Recent advances in generative video models have led to significant breakthroughs in high-fidelity video synthesis, specifically in controllable video generation where the generated video is conditioned on text and action inputs, e.g., in instruction-guided video editing and world modeling in robotics. Despite these exceptional capabilities, controllable video models often hallucinate - generating future video frames that are misaligned with physical reality - which raises serious concerns in many tasks such as robot policy evaluation and planning. However, state-of-the-art video models lack the ability to assess and express their confidence, impeding hallucination mitigation. To rigorously address this challenge, we propose C3, an uncertainty quantification (UQ) method for training continuous-scale calibrated controllable video models for dense confidence estimation at the subpatch level, precisely localizing the uncertainty in each generated video frame. Our UQ method introduces three core innovations to empower video models to estimate their uncertainty. First, our method develops a novel framework that trains video models for correctness and calibration via strictly proper scoring rules. Second, we estimate the video model's uncertainty in latent space, avoiding training instability and prohibitive training costs associated with pixel-space approaches. Third, we map the dense latent-space uncertainty to interpretable pixel-level uncertainty in the RGB space for intuitive visualization, providing high-resolution uncertainty heatmaps that identify untrustworthy regions. Through extensive experiments on large-scale robot learning datasets (Bridge and DROID) and real-world evaluations, we demonstrate that our method not only provides calibrated uncertainty estimates within the training distribution, but also enables effective out-of-distribution detection.

Chain-of-thought (CoT) prompting enables Large Language Models to solve complex problems, but deploying these models safely requires reliable confidence estimates, a capability where existing methods suffer from poor calibration and severe overconfidence on incorrect predictions. We propose Enhanced Dirichlet and Topology Risk (EDTR), a novel decoding strategy that combines topological analysis with Dirichlet-based uncertainty quantification to measure LLM confidence across multiple reasoning paths. EDTR treats each CoT as a vector in high-dimensional space and extracts eight topological risk features capturing the geometric structure of reasoning distributions: tighter, more coherent clusters indicate higher confidence while dispersed, inconsistent paths signal uncertainty. We evaluate EDTR against three state-of-the-art calibration methods across four diverse reasoning benchmarks spanning olympiad-level mathematics (AIME), grade school math (GSM8K), commonsense reasoning, and stock price prediction \cite{zhang2025aime, cobbe2021training, talmor-etal-2019-commonsenseqa, yahoo_finance}. EDTR achieves 41\% better calibration than competing methods with an average ECE of 0.287 and the best overall composite score of 0.672, while notably achieving perfect accuracy on AIME and exceptional calibration on GSM8K with an ECE of 0.107, domains where baselines exhibit severe overconfidence. Our work provides a geometric framework for understanding and quantifying uncertainty in multi-step LLM reasoning, enabling more reliable deployment where calibrated confidence estimates are essential.

When does a large language model (LLM) know what it does not know? Uncertainty quantification (UQ) provides measures of uncertainty, such as an estimate of the confidence in an LLM's generated output, and is therefore increasingly recognized as a crucial component of trusted AI systems. Black-box UQ methods do not require access to internal model information from the generating LLM and therefore have numerous real-world advantages, such as robustness to system changes, adaptability to choice of LLM, reduced costs, and computational tractability. In this paper, we investigate the effectiveness of UQ techniques that are primarily but not necessarily entirely black-box, where the consistency between a generated output and other sampled generations is used as a proxy for confidence in its correctness. We propose a high-level non-verbalized similarity-based aggregation framework that subsumes a broad swath of UQ approaches suitable for complex generative tasks, as well as introduce specific novel techniques from the framework that train confidence estimation models using small training sets. Through an empirical study with datasets spanning the diverse tasks of question answering, summarization, and text-to-SQL, we demonstrate that our proposed similarity-based methods can yield better calibrated confidences than baselines.

Uncertainty quantification for LLMs is a key research direction towards addressing hallucination and other issues that limit their reliable deployment. In this work, we show that reasoning trace length is a simple and useful confidence estimator in large reasoning models. Through comprehensive experiments across multiple models, datasets, and prompts, we show that trace length performs in comparable but complementary ways to other zero-shot confidence estimators such as verbalized confidence. Our work reveals that reasoning post-training fundamentally alters the relationship between trace length and accuracy, going beyond prior work that had shown that post-training causes traces to grow longer in general (e.g., "overthinking"). We investigate the mechanisms behind trace length's performance as a confidence signal, observing that the effect remains even after adjusting for confounders such as problem difficulty and GRPO-induced length bias. We identify high-entropy or "forking" tokens as playing a key role in the mechanism. Our findings demonstrate that reasoning post-training enhances uncertainty quantification beyond verbal expressions, and establish trace length as a practical confidence measure for large reasoning models.

As Large Language Models (LLMs) are increasingly deployed in decision-critical domains, it becomes essential to ensure that their confidence estimates faithfully correspond to their actual correctness. Existing calibration methods have primarily focused on post-hoc adjustments or auxiliary model training; however, many of these approaches necessitate additional supervision or parameter updates. In this work, we propose a novel prompt-based calibration framework inspired by the Credence Calibration Game. Our method establishes a structured interaction loop wherein LLMs receive feedback based on the alignment of their predicted confidence with correctness. Through feedback-driven prompting and natural language summaries of prior performance, our framework dynamically improves model calibration. Extensive experiments across models and game configurations demonstrate consistent improvements in evaluation metrics. Our results highlight the potential of game-based prompting as an effective strategy for LLM calibration. Code and data are available at https://anonymous.4open.science/r/LLM-Calibration/.

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.

Reasoning language models have set state-of-the-art (SOTA) records on many challenging benchmarks, enabled by multi-step reasoning induced using reinforcement learning. However, like previous language models, reasoning models are prone to generating confident, plausible responses that are incorrect (hallucinations). Knowing when and how much to trust these models is critical to the safe deployment of reasoning models in real-world applications. To this end, we explore uncertainty quantification of reasoning models in this work. Specifically, we ask three fundamental questions: First, are reasoning models well-calibrated? Second, does deeper reasoning improve model calibration? Finally, inspired by humans' innate ability to double-check their thought processes to verify the validity of their answers and their confidence, we ask: can reasoning models improve their calibration by explicitly reasoning about their chain-of-thought traces? We introduce introspective uncertainty quantification (UQ) to explore this direction. In extensive evaluations on SOTA reasoning models across a broad range of benchmarks, we find that reasoning models: (i) are typically overconfident, with self-verbalized confidence estimates often greater than 85% particularly for incorrect responses, (ii) become even more overconfident with deeper reasoning, and (iii) can become better calibrated through introspection (e.g., o3-Mini and DeepSeek R1) but not uniformly (e.g., Claude 3.7 Sonnet becomes more poorly calibrated). Lastly, we conclude with important research directions to design necessary UQ benchmarks and improve the calibration of reasoning models.

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

Large language models ($\textbf{LLMs}$) have emerged as a powerful method for discovery. Instead of utilizing numerical data, LLMs utilize associated variable $\textit{semantic metadata}$ to predict variable relationships. Simultaneously, LLMs demonstrate impressive abilities to act as black-box optimizers when given an objective $f$ and sequence of trials. We study LLMs at the intersection of these two capabilities by applying LLMs to the task of $\textit{interactive graph discovery}$: given a ground truth graph $G^*$ capturing variable relationships and a budget of $I$ edge experiments over $R$ rounds, minimize the distance between the predicted graph $\hat{G}_R$ and $G^*$ at the end of the $R$-th round. To solve this task we propose $\textbf{IGDA}$, a LLM-based pipeline incorporating two key components: 1) an LLM uncertainty-driven method for edge experiment selection 2) a local graph update strategy utilizing binary feedback from experiments to improve predictions for unselected neighboring edges. Experiments on eight different real-world graphs show our approach often outperforms all baselines including a state-of-the-art numerical method for interactive graph discovery. Further, we conduct a rigorous series of ablations dissecting the impact of each pipeline component. Finally, to assess the impact of memorization, we apply our interactive graph discovery strategy to a complex, new (as of July 2024) causal graph on protein transcription factors, finding strong performance in a setting where memorization is impossible. Overall, our results show IGDA to be a powerful method for graph discovery complementary to existing numerically driven approaches.

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