Daily Papers

Large language models (LLMs) excel at many language understanding tasks but struggle to reason over knowledge that evolves. To address this, recent work has explored augmenting LLMs with knowledge graphs (KGs) to provide structured, up-to-date information. However, many existing approaches assume a static snapshot of the KG and overlook the temporal dynamics and factual inconsistencies inherent in real-world data. To address the challenge of reasoning over temporally shifting knowledge, we propose EvoReasoner, a temporal-aware multi-hop reasoning algorithm that performs global-local entity grounding, multi-route decomposition, and temporally grounded scoring. To ensure that the underlying KG remains accurate and up-to-date, we introduce EvoKG, a noise-tolerant KG evolution module that incrementally updates the KG from unstructured documents through confidence-based contradiction resolution and temporal trend tracking. We evaluate our approach on temporal QA benchmarks and a novel end-to-end setting where the KG is dynamically updated from raw documents. Our method outperforms both prompting-based and KG-enhanced baselines, effectively narrowing the gap between small and large LLMs on dynamic question answering. Notably, an 8B-parameter model using our approach matches the performance of a 671B model prompted seven months later. These results highlight the importance of combining temporal reasoning with KG evolution for robust and up-to-date LLM performance. Our code is publicly available at github.com/junhongmit/TREK.

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.

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.

Retrieval-Augmented Generation (RAG) integrates large language models (LLMs) with external sources, but unresolved contradictions in retrieved evidence often lead to hallucinations and legally unsound outputs. Benchmarks currently used for contradiction detection lack domain realism, cover only limited conflict types, and rarely extend beyond single-sentence pairs, making them unsuitable for legal applications. Controlled generation of documents with embedded contradictions is therefore essential: it enables systematic stress-testing of models, ensures coverage of diverse conflict categories, and provides a reliable basis for evaluating contradiction detection and resolution. We present a multi-agent contradiction-aware benchmark framework for the legal domain that generates synthetic legal-style documents, injects six structured contradiction types, and models both self- and pairwise inconsistencies. Automated contradiction mining is combined with human-in-the-loop validation to guarantee plausibility and fidelity. This benchmark offers one of the first structured resources for contradiction-aware evaluation in legal RAG pipelines, supporting more consistent, interpretable, and trustworthy systems.

Current artificial intelligence systems exhibit a fundamental architectural limitation: they resolve ambiguity prematurely. This premature semantic collapse--collapsing multiple valid interpretations into single outputs--stems from classical identity assumptions in neural architectures. We propose Non-Resolution Reasoning (NRR), a framework treating ambiguity retention as a valid reasoning mode. NRR introduces three principles: (1) Non-Identity (A neq A)--the same symbol refers to different entities across contexts; (2) Approximate Identity (A approx A)--entities share partial structural overlap without being identical; (3) Non-Resolution--conflicting interpretations coexist without forced convergence. We formalize these through Multi-Vector Embeddings for context-dependent representation, Non-Collapsing Attention for parallel interpretation retention, and Contextual Identity Tracking (CIT) for maintaining A neq A across inference. We illustrate NRR through case studies in paradox handling, creative generation, and context-dependent reasoning. Functional verification in a synthetic two-turn disambiguation task shows NRR-lite maintains high entropy (H = 0.91 bits, near-maximum 1.0) at ambiguous turns while standard architectures collapse early (H = 0.15 bits), preserving interpretive flexibility until context arrives. NRR challenges the assumption that meaning must collapse to be useful. The question is not whether AI should resolve ambiguity, but when, how, and under whose control.

Large language models (LLMs) can exhibit advanced reasoning yet still generate incorrect answers. We hypothesize that such errors frequently stem from spurious beliefs, propositions the model internally considers true but are incorrect. To address this, we propose a method to rectify the belief space by suppressing these spurious beliefs while simultaneously enhancing true ones, thereby enabling more reliable inferences. Our approach first identifies the beliefs that lead to incorrect or correct answers by prompting the model to generate textual explanations, using our Forward-Backward Beam Search (FBBS). We then apply unlearning to suppress the identified spurious beliefs and enhance the true ones, effectively rectifying the model's belief space. Empirical results on multiple QA datasets and LLMs show that our method corrects previously misanswered questions without harming overall model performance. Furthermore, our approach yields improved generalization on unseen data, suggesting that rectifying a model's belief space is a promising direction for mitigating errors and enhancing overall reliability.

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

Large 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.

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.

While large language models (LLMs) are proficient at question-answering (QA), it is not always clear how (or even if) an answer follows from their latent "beliefs". This lack of interpretability is a growing impediment to widespread use of LLMs. To address this, our goals are to make model beliefs and their inferential relationships explicit, and to resolve inconsistencies that may exist, so that answers are supported by interpretable chains of reasoning drawn from a consistent network of beliefs. Our approach, which we call REFLEX, is to add a rational, self-reflecting layer on top of the LLM. First, given a question, we construct a belief graph using a backward-chaining process to materialize relevant model beliefs (including beliefs about answer candidates) and their inferential relationships. Second, we identify and minimize contradictions in that graph using a formal constraint reasoner. We find that REFLEX significantly improves consistency (by 8%-11% absolute) without harming overall answer accuracy, resulting in answers supported by faithful chains of reasoning drawn from a more consistent belief system. This suggests a new style of system architecture in which an LLM extended with a rational layer can provide an interpretable window into system beliefs, add a systematic reasoning capability, and repair latent inconsistencies present in the LLM.

Large language models (large LMs) are susceptible to producing text with hallucinated content. Self-contradiction, where the LM generates two contradictory sentences within the same context, is an important form of hallucination. In this work, we present a comprehensive analysis on self-contradiction for state-of-the-art, instruction-tuned LMs, including evaluation, detection, and mitigation. To effectively trigger self-contradictions, we design a framework that constrains LMs to generate appropriate sentence pairs. Our evaluation on these sentence pairs reveals that self-contradictions occur frequently across different LMs for both famous and lesser-known topics. Next, we prompt the LMs to detect self-contradictions. Our results indicate that ChatGPT and GPT-4 are able to accurately identify self-contradictions, while Vicuna-13B struggles to do so. For example, with our best prompting method, ChatGPT achieves 91.0% precision and 80.5% recall on the sentence pairs generated by itself. To automatically mitigate self-contradictions, we develop an iterative algorithm that prompts the LMs to remove the detected self-contradictions from the generated text. Our algorithm successfully revises the text such that self-contradictions are significantly reduced, while maintaining its fluency and informativeness. Importantly, our entire pipeline of triggering, detecting, and mitigating self-contradictions is applicable to black-box LMs and does not require any external grounded knowledge.

As LLMs generate increasingly long outputs, effective uncertainty estimation must identify errors at fine-grained levels rather than discard entire responses. While such methods exist, evaluating uncertainty at any resolution (token to an entire generation) is challenging and highly sensitive to label imperfections, making zero-noise benchmarks essential; yet, long-form generation benchmarks tend to rely on fallible labels rather than deterministic ground truth. We introduce Single-answer Atomic Long-form Target (SALT), a benchmark of six procedurally generated tasks with single deterministic long textual ground truths, enabling unit-level evaluation of correctness, calibration, and ranking without external judges. Equipped with SALT, our analysis of 50+ LLMs reveals key insights: We identify which confidence functions dominate each uncertainty aspect and show that confidence ranking largely breaks at atomic resolution, even when clearer separability emerges at coarser line-level units. SALT further enables controlled atom-level interventions throughout generation, revealing two separable drivers of future errors: propagation from corrupted prefixes, dominated by global context correctness, and bounded degradation from increasing answer-context length. Finally, we demonstrate that reasoning, via Chain-of-Thought prompting or internalized through training, introduces a trade-off, improving accuracy while degrading confidence ranking. These findings directly impact risk-critical applications requiring reliable error identification and mitigation.

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

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.

To quantify how well natural language understanding models can capture consistency in a general conversation, we introduce the DialoguE COntradiction DEtection task (DECODE) and a new conversational dataset containing both human-human and human-bot contradictory dialogues. We then compare a structured utterance-based approach of using pre-trained Transformer models for contradiction detection with the typical unstructured approach. Results reveal that: (i) our newly collected dataset is notably more effective at providing supervision for the dialogue contradiction detection task than existing NLI data including those aimed to cover the dialogue domain; (ii) the structured utterance-based approach is more robust and transferable on both analysis and out-of-distribution dialogues than its unstructured counterpart. We also show that our best contradiction detection model correlates well with human judgments and further provide evidence for its usage in both automatically evaluating and improving the consistency of state-of-the-art generative chatbots.

Though chatbots based on large neural models can often produce fluent responses in open domain conversations, one salient error type is contradiction or inconsistency with the preceding conversation turns. Previous work has treated contradiction detection in bot responses as a task similar to natural language inference, e.g., detect the contradiction between a pair of bot utterances. However, utterances in conversations may contain co-references or ellipsis, and using these utterances as is may not always be sufficient for identifying contradictions. This work aims to improve the contradiction detection via rewriting all bot utterances to restore antecedents and ellipsis. We curated a new dataset for utterance rewriting and built a rewriting model on it. We empirically demonstrate that this model can produce satisfactory rewrites to make bot utterances more complete. Furthermore, using rewritten utterances improves contradiction detection performance significantly, e.g., the AUPR and joint accuracy scores (detecting contradiction along with evidence) increase by 6.5% and 4.5% (absolute increase), respectively.

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.

With the widespread adoption of large language models (LLMs), hallucinations, which are non-factual fabrications in model outputs, have become serious concerns. Reasoning capabilities have received attention as a self-verification process to improve output reliability. However, the effect of reasoning within a closed system where LLMs cannot rely on external tools or knowledge has yet to be clarified. We therefore conduct experiments under strict constraints (recommending peer-reviewed journal articles in computer science) to examine the effect of reasoning across multiple models (GPT-5.2 and Gemini 3 Flash). Our results reveal a problematic trade-off between constraint compliance and factual accuracy. Non-reasoning models exhibit high constraint violation rates (66-75%) but maintain factual accuracy, while reasoning models reduce violations (13-26%) but systematically distort known facts to satisfy constraints and increase complete fabrication. This trade-off pattern is consistent across both models despite different architectures, indicating a fundamental limitation of reasoning. Furthermore, reasoning does not uniformly improve output authenticity: effects diverge by model, reflecting different allocations of the compliance-truthfulness trade-off. These findings challenge the assumption that reasoning universally improves reliability: reasoning models trade honest constraint violations for detection-resistant distortions.

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.

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.

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.

The rise of large language models (LLMs) has significantly influenced the quality of information in decision-making systems, leading to the prevalence of AI-generated content and challenges in detecting misinformation and managing conflicting information, or "inter-evidence conflicts." This study introduces a method for generating diverse, validated evidence conflicts to simulate real-world misinformation scenarios. We evaluate conflict detection methods, including Natural Language Inference (NLI) models, factual consistency (FC) models, and LLMs, on these conflicts (RQ1) and analyze LLMs' conflict resolution behaviors (RQ2). Our key findings include: (1) NLI and LLM models exhibit high precision in detecting answer conflicts, though weaker models suffer from low recall; (2) FC models struggle with lexically similar answer conflicts, while NLI and LLM models handle these better; and (3) stronger models like GPT-4 show robust performance, especially with nuanced conflicts. For conflict resolution, LLMs often favor one piece of conflicting evidence without justification and rely on internal knowledge if they have prior beliefs.

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

Large language models (LLMs) are prone to hallucinations in question-answering (QA) tasks when faced with ambiguous questions. Users often assume that LLMs share their cognitive alignment, a mutual understanding of context, intent, and implicit details, leading them to omit critical information in the queries. However, LLMs generate responses based on assumptions that can misalign with user intent, which may be perceived as hallucinations if they misalign with the user's intent. Therefore, identifying those implicit assumptions is crucial to resolve ambiguities in QA. Prior work, such as AmbigQA, reduces ambiguity in queries via human-annotated clarifications, which is not feasible in real application. Meanwhile, ASQA compiles AmbigQA's short answers into long-form responses but inherits human biases and fails capture explicit logical distinctions that differentiates the answers. We introduce Conditional Ambiguous Question-Answering (CondAmbigQA), a benchmark with 200 ambiguous queries and condition-aware evaluation metrics. Our study pioneers the concept of ``conditions'' in ambiguous QA tasks, where conditions stand for contextual constraints or assumptions that resolve ambiguities. The retrieval-based annotation strategy uses retrieved Wikipedia fragments to identify possible interpretations for a given query as its conditions and annotate the answers through those conditions. Such a strategy minimizes human bias introduced by different knowledge levels among annotators. By fixing retrieval results, CondAmbigQA evaluates how RAG systems leverage conditions to resolve ambiguities. Experiments show that models considering conditions before answering improve performance by 20%, with an additional 5% gain when conditions are explicitly provided. These results underscore the value of conditional reasoning in QA, offering researchers tools to rigorously evaluate ambiguity resolution.

Despite significant strides in factual reliability, errors -- often termed hallucinations -- remain a major concern for generative AI, especially as LLMs are increasingly expected to be helpful in more complex or nuanced setups. Yet even in the simplest setting -- factoid question-answering with clear ground truth-frontier models without external tools continue to hallucinate. We argue that most factuality gains in this domain have come from expanding the model's knowledge boundary (encoding more facts) rather than improving awareness of that boundary (distinguishing known from unknown). We conjecture that the latter is inherently difficult: models may lack the discriminative power to perfectly separate truths from errors, creating an unavoidable tradeoff between eliminating hallucinations and preserving utility. This tradeoff dissolves under a different framing. If we understand hallucinations as confident errors -- incorrect information delivered without appropriate qualification -- a third path emerges beyond the answer-or-abstain dichotomy: expressing uncertainty. We propose faithful uncertainty: aligning linguistic uncertainty with intrinsic uncertainty. This is one facet of metacognition -- the ability to be aware of one's own uncertainty and to act on it. For direct interaction, acting on uncertainty means communicating it honestly; for agentic systems, it becomes the control layer governing when to search and what to trust. Metacognition is thus essential for LLMs to be both trustworthy and capable; we conclude by highlighting open problems for progress towards this objective.

Retrieval-augmented language models are being increasingly tasked with subjective, contentious, and conflicting queries such as "is aspartame linked to cancer". To resolve these ambiguous queries, one must search through a large range of websites and consider "which, if any, of this evidence do I find convincing?". In this work, we study how LLMs answer this question. In particular, we construct ConflictingQA, a dataset that pairs controversial queries with a series of real-world evidence documents that contain different facts (e.g., quantitative results), argument styles (e.g., appeals to authority), and answers (Yes or No). We use this dataset to perform sensitivity and counterfactual analyses to explore which text features most affect LLM predictions. Overall, we find that current models rely heavily on the relevance of a website to the query, while largely ignoring stylistic features that humans find important such as whether a text contains scientific references or is written with a neutral tone. Taken together, these results highlight the importance of RAG corpus quality (e.g., the need to filter misinformation), and possibly even a shift in how LLMs are trained to better align with human judgements.

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

Large language models (LLMs) 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.

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.

Existing metrics for factuality and faithfulness evaluate whether an answer is supported or contradicted by its grounding documents, but they fail to capture when both supporting and contradicting evidence coexist. We introduce ConflictScore, a novel metric that quantifies how well a model's response acknowledges conflicting evidence in its grounding documents. Our framework decomposes responses into atomic claims, labels each claim against each grounding document, and then aggregates these labels into two complementary measures: ConflictScore-Count (CS-C), the proportion of claims exhibiting conflicts, and ConflictScore-Ratio (CS-R), the balance between supporting and contradicting evidence. We develop ConflictBench, a benchmark covering diverse forms of conflicts such as ambiguity, contradiction, and divergent opinions, to systematically evaluate our metric. Experiments show that ConflictScore effectively detects overconfident claims across domains and can serve as a corrective feedback mechanism that improves truthfulness on TruthfulQA.

Large language models (LLMs) define a distribution over text, which can be viewed as a probabilistic representation of uncertainty: sampling K responses yields a belief state - responses a model deems plausible. Existing work exploits this representation for narrow tasks like either decoding or selective prediction, and often requires manual interventions, not controlling generation directly. We propose Belief-Augmented Generation (BAG): grounding LLMs in their own belief state via the prompt and letting them reason over these K samples to decide on a conversational strategy: answer, clarify, or abstain. In a multi-turn ambiguous QA setting, we find that LLMs by default rarely clarify or abstain, ignoring uncertainty about the input or facts. BAG improves QA accuracy across six models and yields strategy decisions more faithful to the belief state than prompt-only baselines. Disentangling when to clarify from when to abstain, however, remains challenging.

Large Language Models (LLMs) have limited performance when solving arithmetic reasoning tasks and often provide incorrect answers. Unlike natural language understanding, math problems typically have a single correct answer, making the task of generating accurate solutions more challenging for LLMs. To the best of our knowledge, we are not aware of any LLMs that indicate their level of confidence in their responses which fuels a trust deficit in these models impeding their adoption. To address this deficiency, we propose `MathPrompter', a technique that improves performance of LLMs on arithmetic problems along with increased reliance in the predictions. MathPrompter uses the Zero-shot chain-of-thought prompting technique to generate multiple Algebraic expressions or Python functions to solve the same math problem in different ways and thereby raise the confidence level in the output results. This is in contrast to other prompt based CoT methods, where there is no check on the validity of the intermediate steps followed. Our technique improves over state-of-the-art on the MultiArith dataset (78.7%rightarrow92.5%) evaluated using 175B parameter GPT-based LLM.

We present BIS Reasoning 1.0, the first large-scale Japanese dataset of syllogistic reasoning problems explicitly designed to evaluate belief-inconsistent reasoning in large language models (LLMs). Unlike prior datasets such as NeuBAROCO and JFLD, which focus on general or belief-aligned reasoning, BIS Reasoning 1.0 introduces logically valid yet belief-inconsistent syllogisms to uncover reasoning biases in LLMs trained on human-aligned corpora. We benchmark state-of-the-art models - including GPT models, Claude models, and leading Japanese LLMs - revealing significant variance in performance, with GPT-4o achieving 79.54% accuracy. Our analysis identifies critical weaknesses in current LLMs when handling logically valid but belief-conflicting inputs. These findings have important implications for deploying LLMs in high-stakes domains such as law, healthcare, and scientific literature, where truth must override intuitive belief to ensure integrity and safety.

Automated reasoning with unstructured natural text is a key requirement for many potential applications of NLP and for developing robust AI systems. Recently, Language Models (LMs) have demonstrated complex reasoning capacities even without any finetuning. However, existing evaluation for automated reasoning assumes access to a consistent and coherent set of information over which models reason. When reasoning in the real-world, the available information is frequently inconsistent or contradictory, and therefore models need to be equipped with a strategy to resolve such conflicts when they arise. One widely-applicable way of resolving conflicts is to impose preferences over information sources (e.g., based on source credibility or information recency) and adopt the source with higher preference. In this paper, we formulate the problem of reasoning with contradictory information guided by preferences over sources as the classical problem of defeasible reasoning, and develop a dataset called BoardgameQA for measuring the reasoning capacity of LMs in this setting. BoardgameQA also incorporates reasoning with implicit background knowledge, to better reflect reasoning problems in downstream applications. We benchmark various LMs on BoardgameQA and the results reveal a significant gap in the reasoning capacity of state-of-the-art LMs on this problem, showing that reasoning with conflicting information does not surface out-of-the-box in LMs. While performance can be improved with finetuning, it nevertheless remains poor.

Natural language reasoning plays an increasingly important role in improving language models' ability to solve complex language understanding tasks. An interesting use case for reasoning is the resolution of context-dependent ambiguity. But no resources exist to evaluate how well Large Language Models can use explicit reasoning to resolve ambiguity in language. We propose to use ambiguous definite descriptions for this purpose and create and publish the first benchmark dataset consisting of such phrases. Our method includes all information required to resolve the ambiguity in the prompt, which means a model does not require anything but reasoning to do well. We find this to be a challenging task for recent LLMs. Code and data available at: https://github.com/sfschouten/exploiting-ambiguity

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.

Large language models (LLMs) often present answers with high apparent confidence despite lacking an explicit mechanism for reasoning about certainty or truth. While existing benchmarks primarily evaluate single-turn accuracy, truthfulness or confidence calibration, they do not capture how models behave when their responses are challenged in interactive settings. We introduce the Certainty Robustness Benchmark, a two-turn evaluation framework that measures how LLMs balance stability and adaptability under self-challenging prompts such as uncertainty ("Are you sure?") and explicit contradiction ("You are wrong!"), alongside numeric confidence elicitation. Using 200 reasoning and mathematics questions from LiveBench, we evaluate four state-of-the-art LLMs and distinguish between justified self-corrections and unjustified answer changes. Our results reveal substantial differences in interactive reliability that are not explained by baseline accuracy alone: some models abandon correct answers under conversational pressure, while others demonstrate strong resistance to challenge and better alignment between confidence and correctness. These findings identify certainty robustness as a distinct and critical dimension of LLM evaluation, with important implications for alignment, trustworthiness and real-world deployment.

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.

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

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

Large language models (LLMs) excel at many natural language tasks, yet their reasoning reliability under structured perturbations of rule-based systems remains brittle. We present a controlled evaluation framework consisting of four stress tests: (1) rule deletion (redundant vs. essential), (2) contradictory evidence injection, (3) logic-preserving rewrites, and (4) multi-law equivalence stacking. While representative model families (BERT, Qwen2, and TinyLlama) achieve Acc = 1.0000 on base tasks, our framework reveals a critical failure mode termed Logic Inertia - a total breakdown with Acc = 0.0000 under contradictions, where deductive momentum overrides factual reality. To address this, we propose Conflict-Aware Fusion (Fusion-Conflict), a framework grounded in the Cognitive Structure Hypothesis, which posits that robust reasoning requires an explicit structural inductive bias. By imposing a dual-process architecture that separates premise verification from logical deduction, Conflict-Aware Fusion effectively mitigates logic inertia under the proposed evaluation framework, achieving 1.0000 accuracy on both base and contradictory stress tests. It also significantly enhances robustness to missing evidence. Our results demonstrate that, for reliable multi-step reasoning, structural verification discipline is as critical as training data scale, providing a potential blueprint for building robust, contradiction-aware AI systems this https://github.com/14H034160212/lemo . See the OpenAI/Evals pull request this https://github.com/openai/evals/pull/1622 .

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

Large language models (LLMs) can generate fluent reasoning traces that nevertheless lead to incorrect answers, making response-level uncertainty estimation important for abstention, human review, and adaptive compute allocation. Existing approaches generally fall into three categories: passive single-trace methods use token-level confidence signals, sampling-based methods compare multiple complete traces at higher generation cost, and active prefix-based methods probe partial traces to study answer stabilization or preference transitions. However, none actively re-elicits an answer from a completed reasoning trace to measure its consistency with and support for the original answer. To address this gap, we introduce Trace-Conditioned Answer Consistency (TrAC), a correctness-supervised uncertainty quantification framework that combines active and passive signals anchored to one completed reasoning trace. Its active component, Prefix-Conditioned Elicitation (PCE), re-elicits a short answer conditioned on the completed trace and represents both its consistency with the original answer and its token-level probabilistic support. Its passive component, Trace Uncertainty Profile (TUP), summarizes how token-level uncertainty evolves throughout the original generation without additional decoding. A lightweight head then integrates the two representations into a response-correctness score. Across five mathematical reasoning benchmarks and three LLM families, TrAC improves macro AUROC by 1.8% and reduces AURC by 3.4% relative to eight-sample self-consistency, while using one complete reasoning trace and a short cached answer probe. When eight samples are already available, augmenting sample consensus with re-elicitation further improves macro AUROC by 4.3% and reduces AURC by 8.3%, without additional full-trace generation.

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.

LLMs are increasingly deployed in high-stakes domains such as medical triage and legal assistance, often as document-grounded QA systems in which a user provides a description, relevant sources are retrieved, and an LLM generates a prediction. In practice, initial user queries are often underspecified, and a single retrieval pass is insufficient for reliable decision-making, leading to incorrect and overly confident answers. While follow-up questioning can elicit missing information, existing methods typically depend on implicit, unstructured confidence signals from the LLM, making it difficult to determine what remains unknown, what information matters most, and when to stop asking questions. We propose InfoGatherer, a framework that gathers missing information from two complementary sources: retrieved domain documents and targeted follow-up questions to the user. InfoGatherer models uncertainty using Dempster-Shafer belief assignments over a structured evidential network, enabling principled fusion of incomplete and potentially contradictory evidence from both sources without prematurely collapsing to a definitive answer. Across legal and medical tasks, InfoGatherer outperforms strong baselines while requiring fewer turns. By grounding uncertainty in formal evidential theory rather than heuristic LLM signals, InfoGatherer moves towards trustworthy, interpretable decision support in domains where reliability is critical.

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

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

Large language models exhibit a systematic tendency toward early semantic commitment: given ambiguous input, they collapse multiple valid interpretations into a single response before sufficient context is available. This premature collapse discards information that may prove essential as dialogue evolves. We present a formal framework for text-to-state mapping (phi: T -> S) that transforms natural language into a non-collapsing state space where multiple interpretations coexist. The mapping decomposes into three stages: conflict detection, interpretation extraction, and state construction. We instantiate phi with a hybrid extraction pipeline that combines rule-based segmentation for explicit conflict markers (adversative conjunctions, hedging expressions) with LLM-based enumeration of implicit ambiguity (epistemic, lexical, structural). On a test set of 68 ambiguous sentences, the resulting states preserve interpretive multiplicity: using hybrid extraction, we obtain mean state entropy H = 1.087 bits across ambiguity categories, compared to H = 0 for collapse-based baselines that commit to a single interpretation. We additionally instantiate the rule-based conflict detector for Japanese markers (kedo, kamoshirenai, etc.) to illustrate cross-lingual portability of the conflict detection stage. This framework extends Non-Resolution Reasoning (NRR) by providing the missing algorithmic bridge between text and the NRR state space, enabling architectural collapse deferment in LLM inference. Design principles for state-to-state transformations are detailed in the Appendix, with empirical validation on 580 test cases (180 single states, 200 contradictory pairs, 200 temporal pairs), demonstrating 0% collapse for principle-satisfying operators versus up to 17.8% for violating operators.

While large language models (LLMs) are increasingly used as automatic judges for question answering (QA) and other reference-conditioned evaluation tasks, little is known about their ability to adhere to a provided reference. We identify a critical failure mode of such reference-based LLM QA evaluation: when the provided reference conflicts with the judge model's parametric knowledge, the resulting scores become unreliable, substantially degrading evaluation fidelity. To study this phenomenon systematically, we introduce a controlled swapped-reference QA framework that induces reference-belief conflicts. Specifically, we replace the reference answer with an incorrect entity and construct diverse pairings of original and swapped references with correspondingly aligned candidate answers. Surprisingly, grading reliability drops sharply under swapped references across a broad set of judge models. We empirically show that this vulnerability is driven by judges' over-reliance on parametric knowledge, leading judges to disregard the given reference under conflict. Finally, we find that this failure persists under common prompt-based mitigation strategies, highlighting a fundamental limitation of LLM-as-a-judge evaluation and motivating reference-based protocols that enforce stronger adherence to the provided reference.

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

Task-oriented dialogues must maintain consistency both within the dialogue itself, ensuring logical coherence across turns, and with the conversational domain, accurately reflecting external knowledge. We propose to conceptualize dialogue consistency as a Constraint Satisfaction Problem (CSP), wherein variables represent segments of the dialogue referencing the conversational domain, and constraints among variables reflect dialogue properties, including linguistic, conversational, and domain-based aspects. To demonstrate the feasibility of the approach, we utilize a CSP solver to detect inconsistencies in dialogues re-lexicalized by an LLM. Our findings indicate that: (i) CSP is effective to detect dialogue inconsistencies; and (ii) consistent dialogue re-lexicalization is challenging for state-of-the-art LLMs, achieving only a 0.15 accuracy rate when compared to a CSP solver. Furthermore, through an ablation study, we reveal that constraints derived from domain knowledge pose the greatest difficulty in being respected. We argue that CSP captures core properties of dialogue consistency that have been poorly considered by approaches based on component pipelines.

Large reasoning models (LRMs) show strong capabilities in complex reasoning, yet their marginal gains on evidence-dependent factual questions are limited. We find this limitation is partially attributable to a reasoning-answer hit gap, where the model identifies the correct facts during reasoning but fails to incorporate them into the final response, thereby reducing factual fidelity. To address this issue, we propose MR-ALIGN, a Meta-Reasoning informed alignment framework that enhances factuality without relying on external verifiers. MR-ALIGN quantifies state transition probabilities along the model's thinking process and constructs a transition-aware implicit reward that reinforces beneficial reasoning patterns while suppressing defective ones at the atomic thinking segments. This re-weighting reshapes token-level signals into probability-aware segment scores, encouraging coherent reasoning trajectories that are more conducive to factual correctness. Empirical evaluations across four factual QA datasets and one long-form factuality benchmark show that MR-ALIGN consistently improves accuracy and truthfulness while reducing misleading reasoning. These results highlight that aligning the reasoning process itself, rather than merely the outputs, is pivotal for advancing factuality in LRMs.

As Multimodal Large Language Models (MLLMs) evolve into sophisticated interactive assistants, their reliability depends not only on following instructions but also on validating them. We define Proactive Critique as the model's autonomous ability to identify, analyze and fix faulty user inputs without extra prompts. However, evaluations mainly test models under ideal circumstances or simple refusal behaviors, largely ignoring active error processing. To fill this gap, we propose MMPCBench, a comprehensive framework for evaluating MLLMs' proactive critique competence. It features a fine-grained taxonomy of 4 primary error types spanning 12 subcategories, ranging from cross-modal contradictions to missing visual premises. We adopt a hierarchical evaluation protocol to measure models' error detection, diagnosis and resolution performance, and apply alignment-aware metrics to assess the coherence between internal reasoning and final responses. Tests on 14 mainstream MLLMs show obvious weaknesses in proactive critique, especially in dealing with subtle visual anomalies. Notably, we identify a pervasive "consistency gap": reasoning models can often correctly identify and analyze errors during internal reasoning yet suppress these valid insights in final outputs to prioritize response compliance. The code and data is available at https://github.com/ALIENS32/MMPCBench.

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

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

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.

In this work, we propose a novel method named Automated Process-Supervised Verifier (\textsc{AutoPSV}) to enhance the reasoning capabilities of large language models (LLMs) by automatically annotating the reasoning steps. AutoPSV begins by training a verification model on the correctness of final answers, enabling it to generate automatic process annotations. This verification model assigns a confidence score to each reasoning step, indicating the probability of arriving at the correct final answer from that point onward. We detect relative changes in the verification's confidence scores across reasoning steps to automatically annotate the reasoning process, enabling error detection even in scenarios where ground truth answers are unavailable. This alleviates the need for numerous manual annotations or the high computational costs associated with model-induced annotation approaches. We experimentally validate that the step-level confidence changes learned by the verification model trained on the final answer correctness can effectively identify errors in the reasoning steps. We demonstrate that the verification model, when trained on process annotations generated by AutoPSV, exhibits improved performance in selecting correct answers from multiple LLM-generated outputs. Notably, we achieve substantial improvements across five datasets in mathematics and commonsense reasoning. The source code of AutoPSV is available at https://github.com/rookie-joe/AutoPSV.

We provide here a dataset for tasks related to natural language understanding and natural language inference. The dataset contains logical puzzles in natural language from three domains: comparing puzzles, knighs and knaves, and zebra puzzles. Each puzzle is associated with the entire set of atomic questions that can be generated based on the relations and individuals occurring in the text. For each question we provide the correct answer: entailment, contradiction or ambiguity. The answer's correctness is verified against theorem provers. Good puzzles have two properties: (i) each piece of information is necessary and (ii) no unnecessary information is provided. These properties make puzzles interesting candidates for machine comprehension tasks.

Think-Answer reasoners such as DeepSeek-R1 have made notable progress by leveraging interpretable internal reasoning. However, despite the frequent presence of self-reflective cues like "Oops!", they remain vulnerable to output errors during single-pass inference. To address this limitation, we propose an efficient Recursive Think-Answer Process (R-TAP) that enables models to engage in iterative reasoning cycles and generate more accurate answers, going beyond conventional single-pass approaches. Central to this approach is a confidence generator that evaluates the certainty of model responses and guides subsequent improvements. By incorporating two complementary rewards-Recursively Confidence Increase Reward and Final Answer Confidence Reward-we show that R-TAP-enhanced models consistently outperform conventional single-pass methods for both large language models (LLMs) and vision-language models (VLMs). Moreover, by analyzing the frequency of "Oops"-like expressions in model responses, we find that R-TAP-applied models exhibit significantly fewer self-reflective patterns, resulting in more stable and faster inference-time reasoning. We hope R-TAP pave the way evolving into efficient and elaborated methods to refine the reasoning processes of future AI.

Reliable Large Language Models (LLMs) should abstain when confidence is insufficient. However, prior studies often treat refusal as a generic "I don't know'', failing to distinguish input-level ambiguity (data uncertainty) from capability limitations (model uncertainty). This lack of distinction limits downstream action decisions like requesting clarification or invoking external tools. In this work, we introduce UA-Bench, a benchmark of over 3,500 questions drawn from six datasets spanning knowledge-intensive and reasoning-intensive tasks, designed to evaluate explicit uncertainty attribution. An evaluation of 18 frontier LLMs shows that even state-of-the-art models struggle to reliably discriminate between data uncertainty and model uncertainty, and that high answer accuracy does not necessarily imply strong uncertainty attribution ability. To narrow this gap, we propose a lightweight data synthesis and reinforcement learning strategy. Experiments on both Qwen3-4B-Instruct-2507 and Qwen3-8B in thinking mode show that the proposed method improves uncertainty attribution while preserving answer accuracy. Our code and data are publicly available now.

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

The advancement of Large Language Models (LLMs) has greatly improved our ability to process complex language. However, accurately detecting logical fallacies remains a significant challenge. This study presents a novel and effective prompt formulation approach for logical fallacy detection, applicable in both supervised (fine-tuned) and unsupervised (zero-shot) settings. Our method enriches input text incorporating implicit contextual information -- counterarguments, explanations, and goals -- which we query for validity within the context of the argument. We then rank these queries based on confidence scores to inform classification. We evaluate our approach across multiple datasets from 5 domains, covering 29 distinct fallacy types, using models from the GPT and LLaMA series. The results show substantial improvements over state-of-the-art models, with F1 score increases of up to 0.60 in zero-shot settings and up to 0.45 in fine-tuned models. Extensive analyses further illustrate why and how our method excels.

Large language models (LLMs) demonstrate superior reasoning capabilities compared to small language models (SLMs), but incur substantially higher costs. We propose COllaborative REAsoner (COREA), a system that cascades an SLM with an LLM to achieve a balance between accuracy and cost in complex reasoning tasks. COREA first attempts to answer questions using the SLM, which outputs both an answer and a verbalized confidence score. Questions with confidence below a predefined threshold are deferred to the LLM for more accurate resolution. We introduce a reinforcement learning-based training algorithm that aligns the SLM's confidence through an additional confidence calibration reward. Extensive experiments demonstrate that our method jointly improves the SLM's reasoning ability and confidence calibration across diverse datasets and model backbones. Compared to using the LLM alone, COREA reduces cost by 21.5% and 16.8% on out-of-domain math and non-math datasets, respectively, with only an absolute pass@1 drop within 2%.

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.

Multimodal large language models (MLLMs) are increasingly deployed in open-ended, real-world environments where inputs are messy, underspecified, and not always trustworthy. Unlike curated benchmarks, these settings frequently involve instructions that refer to missing objects or contradictory facts, rely on ambiguous references, or request infeasible actions. In such cases, success hinges not on task execution alone, but on a model's ability to detect when something is silently wrong. This paper presents a systematic analysis of how current MLLMs handle such implicit reasoning scenarios: cases where the flaw is not explicitly stated but must be inferred from context. Using a curated diagnostic suite spanning four categories of real-world failure modes, we evaluate six MLLMs, including o3 and GPT-4o, and find that models frequently fail to surface hidden issues, even when they possess the necessary perceptual and reasoning skills. Explicit prompting reveals that the underlying capabilities exist but are often suppressed in favor of user compliance. We further show that simple inference-time interventions, such as cautious persona prompting and, in particular, requiring a clarifying question, can dramatically recover performance. Our findings highlight a persistent gap between reasoning competence and behavioral compliance in current MLLMs and suggest practical strategies for making these models more trustworthy in underconstrained environments.

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

Vision-language models (VLMs) are increasingly deployed in high-stakes settings where reliable uncertainty quantification (UQ) is as important as predictive accuracy. Extended reasoning via chain-of-thought (CoT) prompting or reasoning-trained models has become ubiquitous in modern VLM pipelines, yet its effect on UQ reliability remains poorly understood. We show that reasoning consistently degrades the quality of most uncertainty estimates, even when it improves task accuracy. We identify implicit answer conditioning as the primary mechanism: as reasoning traces converge on a conclusion before the final answer is generated, token probabilities increasingly reflect consistency with the model's own reasoning trace rather than uncertainty about correctness. In effect, the model becomes overconfident in its answer. In contrast, agreement-based consistency remains robust and often improves under reasoning, making it a practical choice for uncertainty estimation in reasoning-enabled VLMs.

A prominent weakness of modern language models (LMs) is their tendency to generate factually incorrect text, which hinders their usability. A natural question is whether such factual errors can be detected automatically. Inspired by truth-seeking mechanisms in law, we propose a factuality evaluation framework for LMs that is based on cross-examination. Our key idea is that an incorrect claim is likely to result in inconsistency with other claims that the model generates. To discover such inconsistencies, we facilitate a multi-turn interaction between the LM that generated the claim and another LM (acting as an examiner) which introduces questions to discover inconsistencies. We empirically evaluate our method on factual claims made by multiple recent LMs on four benchmarks, finding that it outperforms existing methods and baselines, often by a large gap. Our results demonstrate the potential of using interacting LMs for capturing factual errors.

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

Emerging personal AI agents are moving toward persistent, multi-source memory. This creates an evaluation problem: systems must decide how to use conflicting or incomplete evidence; they cannot just retrieve facts from one clean history. Existing benchmarks rarely show whether an error came from the evidence given to a method or from the method's conflict-resolution step. We study this as selective QA over conflicting multi-source personal memory: systems answer based on conflicting, sometimes incomplete sources, or abstain when evidence is insufficient. We develop a benchmark containing 18 question templates across 8 reasoning types, 480 personas, 4 random seeds, and 34,560 instances, with controlled source distortions and deterministic ground truth. We evaluate the performance of baselines without access to any source, access to a single source, structured fusion methods, and frontier LLMs. The best trained fusion resolver reaches 80.3% accuracy, while the strongest prompt-only LLM baseline reaches 70.0%. With abstention, the same resolver reaches 85.3% selective accuracy at 78.3% coverage and the best LLM reaches 71.0% selective accuracy at 95.4% coverage. Different models have different strengths across reasoning types. We release the data, code, cached model outputs, and data-generating process for reuse.

The deployment of pre-trained perception models in novel environments often leads to performance degradation due to distributional shifts. Although recent artificial intelligence approaches for metacognition use logical rules to characterize and filter model errors, improving precision often comes at the cost of reduced recall. This paper addresses the hypothesis that leveraging multiple pre-trained models can mitigate this recall reduction. We formulate the challenge of identifying and managing conflicting predictions from various models as a consistency-based abduction problem. The input predictions and the learned error detection rules derived from each model are encoded in a logic program. We then seek an abductive explanation--a subset of model predictions--that maximizes prediction coverage while ensuring the rate of logical inconsistencies (derived from domain constraints) remains below a specified threshold. We propose two algorithms for this knowledge representation task: an exact method based on Integer Programming (IP) and an efficient Heuristic Search (HS). Through extensive experiments on a simulated aerial imagery dataset featuring controlled, complex distributional shifts, we demonstrate that our abduction-based framework outperforms individual models and standard ensemble baselines, achieving, for instance, average relative improvements of approximately 13.6% in F1-score and 16.6% in accuracy across 15 diverse test datasets when compared to the best individual model. Our results validate the use of consistency-based abduction as an effective mechanism to robustly integrate knowledge from multiple imperfect reasoners in challenging, novel scenarios.

We explore the task of improving persona consistency of dialogue agents. Recent models tackling consistency often train with additional Natural Language Inference (NLI) labels or attach trained extra modules to the generative agent for maintaining consistency. However, such additional labels and training can be demanding. Also, we find even the best-performing persona-based agents are insensitive to contradictory words. Inspired by social cognition and pragmatics, we endow existing dialogue agents with public self-consciousness on the fly through an imaginary listener. Our approach, based on the Rational Speech Acts framework (Frank and Goodman, 2012), can enforce dialogue agents to refrain from uttering contradiction. We further extend the framework by learning the distractor selection, which has been usually done manually or randomly. Results on Dialogue NLI (Welleck et al., 2019) and PersonaChat (Zhang et al., 2018) dataset show that our approach reduces contradiction and improves consistency of existing dialogue models. Moreover, we show that it can be generalized to improve context-consistency beyond persona in dialogues.

Knowledge graph-based retrieval-augmented generation seeks to mitigate hallucinations in Large Language Models (LLMs) caused by insufficient or outdated knowledge. However, existing methods often fail to fully exploit the prior knowledge embedded in knowledge graphs (KGs), particularly their structural information and explicit or implicit constraints. The former can enhance the faithfulness of LLMs' reasoning, while the latter can improve the reliability of response generation. Motivated by these, we propose a trustworthy reasoning framework, termed Deliberation over Priors (DP), which sufficiently utilizes the priors contained in KGs. Specifically, DP adopts a progressive knowledge distillation strategy that integrates structural priors into LLMs through a combination of supervised fine-tuning and Kahneman-Tversky optimization, thereby improving the faithfulness of relation path generation. Furthermore, our framework employs a reasoning-introspection strategy, which guides LLMs to perform refined reasoning verification based on extracted constraint priors, ensuring the reliability of response generation. Extensive experiments on three benchmark datasets demonstrate that DP achieves new state-of-the-art performance, especially a Hit@1 improvement of 13% on the ComplexWebQuestions dataset, and generates highly trustworthy responses. We also conduct various analyses to verify its flexibility and practicality. The code is available at https://github.com/reml-group/Deliberation-on-Priors.

Large language models (LLMs) are trained on extensive datasets that encapsulate substantial world knowledge. However, their outputs often include confidently stated inaccuracies. Earlier works suggest that LLMs encode truthfulness as a distinct linear feature, termed the "truth direction", which can classify truthfulness reliably. We address several open questions about the truth direction: (i) whether LLMs universally exhibit consistent truth directions; (ii) whether sophisticated probing techniques are necessary to identify truth directions; and (iii) how the truth direction generalizes across diverse contexts. Our findings reveal that not all LLMs exhibit consistent truth directions, with stronger representations observed in more capable models, particularly in the context of logical negation. Additionally, we demonstrate that truthfulness probes trained on declarative atomic statements can generalize effectively to logical transformations, question-answering tasks, in-context learning, and external knowledge sources. Finally, we explore the practical application of truthfulness probes in selective question-answering, illustrating their potential to improve user trust in LLM outputs. These results advance our understanding of truth directions and provide new insights into the internal representations of LLM beliefs. Our code is public at https://github.com/colored-dye/truthfulness_probe_generalization

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.

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

Large Language Models (LLMs) are known to acquire reasoning capabilities through shared inference patterns in pre-training data, which are further elicited via Chain-of-Thought (CoT) practices. However, whether fundamental reasoning patterns, such as induction, deduction, and abduction, can be decoupled from specific problem instances remains a critical challenge for model controllability, and for shedding light on reasoning controllability. In this paper, we present the first systematic investigation of this problem through the lens of reasoning conflicts: an explicit tension between parametric and contextual information induced by mandating logical schemata that deviate from those expected for a target task. Our evaluation reveals that LLMs consistently prioritize sensibility over compliance, favoring task-appropriate reasoning patterns despite conflicting instructions. Notably, task accuracy is not strictly determined by sensibility, with models often maintaining high performance even when using conflicting patterns, suggesting a reliance on internalized parametric memory that increases with model size. We further demonstrate that reasoning conflicts are internally detectable, as confidence scores significantly drop during conflicting episodes. Probing experiments confirm that reasoning types are linearly encoded from middle-to-late layers, indicating the potential for activation-level controllability. Leveraging these insights, we steer models towards compliance, increasing instruction following by up to 29%. Overall, our findings establish that while LLM reasoning is anchored to concrete instances, active mechanistic interventions can effectively decouple logical schemata from data, offering a path toward improved controllability, faithfulness, and generalizability.

Large Language Models (LLMs) have shown remarkable capabilities in general natural language processing tasks but often fall short in complex reasoning tasks. Recent studies have explored human-like problem-solving strategies, such as self-correct, to push further the boundary of single-model reasoning ability. In this work, we let a single model "step outside the box" by engaging multiple models to correct each other. We introduce a multi-agent collaboration strategy that emulates the academic peer review process. Each agent independently constructs its own solution, provides reviews on the solutions of others, and assigns confidence levels to its reviews. Upon receiving peer reviews, agents revise their initial solutions. Extensive experiments on three different types of reasoning tasks show that our collaboration approach delivers superior accuracy across all ten datasets compared to existing methods. Further study underscores the effectiveness of integrating confidence in reviews, demonstrates the superiority of feedback exchange over mere solution sharing, and highlights the role of capability and diversity in fostering successful collaboration.

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.

Recent advances in reasoning-centric models promise improved robustness through mechanisms such as chain-of-thought prompting and test-time scaling. However, their ability to withstand misleading user input remains underexplored. In this paper, we conduct a systematic evaluation of three state-of-the-art reasoning models, i.e., OpenAI's o4-mini, Claude-3.7-Sonnet and Gemini-2.5-Flash, across three multimodal benchmarks: MMMU, MathVista, and CharXiv. Our evaluation reveals significant accuracy drops (25-29% on average) following gaslighting negation prompts, indicating that even top-tier reasoning models struggle to preserve correct answers under manipulative user feedback. Built upon the insights of the evaluation and to further probe this vulnerability, we introduce GaslightingBench-R, a new diagnostic benchmark specifically designed to evaluate reasoning models' susceptibility to defend their belief under gaslighting negation prompt. Constructed by filtering and curating 1,025 challenging samples from the existing benchmarks, GaslightingBench-R induces even more dramatic failures, with accuracy drops exceeding 53% on average. Our findings reveal fundamental limitations in the robustness of reasoning models, highlighting the gap between step-by-step reasoning and belief persistence.

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.

Most prior works focused on conflicts between an LLM's internal parametric knowledge and externally provided context. In contrast, we investigate how LLMs handle conflicts that arise within contextual knowledge itself. We introduce a taxonomy of six types of contextual conflicts (factual, inferential, temporal, granularity, perspective, and ambiguity) and contribute a comprehensive dataset ContextConflict for this setting. The dataset contains 5,781 samples, covers both reasoning and summarization tasks, and includes both explicit contradictions and implicit conflicts that require multi-step reasoning. Experiments on nine LLMs show that current models still fall short in resolving contextual knowledge conflicts. We further provide mechanistic interpretability insights into how LLMs process such conflicts, revealing their latent awareness of conflicts and the representational geometry underlying conflict processing. In addition, our analysis uncovers a consistent model bias towards earlier evidence, and this positional preference serves as a key obstacle to effective conflict resolution. Motivated by these findings, we further propose a simple training-free, label-free steering method that steers activations to encourage a more comprehensive incorporation of evidences for better conflict resolution. On our dataset, the method consistently improves accuracy on reasoning tasks and generates higher-quality, more balanced summaries for summarization tasks.

Recent advancements in large language models (LLMs) have demonstrated remarkable reasoning capabilities. However, single-shot inference often yields unreliable results for complex reasoning tasks, leading researchers to explore multiple reasoning paths through methods such as perplexity and self-consistency. In this paper, we present the first theoretical error decomposition analysis of these techniques, breaking down their error into estimation error and model error. Our analysis reveals a fundamental trade-off: perplexity methods suffer from substantial model error due to the absence of a proper consistency function, while self-consistency exhibits high estimation error due to a slow error convergence rate. To overcome these limitations, we propose Reasoning-Pruning Perplexity Consistency (RPC). This approach combines Perplexity Consistency, which seamlessly integrates LLM perplexity with self-consistency, and Reasoning Pruning, which eliminates low-probability reasoning paths to effectively prevent the degeneration of estimation error reduction. Theoretical analysis demonstrates that RPC not only accelerates the convergence rate of estimation error to an exponential level but also holds strong potential for further reducing model error. Extensive empirical evaluations on seven benchmark datasets confirm that RPC can significantly improve reasoning performance, sample efficiency, and confidence reliability.

Recent large language models often answer factual questions correctly. But users can't trust any given claim a model makes without fact-checking, because language models can hallucinate convincing nonsense. In this work we use reinforcement learning from human preferences (RLHP) to train "open-book" QA models that generate answers whilst also citing specific evidence for their claims, which aids in the appraisal of correctness. Supporting evidence is drawn from multiple documents found via a search engine, or from a single user-provided document. Our 280 billion parameter model, GopherCite, is able to produce answers with high quality supporting evidence and abstain from answering when unsure. We measure the performance of GopherCite by conducting human evaluation of answers to questions in a subset of the NaturalQuestions and ELI5 datasets. The model's response is found to be high-quality 80\% of the time on this Natural Questions subset, and 67\% of the time on the ELI5 subset. Abstaining from the third of questions for which it is most unsure improves performance to 90\% and 80\% respectively, approaching human baselines. However, analysis on the adversarial TruthfulQA dataset shows why citation is only one part of an overall strategy for safety and trustworthiness: not all claims supported by evidence are true.

Large language Models (LLMs) have achieved promising performance on arithmetic reasoning tasks by incorporating step-by-step chain-of-thought (CoT) prompting. However, LLMs face challenges in maintaining factual consistency during reasoning, exhibiting tendencies to condition overlooking, question misinterpretation, and condition hallucination over given problems. Existing methods use coarse-grained feedback (e.g., whether the answer is correct) to improve factual consistency. In this work, we propose RCoT (Reversing Chain-of-Thought), a novel method to improve LLMs' reasoning abilities by automatically detecting and rectifying factual inconsistency in LLMs' generated solutions. To detect factual inconsistency, RCoT first asks LLMs to reconstruct the problem based on generated solutions. Then fine-grained comparisons between the original problem and the reconstructed problem expose the factual inconsistency in the original solutions. To rectify the solution, RCoT formulates detected factual inconsistency into fine-grained feedback to guide LLMs in revising solutions. Experimental results demonstrate consistent improvements of RCoT over standard CoT across seven arithmetic datasets. Moreover, we find that manually written fine-grained feedback can dramatically improve LLMs' reasoning abilities (e.g., ChatGPT reaches 94.6% accuracy on GSM8K), encouraging the community to further explore the fine-grained feedback generation methods.

Best-of-n sampling improves the accuracy of large language models (LLMs) and large reasoning models (LRMs) by generating multiple candidate solutions and selecting the one with the highest reward. The key challenge for reasoning tasks is designing a scoring function that can identify correct reasoning chains without access to ground-truth answers. We propose Probabilistic Confidence Selection And Ranking (PiCSAR): a simple, training-free method that scores each candidate generation using the joint log-likelihood of the reasoning and final answer. The joint log-likelihood of the reasoning and final answer naturally decomposes into reasoning confidence and answer confidence. PiCSAR achieves substantial gains across diverse benchmarks (+10.18 on MATH500, +9.81 on AIME2025), outperforming baselines with at least 2x fewer samples in 16 out of 20 comparisons. Our analysis reveals that correct reasoning chains exhibit significantly higher reasoning and answer confidence, justifying the effectiveness of PiCSAR.

Knights and knaves problems represent a classic genre of logical puzzles where characters either tell the truth or lie. The objective is to logically deduce each character's identity based on their statements. The challenge arises from the truth-telling or lying behavior, which influences the logical implications of each statement. Solving these puzzles requires not only direct deductions from individual statements, but the ability to assess the truthfulness of statements by reasoning through various hypothetical scenarios. As such, knights and knaves puzzles serve as compelling examples of suppositional reasoning. In this paper, we introduce TruthQuest, a benchmark for suppositional reasoning based on the principles of knights and knaves puzzles. Our benchmark presents problems of varying complexity, considering both the number of characters and the types of logical statements involved. Evaluations on TruthQuest show that large language models like Llama 3 and Mixtral-8x7B exhibit significant difficulties solving these tasks. A detailed error analysis of the models' output reveals that lower-performing models exhibit a diverse range of reasoning errors, frequently failing to grasp the concept of truth and lies. In comparison, more proficient models primarily struggle with accurately inferring the logical implications of potentially false statements.

Large Language Models have demonstrated remarkable capabilities across diverse tasks, yet they frequently generate hallucinations outputs that are fluent but factually incorrect or unsupported. We propose Counterfactual Probing, a novel approach for detecting and mitigating hallucinations in LLM outputs. Our method dynamically generates counterfactual statements that appear plausible but contain subtle factual errors, then evaluates the model's sensitivity to these perturbations. We hypothesize that genuine knowledge exhibits robustness to counterfactual variations, while hallucinated content shows inconsistent confidence patterns when confronted with plausible alternatives. Our comprehensive evaluation on TruthfulQA, factual statement datasets, and curated hallucination examples demonstrates that counterfactual probing achieves superior detection performance compared to baseline methods, while our adaptive mitigation strategies reduce hallucination scores by an average of 24.5%. The approach requires no model retraining and can be integrated into existing LLM pipelines as a realtime verification mechanism.

Language models (LMs) are said to be exhibiting reasoning, but what does this entail? We assess definitions of reasoning and how key papers in the field of natural language processing (NLP) use the notion and argue that the definitions provided are not consistent with how LMs are trained, process information, and generate new tokens. To illustrate this incommensurability we assume the view that transformer-based LMs implement an implicit finite-order Markov kernel mapping contexts to conditional token distributions. In this view, reasoning-like outputs correspond to statistical regularities and approximate statistical invariances in the learned kernel rather than the implementation of explicit logical mechanisms. This view is illustrative of the claim that LMs are "statistical pattern matchers"" and not genuine reasoners and provides a perspective that clarifies why reasoning-like outputs arise in LMs without any guarantees of logical consistency. This distinction is fundamental to how epistemic uncertainty is evaluated in LMs. We invite a discussion on the importance of how the computational processes of the systems we build and analyze in NLP research are described.

Large Language Models (LLMs) demonstrate impressive reasoning capabilities in familiar contexts, but struggle when the context conflicts with their parametric knowledge. To investigate this phenomenon, we introduce CounterLogic, a dataset containing 1,800 examples across 9 logical schemas, explicitly designed to evaluate logical reasoning through counterfactual (hypothetical knowledge-conflicting) scenarios. Our systematic evaluation of 11 LLMs across 6 different datasets reveals a consistent performance degradation, with accuracies dropping by 27% on average when reasoning through counterfactual information. We propose Self-Segregate, a prompting method enabling metacognitive awareness (explicitly identifying knowledge conflicts) before reasoning. Our method dramatically narrows the average performance gaps from 27% to just 11%, while significantly increasing the overall accuracy (+7.5%). We discuss the implications of these findings and draw parallels to human cognitive processes, particularly on how humans disambiguate conflicting information during reasoning tasks. Our findings offer practical insights for understanding and enhancing LLMs reasoning capabilities in real-world applications, especially where models must logically reason independently of their factual knowledge.

Large language models are characterized by three key properties: capability, alignment, and faithfulness. Prior work studies the tradeoffs between capability and alignment, and between capability and faithfulness, but a third tension remains underexplored: the alignment-faithfulness conflict. We show that aligned models systematically deviate from their inputs on unsafe or sensitive content without disclosing the modification, a failure mode we call alignment-induced unfaithfulness (AIU). Unlike capability-driven unfaithfulness, which comes from errors in knowledge or reasoning, this is induced by post-training mechanisms that override adherence to the input. We introduce FaithConflict, a controlled dataset isolating both conflicts, and two complementary taxonomies: behavioral (B1-B8) and chain-of-thought reasoning (C0-C6). Across models, AIU increases with scale and more sharply than capability-driven unfaithfulness, a reverse scaling law; intermediate checkpoints show it is amplified during post-training, with DPO the stage at which the gap both grows most and becomes least visible. Prompting-based mitigation does not resolve it, revealing a capability-alignment-faithfulness trilemma in the design and evaluation of LLMs.

Large Language Models (LLMs) have recently made significant strides in complex reasoning tasks through the Chain-of-Thought technique. Despite this progress, their reasoning is often constrained by their intrinsic understanding, lacking external insights. To address this, we propose Exchange-of-Thought (EoT), a novel framework that enables cross-model communication during problem-solving. Drawing inspiration from network topology, EoT integrates four unique communication paradigms: Memory, Report, Relay, and Debate. This paper delves into the communication dynamics and volume associated with each paradigm. To counterbalance the risks of incorrect reasoning chains, we implement a robust confidence evaluation mechanism within these communications. Our experiments across diverse complex reasoning tasks demonstrate that EoT significantly surpasses established baselines, underscoring the value of external insights in enhancing LLM performance. Furthermore, we show that EoT achieves these superior results in a cost-effective manner, marking a promising advancement for efficient and collaborative AI problem-solving.

Fact verification is essential for ensuring the reliability of LLM applications. In this study, we evaluate 12 pre-trained LLMs and one specialized fact-verifier, including frontier LLMs and open-weight reasoning LLMs, using a collection of examples from 14 fact-checking benchmarks. We share three findings intended to guide future development of more robust fact verifiers. First, we highlight the importance of addressing annotation errors and ambiguity in datasets, demonstrating that approximately 16\% of ambiguous or incorrectly labeled data substantially influences model rankings. Neglecting this issue may result in misleading conclusions during comparative evaluations, and we suggest using a systematic pipeline utilizing LLM-as-a-judge to help identify these issues at scale. Second, we discover that frontier LLMs with few-shot in-context examples, often overlooked in previous works, achieve top-tier performance. We therefore recommend future studies include comparisons with these simple yet highly effective baselines. Lastly, despite their effectiveness, frontier LLMs incur substantial costs, motivating the development of small, fine-tuned fact verifiers. We show that these small models still have room for improvement, particularly on instances that require complex reasoning. Encouragingly, we demonstrate that augmenting training with synthetic multi-hop reasoning data significantly enhances their capabilities in such instances. We release our code, model, and dataset at https://github.com/just1nseo/verifying-the-verifiers

Despite their strengths, large language models (LLMs) often fail to communicate their confidence accurately, making it difficult to assess when they might be wrong and limiting their reliability. In this work, we demonstrate that reasoning models-LLMs that engage in extended chain-of-thought (CoT) reasoning-exhibit superior performance not only in problem-solving but also in accurately expressing their confidence. Specifically, we benchmark six reasoning models across six datasets and find that they achieve strictly better confidence calibration than their non-reasoning counterparts in 33 out of the 36 settings. Our detailed analysis reveals that these gains in calibration stem from the slow thinking behaviors of reasoning models-such as exploring alternative approaches and backtracking-which enable them to adjust their confidence dynamically throughout their CoT, making it progressively more accurate. In particular, we find that reasoning models become increasingly better calibrated as their CoT unfolds, a trend not observed in non-reasoning models. Moreover, removing slow thinking behaviors from the CoT leads to a significant drop in calibration. Lastly, we show that these gains are not exclusive to reasoning models-non-reasoning models also benefit when guided to perform slow thinking via in-context learning.

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.

Large language models frequently encounter conflicts between their parametric knowledge and contextual input, often resulting in factual inconsistencies or hallucinations. We propose Self-Reflective Debate for Contextual Reliability (SR-DCR), a lightweight framework that integrates token-level self-confidence with an asymmetric multi-agent debate to adjudicate such conflicts. A critic, deprived of context, challenges a defender who argues from the given passage; a judge model evaluates the debate and determines the context's reliability. The final answer is selected by combining the verdict with model confidence. Experiments on the ClashEval benchmark demonstrate that SR-DCR consistently enhances robustness to misleading context while maintaining accuracy on trustworthy inputs, outperforming both classical debate and confidence-only baselines with minimal computational overhead. The code is available at https://github.com/smiles724/Self-Reflective-Debates.

Retrieval Augmented Generation (RAG) systems have emerged as a powerful method for enhancing large language models (LLMs) with up-to-date information. However, the retrieval step in RAG can sometimes surface documents containing contradictory information, particularly in rapidly evolving domains such as news. These contradictions can significantly impact the performance of LLMs, leading to inconsistent or erroneous outputs. This study addresses this critical challenge in two ways. First, we present a novel data generation framework to simulate different types of contradictions that may occur in the retrieval stage of a RAG system. Second, we evaluate the robustness of different LLMs in performing as context validators, assessing their ability to detect contradictory information within retrieved document sets. Our experimental results reveal that context validation remains a challenging task even for state-of-the-art LLMs, with performance varying significantly across different types of contradictions. While larger models generally perform better at contradiction detection, the effectiveness of different prompting strategies varies across tasks and model architectures. We find that chain-of-thought prompting shows notable improvements for some models but may hinder performance in others, highlighting the complexity of the task and the need for more robust approaches to context validation in RAG systems.

Large Language Models (LLMs) augmented with retrieval mechanisms have demonstrated significant potential in fact-checking tasks by integrating external knowledge. However, their reliability decreases when confronted with conflicting evidence from sources of varying credibility. This paper presents the first systematic evaluation of Retrieval-Augmented Generation (RAG) models for fact-checking in the presence of conflicting evidence. To support this study, we introduce CONFACT (Conflicting Evidence for Fact-Checking) (Dataset available at https://github.com/zoeyyes/CONFACT), a novel dataset comprising questions paired with conflicting information from various sources. Extensive experiments reveal critical vulnerabilities in state-of-the-art RAG methods, particularly in resolving conflicts stemming from differences in media source credibility. To address these challenges, we investigate strategies to integrate media background information into both the retrieval and generation stages. Our results show that effectively incorporating source credibility significantly enhances the ability of RAG models to resolve conflicting evidence and improve fact-checking performance.

Large language models (LLMs) have demonstrated impressive performance on reasoning tasks, including mathematical reasoning. However, the current evaluation mostly focuses on carefully constructed benchmarks and neglects the consideration of real-world reasoning problems that present missing or contradictory conditions, known as ill-defined problems. To further study this problem, we develop a largescale benchmark called Problems with Missing and Contradictory conditions ( PMC) containing over 5,000 validated ill-defined mathematical problems. Our preliminary experiments through PMC reveal two challenges about existing methods: (1) traditional methods exhibit a trade-off between solving accuracy and rejection capabilities, and (2) formal methods struggle with modeling complex problems. To address these challenges, We develop Variable-Constraint Search (VCSEARCH), a trainingfree framework that leverages formal language to detect ill-defined problems, where a variableconstraint pair search strategy is incorporated to improve the modeling capability of formal language. Extensive experiments demonstrate that VCSEARCH improves the accuracy of identifying unsolvable problems by at least 12% across different LLMs, thus achieving stronger robust mathematical reasoning ability.

Retrieval-Augmented Generation (RAG) has emerged as a widely adopted approach for enhancing LLMs in scenarios that demand extensive factual knowledge. However, current RAG evaluations concentrate primarily on correctness, which may not fully capture the impact of retrieval on LLM uncertainty and reliability. To bridge this gap, we introduce URAG, a comprehensive benchmark designed to assess the uncertainty of RAG systems across various fields like healthcare, programming, science, math, and general text. By reformulating open-ended generation tasks into multiple-choice question answering, URAG allows for principled uncertainty quantification via conformal prediction. We apply the evaluation pipeline to 8 standard RAG methods, measuring their performance through both accuracy and prediction-set sizes based on LAC and APS metrics. Our analysis shows that (1) accuracy gains often coincide with reduced uncertainty, but this relationship breaks under retrieval noise; (2) simple modular RAG methods tend to offer better accuracy-uncertainty trade-offs than more complex reasoning pipelines; and (3) no single RAG approach is universally reliable across domains. We further show that (4) retrieval depth, parametric knowledge dependence, and exposure to confidence cues can amplify confident errors and hallucinations. Ultimately, URAG establishes a systematic benchmark for analyzing and enhancing the trustworthiness of retrieval-augmented systems. Our code is available on GitHub.

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

Dialogue contradiction is a critical issue in open-domain dialogue systems. The contextualization nature of conversations makes dialogue contradiction detection rather challenging. In this work, we propose a benchmark for Contradiction Detection in Chinese Conversations, namely CDConv. It contains 12K multi-turn conversations annotated with three typical contradiction categories: Intra-sentence Contradiction, Role Confusion, and History Contradiction. To efficiently construct the CDConv conversations, we devise a series of methods for automatic conversation generation, which simulate common user behaviors that trigger chatbots to make contradictions. We conduct careful manual quality screening of the constructed conversations and show that state-of-the-art Chinese chatbots can be easily goaded into making contradictions. Experiments on CDConv show that properly modeling contextual information is critical for dialogue contradiction detection, but there are still unresolved challenges that require future research.

Large Language Models (LLMs) have demonstrated impressive reasoning capabilities, leading to their adoption in high-stakes domains such as healthcare, law, and scientific research. However, their reasoning often contains subtle logical errors masked by fluent language, posing significant risks for critical applications. While existing approaches like fact-checking, self-consistency methods, and rule-based validation provide partial solutions, they fail to detect complex logical flaws in multi-step reasoning. To overcome these challenges, we present MATP, an evaluation framework for systematically verifying LLM reasoning via Multi-step Automatic Theorem Proving. MATP translates natural language reasoning into First-Order Logic (FOL) and applies automated theorem provers to assess step-by-step logical validity. This approach identifies hidden logical errors and provides fine-grained classifications of reasoning correctness. Evaluations on a benchmark comprising 10,830 reasoning instances generated by 10 LLMs across tasks from PrOntoQA-OOD, ProofWriter, and FOLIO show that MATP surpasses prompting-based baselines by over 42 percentage points in reasoning step verification. It further reveals model-level disparities, with reasoning models generating more logically coherent outputs than general models. These results demonstrate MATP's potential to enhance the trustworthiness of LLM-generated reasoning.

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

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.

Factual hallucination remains a central challenge for large language models (LLMs). Existing mitigation approaches primarily rely on either external post-hoc verification or mapping uncertainty directly to abstention during fine-tuning, often resulting in overly conservative behavior. We propose VeriFY, a training-time framework that teaches LLMs to reason about factual uncertainty through consistency-based self-verification. VeriFY augments training with structured verification traces that guide the model to produce an initial answer, generate and answer a probing verification query, issue a consistency judgment, and then decide whether to answer or abstain. To address the risk of reinforcing hallucinated content when training on augmented traces, we introduce a stage-level loss masking approach that excludes hallucinated answer stages from the training objective while preserving supervision over verification behavior. Across multiple model families and scales, VeriFY reduces factual hallucination rates by 9.7 to 53.3 percent, with only modest reductions in recall (0.4 to 5.7 percent), and generalizes across datasets when trained on a single source. The source code, training data, and trained model checkpoints will be released upon acceptance.

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

Large language models (LLMs) produce outputs with varying levels of uncertainty, and, just as often, varying levels of correctness; making their practical reliability far from guaranteed. To quantify this uncertainty, we systematically evaluate four approaches for confidence estimation in LLM outputs: VCE, MSP, Sample Consistency, and CoCoA (Vashurin et al., 2025). For the evaluation of the approaches, we conduct experiments on four question-answering tasks using a state-of-the-art open-source LLM. Our results show that each uncertainty metric captures a different facet of model confidence and that the hybrid CoCoA approach yields the best reliability overall, improving both calibration and discrimination of correct answers. We discuss the trade-offs of each method and provide recommendations for selecting uncertainty measures in LLM applications.

Large Language Models (LLMs) hallucinate, generating factually incorrect yet confident assertions. We argue this stems from the Transformer's Softmax function, which creates "Artificial Certainty" by collapsing ambiguous attention scores into a single probability distribution, discarding uncertainty information at each layer. To fix this, we introduce the Credal Transformer, which replaces standard attention with a Credal Attention Mechanism (CAM) based on evidential theory. CAM produces a "credal set" (a set of distributions) instead of a single attention vector, with the set's size directly measuring model uncertainty. We implement this by re-conceptualizing attention scores as evidence masses for a Dirichlet distribution: sufficient evidence recovers standard attention, while insufficient evidence yields a diffuse distribution, representing ambiguity. Empirically, the Credal Transformer identifies out-of-distribution inputs, quantifies ambiguity, and significantly reduces confident errors on unanswerable questions by abstaining. Our contribution is a new architecture to mitigate hallucinations and a design paradigm that integrates uncertainty quantification directly into the model, providing a foundation for more reliable AI.

Advances in training, post-training, and inference-time methods have enabled frontier reasoning models to win gold medals in math competitions and settle challenging open problems. Gaining trust in the responses of these models requires that natural language proofs be checked for errors. LLM judges are increasingly being adopted to meet the growing demand for evaluating such proofs. While verification is considered easier than generation, what model capability does reliable verification actually require? We systematically evaluate four open-source and two frontier LLMs on datasets of human-graded natural language proofs of competition-level problems. We consider two key metrics: verifier accuracy and self-consistency (the rate of agreement across repeated judgments on the same proof). We observe that smaller open-source models are only up to ~10% behind frontier models in accuracy but they are up to ~25% more inconsistent. Furthermore, we see that verifier accuracy is sensitive to prompt choice across all models. We then demonstrate that the smaller models, in fact, do possess the mathematical capabilities to verify proofs at the level of frontier models, but they struggle to reliably elicit these capabilities with general judging prompts. Through an LLM-guided prompt search, we synthesize an ensemble of specialized prompts that overcome the specific failure modes of smaller models, boosting their performance by up to 9.1% in accuracy and 15.9% in self-consistency. These gains are realized across models and datasets, allowing models like Qwen3.5-35B to perform on par with frontier models such as Gemini 3.1 Pro for proof verification.

While there are numerous benchmarks comparing the performance of modern language models (LMs), end-task evaluations often conflate notions of *factual accuracy* ("truth") and *reasoning ability* ("rationality", or "honesty" in the sense of correctly reporting implications of beliefs). Our goal is a dataset that clearly distinguishes these two notions. Our approach is to leverage and extend a collection of human-annotated *entailment trees*, engineered to express both good and bad chains of reasoning, and using a mixture of true and false facts, in particular including counterfactual examples, to avoid belief bias (also known as the "content effect"). The resulting dataset, called BaRDa, contains 3000 entailments (1787 valid, 1213 invalid), using 6681 true and 2319 false statements. Testing on four GPT-series models, GPT3(curie)/GPT3(davinici)/3.5/4, we find factual accuracy (truth) scores of 74.1/80.6/82.6/87.1 and reasoning accuracy scores of 63.1/78.0/71.8/79.2. This shows the clear progression of models towards improved factual accuracy and entailment reasoning, and the dataset provides a new benchmark that more cleanly separates and quantifies these two notions.

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).

One way to increase confidence in the outputs of Large Language Models (LLMs) is to support them with reasoning that is clear and easy to check -- a property we call legibility. We study legibility in the context of solving grade-school math problems and show that optimizing chain-of-thought solutions only for answer correctness can make them less legible. To mitigate the loss in legibility, we propose a training algorithm inspired by Prover-Verifier Game from Anil et al. (2021). Our algorithm iteratively trains small verifiers to predict solution correctness, "helpful" provers to produce correct solutions that the verifier accepts, and "sneaky" provers to produce incorrect solutions that fool the verifier. We find that the helpful prover's accuracy and the verifier's robustness to adversarial attacks increase over the course of training. Furthermore, we show that legibility training transfers to time-constrained humans tasked with verifying solution correctness. Over course of LLM training human accuracy increases when checking the helpful prover's solutions, and decreases when checking the sneaky prover's solutions. Hence, training for checkability by small verifiers is a plausible technique for increasing output legibility. Our results suggest legibility training against small verifiers as a practical avenue for increasing legibility of large LLMs to humans, and thus could help with alignment of superhuman models.

Large Language Models (LLMs) leverage step-by-step reasoning to solve complex problems. Standard evaluation practice involves generating a complete reasoning trace and assessing the correctness of the final answer presented at its conclusion. In this paper, we challenge the reliance on the final answer by posing the following two questions: Does the final answer reliably represent the model's optimal conclusion? Can alternative reasoning paths yield different results? To answer these questions, we analyze intermediate reasoning steps, termed subthoughts, and propose a method based on our findings. Our approach involves segmenting a reasoning trace into sequential subthoughts based on linguistic cues. We start by prompting the model to generate continuations from the end-point of each intermediate subthought. We extract a potential answer from every completed continuation originating from different subthoughts. We find that aggregating these answers by selecting the most frequent one (the mode) often yields significantly higher accuracy compared to relying solely on the answer derived from the original complete trace. Analyzing the consistency among the answers derived from different subthoughts reveals characteristics that correlate with the model's confidence and correctness, suggesting potential for identifying less reliable answers. Our experiments across various LLMs and challenging mathematical reasoning datasets (AIME2024 and AIME2025) show consistent accuracy improvements, with gains reaching up to 13\% and 10\% respectively. Implementation is available at: https://github.com/hammoudhasan/SubthoughtReasoner.

Although contemporary large language models (LMs) demonstrate impressive question-answering capabilities, their answers are typically the product of a single call to the model. This entails an unwelcome degree of opacity and compromises performance, especially on problems that are inherently multi-step. To address these limitations, we show how LMs can be made to perform faithful multi-step reasoning via a process whose causal structure mirrors the underlying logical structure of the problem. Our approach works by chaining together reasoning steps, where each step results from calls to two fine-tuned LMs, one for selection and one for inference, to produce a valid reasoning trace. Our method carries out a beam search through the space of reasoning traces to improve reasoning quality. We demonstrate the effectiveness of our model on multi-step logical deduction and scientific question-answering, showing that it outperforms baselines on final answer accuracy, and generates humanly interpretable reasoning traces whose validity can be checked by the user.

Large language models produce fluent text but struggle with systematic reasoning, often hallucinating confident but unfounded claims. When Apple researchers added irrelevant context to mathematical problems, LLM performance degraded by 65% Apple Machine Learning Research, exposing brittle pattern-matching beneath apparent reasoning. This epistemic gap, the inability to ground claims in traceable evidence, limits AI reliability in domains requiring justification. We introduce Pramana, a novel approach that teaches LLMs explicit epistemological methodology by fine-tuning on Navya-Nyaya logic, a 2,500-year-old Indian reasoning framework. Unlike generic chain-of-thought prompting, Navya-Nyaya enforces structured 6-phase reasoning: SAMSHAYA (doubt analysis), PRAMANA (evidence source identification), PANCHA AVAYAVA (5-member syllogism with universal rules), TARKA (counterfactual verification), HETVABHASA (fallacy detection), and NIRNAYA (ascertainment distinguishing knowledge from hypothesis). This integration of logic and epistemology provides cognitive scaffolding absent from standard reasoning approaches. We fine-tune Llama 3.2-3B and DeepSeek-R1-Distill-Llama-8B on 55 Nyaya-structured logical problems (constraint satisfaction, Boolean SAT, multi-step deduction). Stage 1 achieves 100% semantic correctness on held-out evaluation despite only 40% strict format adherence revealing that models internalize reasoning content even when structural enforcement is imperfect. Ablation studies show format prompting and temperature critically affect performance, with optimal configurations differing by stage. We release all models, datasets, and training infrastructure on Hugging Face to enable further research on epistemic frameworks for AI reasoning.

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

Large Reasoning Models (LRMs) exhibit strong performance, yet often produce rationales that sound plausible but fail to reflect their true decision process, undermining reliability and trust. We introduce a formal framework for reasoning faithfulness, defined by two testable conditions: stance consistency (a coherent stance linking reasoning to answer) and causal influence (the stated reasoning causally drives the answer under output-level interventions), explicitly decoupled from accuracy. To operationalize this, we present RFEval, a benchmark of 7,186 instances across seven tasks that probes faithfulness via controlled, output-level counterfactual interventions. Evaluating twelve open-source LRMs, we find unfaithfulness in 49.7% of outputs, predominantly from stance inconsistency. Failures are concentrated in brittle, convergent domains such as math and code, and correlate more with post-training regimes than with scale: within-family ablations indicate that adding current RL-style objectives on top of supervised fine-tuning can reduce reasoning faithfulness, even when accuracy is maintained. Crucially, accuracy is neither a sufficient nor a reliable proxy for faithfulness: once controlling for model and task, the accuracy-faithfulness link is weak and statistically insignificant. Our work establishes a rigorous methodology for auditing LRM reliability and shows that trustworthy AI requires optimizing not only for correct outcomes but also for the structural integrity of the reasoning process. Our code and dataset can be found at project page: https://aidaslab.github.io/RFEval/}{https://aidaslab.github.io/RFEval/

Large language models (LLMs) are increasingly deployed in settings where reasoning, such as multi-step problem solving and chain-of-thought, is essential. Yet, current evaluation practices overwhelmingly report single-run accuracy while ignoring the intrinsic uncertainty that naturally arises from stochastic decoding. This omission creates a blind spot because practitioners cannot reliably assess whether a method's reported performance is stable, reproducible, or cost-consistent. We introduce ReasonBENCH, the first benchmark designed to quantify the underlying instability in LLM reasoning. ReasonBENCH provides (i) a modular evaluation library that standardizes reasoning frameworks, models, and tasks, (ii) a multi-run protocol that reports statistically reliable metrics for both quality and cost, and (iii) a public leaderboard to encourage variance-aware reporting. Across tasks from different domains, we find that the vast majority of reasoning strategies and models exhibit high instability. Notably, even strategies with similar average performance can display confidence intervals up to four times wider, and the top-performing methods often incur higher and less stable costs. Such instability compromises reproducibility across runs and, consequently, the reliability of reported performance. To better understand these dynamics, we further analyze the impact of prompts, model families, and scale on the trade-off between solve rate and stability. Our results highlight reproducibility as a critical dimension for reliable LLM reasoning and provide a foundation for future reasoning methods and uncertainty quantification techniques. ReasonBENCH is publicly available at https://github.com/au-clan/ReasonBench .

While accurately detecting and correcting factual contradictions in language model outputs has become increasingly important as their capabilities improve, doing so is highly challenging. We propose a novel method, FACTTRACK, for tracking atomic facts and addressing factual contradictions. Crucially, FACTTRACK also maintains time-aware validity intervals for each fact, allowing for change over time. At a high level, FACTTRACK consists of a four-step pipeline to update a world state data structure for each new event: (1) decompose the event into directional atomic facts; (2) determine the validity interval of each atomic fact using the world state; (3) detect contradictions with existing facts in the world state; and finally (4) add new facts to the world state and update existing atomic facts. When we apply FACTTRACK to contradiction detection on structured story outlines, we find that FACTTRACK using LLaMA2-7B-Chat substantially outperforms a fair baseline using LLaMA2-7B-Chat, and achieves performance comparable to a GPT4 baseline. Moreover, when using GPT4, FACTTRACK significantly outperforms the GPT4 baseline.