underlying mechanisms and statistical guarantees remain poorly understood. We present a unified framework for certifiable inference in LLMs, showing that majority voting provides a statistical certificate of self-consistency: under mild assumptions, the aggregated answer coincides with the mode of the model's terminal distribution with high probability. We derive finite-sample and anytime-valid concentration bounds that quantify this confidence, and introduce the Martingale Majority Certificate (MMC), a sequential stopping rule that adaptively determines when sufficient samples have been drawn. We further prove that label-free post-training methods such as TTRL implicitly sharpen the answer distribution by exponentially tilting it toward its mode, thereby reducing the number of samples required for certification. Building on this insight, we propose new post-training objectives that explicitly optimise this trade-off between sharpness and bias. Together, these results explain and connect two central test-time scaling strategies, self-consistency and TTRL, within a single statistical framework for label-free, certifiable reliability in reasoning LLMs.

Pass@k is widely used to report the reasoning performance of LLMs, but it often produces unstable and potentially misleading rankings, especially when the number of trials (samples) is limited and computational resources are constrained. We present a principled Bayesian evaluation framework that replaces Pass@k and average accuracy over N trials (avg@N) with posterior estimates of a model's underlying success probability and credible intervals, yielding stable rankings and a transparent decision rule for differences. Evaluation outcomes are modeled as categorical (not just 0/1) with a Dirichlet prior, giving closed-form expressions for the posterior mean and uncertainty of any weighted rubric and enabling the use of prior evidence when appropriate. Theoretically, under a uniform prior, the Bayesian posterior mean is order-equivalent to average accuracy (Pass@1), explaining its empirical robustness while adding principled uncertainty. Empirically, in simulations with known ground-truth success rates and on AIME'24/'25, HMMT'25, and BrUMO'25, the posterior-based procedure achieves faster convergence and greater rank stability than Pass@k and recent variants, enabling reliable comparisons at far smaller sample counts. The framework clarifies when observed gaps are statistically meaningful (non-overlapping credible intervals) versus noise, and it naturally extends to graded, rubric-based evaluations. Together, these results recommend replacing Pass@k for LLM evaluation and ranking with a posterior-based, compute-efficient protocol that unifies binary and non-binary evaluation while making uncertainty explicit. Source code is available at https://github.com/mohsenhariri/scorio

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.

Organizations deploying AI face two fundamental governance challenges: managing AI risk and sustaining AI value. Both depend on evidence whose sufficiency cannot be taken for granted. We call the shared underlying challenge the AI Evaluability Gap: the condition in which organizations lack sufficient evidence to support high-confidence governance decisions regarding either risk or value. We argue that this gap reflects a category error in current practice. Existing governance approaches focus primarily on properties of systems, such as safety, fairness, reliability, compliance, and value, while paying comparatively little attention to the evidentiary foundations required to justify decisions about those properties. We further argue that AI governance encompasses both operational decisions regarding whether a system may operate and investment decisions regarding whether it merits continued organizational resources. To address this problem, we introduce Evaluability, defined as the capability of a system to generate, maintain, and renew evidence sufficient to support high-confidence governance decisions over time. We formalize governance decisions as functions of calibrated confidence Conf(D|E) and identify six properties of evaluable evidence: observability, attributability, intervenability, verifiability, calibration, and temporal validity. The framework distinguishes Operational Certification, which relies primarily on structural evidence to justify deployment decisions, from Investment Certification, which relies primarily on causal evidence to justify continued resource allocation. We argue that evidence sufficiency is a missing layer of AI governance and that closing the AI Evaluability Gap is a prerequisite for both managing risk and sustaining value in AI-enabled organizations.

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.

User-generated contents (UGCs) on online platforms allow marketing researchers to understand consumer preferences for products and services. With the advance of large language models (LLMs), some studies utilized the models for annotation and sentiment analysis. However, the relationship between the accuracy and the hyper-parameters of LLMs is yet to be thoroughly examined. In addition, the issues of variability and reproducibility of results from each trial of LLMs have rarely been considered in existing literature. Since actual human annotation uses majority voting to resolve disagreements among annotators, this study introduces a majority voting mechanism to a sentiment analysis model using local LLMs. By a series of three analyses of online reviews on restaurant evaluations, we demonstrate that majority voting with multiple attempts using a medium-sized model produces more robust results than using a large model with a single attempt. Furthermore, we conducted further analysis to investigate the effect of each aspect on the overall evaluation.

Scaling the test-time compute of large language models has demonstrated impressive performance on reasoning benchmarks. However, existing evaluations of test-time scaling make the strong assumption that a reasoning system should always give an answer to any question provided. This overlooks concerns about whether a model is confident in its answer, and whether it is appropriate to always provide a response. To address these concerns, we extract confidence scores during reasoning for thresholding model responses. We find that increasing compute budget at inference time not only helps models answer more questions correctly, but also increases confidence in correct responses. We then extend the current paradigm of zero-risk responses during evaluation by considering settings with non-zero levels of response risk, and suggest a recipe for reporting evaluations under these settings.

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

Large language models can arrive at the same answer through reasoning paths that are unstable, contradictory, or difficult to rank consistently -- a failure mode especially prevalent in multi-step deductive reasoning. Existing methods assess reliability primarily through output dispersion -- measuring how much sampled answers differ -- but this discards a complementary signal: whether the model can consistently rank competing reasoning candidates. We propose structural uncertainty, a consistency-aware framework derived from the stability of self-preference-induced rankings over sampled reasoning solutions. Given a query, we generate multiple candidate solutions and ask the model to judge pairwise preferences among its own outputs. We aggregate self-preferences into ranking distributions via Bradley-Terry modeling with PageRank, and decompose the signal into two entropy-based components: across-trial ranking instability and within-trial candidate ambiguity. Across five LLMs and eight benchmarks, structural signals provide information complementary to answer dispersion: on logical and mathematical reasoning tasks, the combination improves identification of unreliable instances, while on factual retrieval the structural signal collapses toward uniformity, diagnosing a regime boundary where reasoning-level consistency evaluation is uninformative. The two components relate differently to accuracy: within-trial ambiguity correlates positively with correctness -- consistent with settings where multiple plausible solution paths remain competitive -- while across-trial instability correlates negatively, signaling unreliable reasoning. Structural uncertainty is best understood not as a universal confidence estimator, but as a regime-sensitive evaluator of logical reasoning consistency.

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.

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.

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.

Ensembling Vision-Language Models (VLMs) from different providers maximizes benchmark accuracy, yet models from the same architectural family share correlated errors that standard voting ignores. We study this structure across 17 VLMs from 8 families on VQAv2, TextVQA, and GQA. Family-correlated errors reduce effective ensemble dimensionality to 2.5-3.6 independent voters and create a Misleading tier (1.5-6.5% of questions) where correlated majority errors destroy accuracy to 0% despite the best model being correct. We propose three family-aware methods. Hierarchical Family Voting (HFV) aggregates within families before voting across them, recovering +18-26 pp on the Misleading tier. QualRCCV, a training-free method weighting models by calibration, family quality, and inverse family size, is the first to beat calibrated voting on all three benchmarks (p<0.05). Learned Candidate Scoring (LCS) trains a cross-validated classifier to re-rank candidate answers using support breadth, family diversity, and model quality, achieving the largest gains: +0.68% VQAv2, +0.61% TextVQA, +2.45% GQA -- all significant -- and is the only learned method that never degrades any benchmark. On VQAv2 test-standard (EvalAI), LCS reaches 87.83% with 12 models, confirming generalization.

We present Turn, a compiled, actor-based programming language -- statically typed for schema inference, dynamically typed at the value level -- for agentic software: programs that reason and act autonomously by delegating inference to large language models (LLMs). Existing approaches augment general-purpose languages with frameworks, encoding critical invariants (bounded context, typed inference output, credential isolation, durable state) as application-level conventions rather than language guarantees. Turn introduces five language-level constructs that address this gap. Cognitive Type Safety makes LLM inference a typed primitive: the compiler generates a JSON Schema from a struct definition and the VM validates model output before binding. The confidence operator enables deterministic control flow gated on model certainty. Turn's actor-based process model, derived from Erlang, gives each agent an isolated context window, persistent memory, and mailbox. A capability-based identity system returns opaque, unforgeable handles from the VM host, ensuring raw credentials never enter agent memory. Finally, compile-time schema absorption (use schema::<protocol>) synthesizes typed API bindings from external specifications at compile time; the openapi adapter is shipped with graphql, fhir, and mcp in active development. We describe the language design, type rules, schema semantics, and a Rust-based bytecode VM, and evaluate Turn against representative agentic workloads. Turn is open source at https://github.com/ekizito96/Turn.

While significant advances exist in pseudo-label generation for semi-supervised semantic segmentation, pseudo-label selection remains understudied. Existing methods typically use fixed confidence thresholds to retain high-confidence predictions as pseudo-labels. However, these methods cannot cope with network overconfidence tendency, where correct and incorrect predictions overlap significantly in high-confidence regions, making separation challenging and amplifying model cognitive bias. Meanwhile, the direct discarding of low-confidence predictions disrupts spatial-semantic continuity, causing critical context loss. We propose Confidence Separable Learning (CSL) to address these limitations. CSL formulates pseudo-label selection as a convex optimization problem within the confidence distribution feature space, establishing sample-specific decision boundaries to distinguish reliable from unreliable predictions. Additionally, CSL introduces random masking of reliable pixels to guide the network in learning contextual relationships from low-reliability regions, thereby mitigating the adverse effects of discarding uncertain predictions. Extensive experimental results on the Pascal, Cityscapes, and COCO benchmarks show that CSL performs favorably against state-of-the-art methods. Code and model weights are available at https://github.com/PanLiuCSU/CSL.

Large Language Models (LLMs) are increasingly deployed in high-stakes domains such as science, law, and healthcare, where accurate expressions of uncertainty are essential for reliability and trust. However, current LLMs are often observed to generate incorrect answers with high confidence, a phenomenon known as "overconfidence". Recent efforts have focused on calibrating LLMs' verbalized confidence: i.e., their expressions of confidence in text form, such as "I am 80% confident that...". Existing approaches either rely on prompt engineering or fine-tuning with heuristically generated uncertainty estimates, both of which have limited effectiveness and generalizability. Motivated by the notion of proper scoring rules for calibration in classical machine learning models, we introduce ConfTuner, a simple and efficient fine-tuning method that introduces minimal overhead and does not require ground-truth confidence scores or proxy confidence estimates. ConfTuner relies on a new loss function, tokenized Brier score, which we theoretically prove to be a proper scoring rule, intuitively meaning that it "correctly incentivizes the model to report its true probability of being correct". ConfTuner improves calibration across diverse reasoning tasks and generalizes to black-box models such as GPT-4o. Our results further show that better-calibrated confidence enables downstream gains in self-correction and model cascade, advancing the development of trustworthy LLM systems. The code is available at https://github.com/liushiliushi/ConfTuner.

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

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}.

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.