Daily Papers

Supervised learning for empathy regression is challenged by noisy self-reported empathy scores. While many algorithms have been proposed for learning with noisy labels in textual classification problems, the regression counterpart is relatively under-explored. We propose UPLME, an uncertainty-aware probabilistic language modelling framework to capture label noise in the regression setting of empathy detection. UPLME includes a probabilistic language model that predicts both empathy score and heteroscedastic uncertainty and is trained using Bayesian concepts with variational model ensembling. We further introduce two novel loss components: one penalises degenerate Uncertainty Quantification (UQ), and another enforces the similarity between the input pairs on which we predict empathy. UPLME provides state-of-the-art performance (Pearson Correlation Coefficient: 0.558rightarrow0.580 and 0.629rightarrow0.634) in terms of the performance reported in the literature in two public benchmarks, having label noise. Through synthetic label noise injection, we show that UPLME is effective in separating noisy and clean samples based on the predicted uncertainty. UPLME further outperform (Calibration error: 0.571rightarrow0.376) a recent variational model ensembling-based UQ method designed for regression problems.

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

Large language models (LLMs) have transformed natural language processing, but their reliable deployment requires effective uncertainty quantification (UQ). Existing UQ methods are often heuristic and lack a probabilistic foundation. This paper begins by providing a theoretical justification for the role of perturbations in UQ for LLMs. We then introduce a dual random walk perspective, modeling input-output pairs as two Markov chains with transition probabilities defined by semantic similarity. Building on this, we propose a fully probabilistic framework based on an inverse model, which quantifies uncertainty by evaluating the diversity of the input space conditioned on a given output through systematic perturbations. Within this framework, we define a new uncertainty measure, Inv-Entropy. A key strength of our framework is its flexibility: it supports various definitions of uncertainty measures, embeddings, perturbation strategies, and similarity metrics. We also propose GAAP, a perturbation algorithm based on genetic algorithms, which enhances the diversity of sampled inputs. In addition, we introduce a new evaluation metric, Temperature Sensitivity of Uncertainty (TSU), which directly assesses uncertainty without relying on correctness as a proxy. Extensive experiments demonstrate that Inv-Entropy outperforms existing semantic UQ methods. The code to reproduce the results can be found at https://github.com/UMDataScienceLab/Uncertainty-Quantification-for-LLMs.

Large Language Models (LLMs) are increasingly employed in real-world applications, driving the need to evaluate the trustworthiness of their generated text. To this end, reliable uncertainty estimation is essential. Since current LLMs generate text autoregressively through a stochastic process, the same prompt can lead to varying outputs. Consequently, leading uncertainty estimation methods generate and analyze multiple output sequences to determine the LLM's uncertainty. However, generating output sequences is computationally expensive, making these methods impractical at scale. In this work, we inspect the theoretical foundations of the leading methods and explore new directions to enhance their computational efficiency. Building on the framework of proper scoring rules, we find that the negative log-likelihood of the most likely output sequence constitutes a theoretically grounded uncertainty measure. To approximate this alternative measure, we propose G-NLL, which has the advantage of being obtained using only a single output sequence generated by greedy decoding. This makes uncertainty estimation more efficient and straightforward, while preserving theoretical rigor. Empirical results demonstrate that G-NLL achieves state-of-the-art performance across various LLMs and tasks. Our work lays the foundation for efficient and reliable uncertainty estimation in natural language generation, challenging the necessity of more computationally involved methods currently leading the field.

This paper introduces Bayesian uncertainty modeling using Stochastic Weight Averaging-Gaussian (SWAG) in Natural Language Understanding (NLU) tasks. We apply the approach to standard tasks in natural language inference (NLI) and demonstrate the effectiveness of the method in terms of prediction accuracy and correlation with human annotation disagreements. We argue that the uncertainty representations in SWAG better reflect subjective interpretation and the natural variation that is also present in human language understanding. The results reveal the importance of uncertainty modeling, an often neglected aspect of neural language modeling, in NLU tasks.

In this paper, we evaluate the capability of transformer-based language models in making inferences over uncertain text that includes uncertain rules of reasoning. We cover both Pre-trained Language Models (PLMs) and generative Large Language Models (LLMs). Our evaluation results show that both generations of language models struggle with reasoning over uncertain text. We propose a novel end-to-end fine-tuning approach, Probabilistic Constraint Training (PCT), that utilizes probabilistic logical rules as constraints in the fine-tuning phase without relying on these rules in the inference stage. To assess the effectiveness of PCT, we utilize the related corpora and, additionally, create a new and more challenging benchmark that, unlike the previous ones, uses instance-specific rules. Our study demonstrates that PCT improves the transformer-based language model's intrinsic reasoning and makes their probabilistic logical reasoning process more explicit and explainable. Furthermore, PCT equips these models to effectively handle novel situations, including higher reasoning depth, new domains, and complex probabilistic structures.

Accurate uncertainty quantification (UQ) in Large Language Models (LLMs) is critical for trustworthy deployment. While real-world language is inherently ambiguous, reflecting aleatoric uncertainty, existing UQ methods are typically benchmarked against tasks with no ambiguity. In this work, we demonstrate that while current uncertainty estimators perform well under the restrictive assumption of no ambiguity, they degrade to close-to-random performance on ambiguous data. To this end, we introduce MAQA* and AmbigQA*, the first ambiguous question-answering (QA) datasets equipped with ground-truth answer distributions estimated from factual co-occurrence. We find this performance deterioration to be consistent across different estimation paradigms: using the predictive distribution itself, internal representations throughout the model, and an ensemble of models. We show that this phenomenon can be theoretically explained, revealing that predictive-distribution and ensemble-based estimators are fundamentally limited under ambiguity. Overall, our study reveals a key shortcoming of current UQ methods for LLMs and motivates a rethinking of current modeling paradigms.

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

Recent advances in language models (LMs) have led to significant improvements in quality on complex NLP tasks, but at the expense of increased inference costs. Cascading offers a simple strategy to achieve more favorable cost-quality tradeoffs: here, a small model is invoked for most "easy" instances, while a few "hard" instances are deferred to the large model. While the principles underpinning cascading are well-studied for classification tasks - with deferral based on predicted class uncertainty favored theoretically and practically - a similar understanding is lacking for generative LM tasks. In this work, we initiate a systematic study of deferral rules for LM cascades. We begin by examining the natural extension of predicted class uncertainty to generative LM tasks, namely, the predicted sequence uncertainty. We show that this measure suffers from the length bias problem, either over- or under-emphasizing outputs based on their lengths. This is because LMs produce a sequence of uncertainty values, one for each output token; and moreover, the number of output tokens is variable across examples. To mitigate this issue, we propose to exploit the richer token-level uncertainty information implicit in generative LMs. We argue that naive predicted sequence uncertainty corresponds to a simple aggregation of these uncertainties. By contrast, we show that incorporating token-level uncertainty through learned post-hoc deferral rules can significantly outperform such simple aggregation strategies, via experiments on a range of natural language benchmarks with FLAN-T5 models. We further show that incorporating embeddings from the smaller model and intermediate layers of the larger model can give an additional boost in the overall cost-quality tradeoff.

Pixel-based language models aim to solve the vocabulary bottleneck problem in language modeling, but the challenge of uncertainty quantification remains open. The novelty of this work consists of analysing uncertainty and confidence in pixel-based language models across 18 languages and 7 scripts, all part of 3 semantically challenging tasks. This is achieved through several methods such as Monte Carlo Dropout, Transformer Attention, and Ensemble Learning. The results suggest that pixel-based models underestimate uncertainty when reconstructing patches. The uncertainty is also influenced by the script, with Latin languages displaying lower uncertainty. The findings on ensemble learning show better performance when applying hyperparameter tuning during the named entity recognition and question-answering tasks across 16 languages.

Estimating uncertainty in Large Language Models (LLMs) is important for properly evaluating LLMs, and ensuring safety for users. However, prior approaches to uncertainty estimation focus on the final answer in generated text, ignoring intermediate steps that might dramatically impact the outcome. We hypothesize that there exist key forking tokens, such that re-sampling the system at those specific tokens, but not others, leads to very different outcomes. To test this empirically, we develop a novel approach to representing uncertainty dynamics across individual tokens of text generation, and applying statistical models to test our hypothesis. Our approach is highly flexible: it can be applied to any dataset and any LLM, without fine tuning or accessing model weights. We use our method to analyze LLM responses on 7 different tasks across 4 domains, spanning a wide range of typical use cases. We find many examples of forking tokens, including surprising ones such as punctuation marks, suggesting that LLMs are often just a single token away from saying something very different.

Uncertainty learning and quantification of models are crucial tasks to enhance the trustworthiness of the models. Importantly, the recent surge of generative language models (GLMs) emphasizes the need for reliable uncertainty quantification due to the concerns on generating hallucinated facts. In this paper, we propose to learn neural prediction set models that comes with the probably approximately correct (PAC) guarantee for quantifying the uncertainty of GLMs. Unlike existing prediction set models, which are parameterized by a scalar value, we propose to parameterize prediction sets via neural networks, which achieves more precise uncertainty quantification but still satisfies the PAC guarantee. We demonstrate the efficacy of our method on four types of language datasets and six types of models by showing that our method improves the quantified uncertainty by 63% on average, compared to a standard baseline method.

Large language models (LLMs) specializing in natural language generation (NLG) have recently started exhibiting promising capabilities across a variety of domains. However, gauging the trustworthiness of responses generated by LLMs remains an open challenge, with limited research on uncertainty quantification (UQ) for NLG. Furthermore, existing literature typically assumes white-box access to language models, which is becoming unrealistic either due to the closed-source nature of the latest LLMs or computational constraints. In this work, we investigate UQ in NLG for black-box LLMs. We first differentiate uncertainty vs confidence: the former refers to the "dispersion" of the potential predictions for a fixed input, and the latter refers to the confidence on a particular prediction/generation. We then propose and compare several confidence/uncertainty metrics, applying them to selective NLG where unreliable results could either be ignored or yielded for further assessment. Experiments were carried out with several popular LLMs on question-answering datasets (for evaluation purposes). Results reveal that a simple metric for the semantic dispersion can be a reliable predictor of the quality of LLM responses, providing valuable insights for practitioners on uncertainty management when adopting LLMs. The code to replicate our experiments is available at https://github.com/zlin7/UQ-NLG.

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

Uncertainty estimation is essential for enhancing the reliability of Large Language Models (LLMs), particularly in high-stakes applications. Existing methods often overlook semantic dependencies, relying on token-level probability measures that fail to capture structural relationships within the generated text. We propose GENUINE: Graph ENhanced mUlti-level uncertaINty Estimation for Large Language Models, a structure-aware framework that leverages dependency parse trees and hierarchical graph pooling to refine uncertainty quantification. By incorporating supervised learning, GENUINE effectively models semantic and structural relationships, improving confidence assessments. Extensive experiments across NLP tasks show that GENUINE achieves up to 29% higher AUROC than semantic entropy-based approaches and reduces calibration errors by over 15%, demonstrating the effectiveness of graph-based uncertainty modeling. The code is available at https://github.com/ODYSSEYWT/GUQ.

Large Language Models (LLMs) that can express interpretable and calibrated uncertainty are crucial in high-stakes domains. While methods to compute uncertainty post-hoc exist, they are often sampling-based and therefore computationally expensive or lack calibration. We propose a three-stage pipeline to post-train LLMs to efficiently infer calibrated uncertainty estimates for their responses. First, we compute fine-grained entropy-based uncertainty scores on the training data, capturing the distributional variability of model outputs in embedding space. Second, these scores are calibrated via Platt scaling, producing reliable and human-interpretable uncertainty signals. Finally, the target LLM is post-trained via reinforcement learning to align its policy with these calibrated signals through a verifiable reward function. Unlike post-hoc uncertainty estimation methods, our approach provides interpretable and computationally efficient uncertainty estimates at test time. Experiments show that models trained with our pipeline achieve better calibration than baselines and generalize to unseen tasks without further processing, suggesting that they learn a robust uncertainty reasoning behavior.

Although large language models (LLMs) are capable of performing various tasks, they still suffer from producing plausible but incorrect responses. To improve the reliability of LLMs, recent research has focused on uncertainty quantification to predict whether a response is correct or not. However, most uncertainty quantification methods have been evaluated on questions requiring a single clear answer, ignoring the existence of data uncertainty that arises from irreducible randomness. Instead, these methods only consider model uncertainty, which arises from a lack of knowledge. In this paper, we investigate previous uncertainty quantification methods under the presence of data uncertainty. Our contributions are two-fold: 1) proposing a new Multi-Answer Question Answering dataset, MAQA, consisting of world knowledge, mathematical reasoning, and commonsense reasoning tasks to evaluate uncertainty quantification regarding data uncertainty, and 2) assessing 5 uncertainty quantification methods of diverse white- and black-box LLMs. Our findings show that entropy and consistency-based methods estimate the model uncertainty well even under data uncertainty, while other methods for white- and black-box LLMs struggle depending on the tasks. Additionally, methods designed for white-box LLMs suffer from overconfidence in reasoning tasks compared to simple knowledge queries. We believe our observations will pave the way for future work on uncertainty quantification in realistic setting.

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

Language models (LM) are capable of remarkably complex linguistic tasks; however, numerical reasoning is an area in which they frequently struggle. An important but rarely evaluated form of reasoning is understanding probability distributions. In this paper, we focus on evaluating the probabilistic reasoning capabilities of LMs using idealized and real-world statistical distributions. We perform a systematic evaluation of state-of-the-art LMs on three tasks: estimating percentiles, drawing samples, and calculating probabilities. We evaluate three ways to provide context to LMs 1) anchoring examples from within a distribution or family of distributions, 2) real-world context, 3) summary statistics on which to base a Normal approximation. Models can make inferences about distributions, and can be further aided by the incorporation of real-world context, example shots and simplified assumptions, even if these assumptions are incorrect or misspecified. To conduct this work, we developed a comprehensive benchmark distribution dataset with associated question-answer pairs that we will release publicly.

When using large language models (LLMs) in high-stakes applications, we need to know when we can trust their predictions. Some works argue that prompting high-performance LLMs is sufficient to produce calibrated uncertainties, while others introduce sampling methods that can be prohibitively expensive. In this work, we first argue that prompting on its own is insufficient to achieve good calibration and then show that fine-tuning on a small dataset of correct and incorrect answers can create an uncertainty estimate with good generalization and small computational overhead. We show that a thousand graded examples are sufficient to outperform baseline methods and that training through the features of a model is necessary for good performance and tractable for large open-source models when using LoRA. We also investigate the mechanisms that enable reliable LLM uncertainty estimation, finding that many models can be used as general-purpose uncertainty estimators, applicable not just to their own uncertainties but also the uncertainty of other models. Lastly, we show that uncertainty estimates inform human use of LLMs in human-AI collaborative settings through a user study.

We introduce a method to measure uncertainty in large language models. For tasks like question answering, it is essential to know when we can trust the natural language outputs of foundation models. We show that measuring uncertainty in natural language is challenging because of "semantic equivalence" -- different sentences can mean the same thing. To overcome these challenges we introduce semantic entropy -- an entropy which incorporates linguistic invariances created by shared meanings. Our method is unsupervised, uses only a single model, and requires no modifications to off-the-shelf language models. In comprehensive ablation studies we show that the semantic entropy is more predictive of model accuracy on question answering data sets than comparable baselines.

Quantifying uncertainty in large language models (LLMs) is important for safety-critical applications because it helps spot incorrect answers, known as hallucinations. One major trend of uncertainty quantification methods is based on estimating the entropy of the distribution of the LLM's potential output sequences. This estimation is based on a set of output sequences and associated probabilities obtained by querying the LLM several times. In this paper, we advocate and experimentally show that the probability of unobserved sequences plays a crucial role, and we recommend future research to integrate it to enhance such LLM uncertainty quantification methods.

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

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

As large language models continue to be widely developed, robust uncertainty quantification techniques will become crucial for their safe deployment in high-stakes scenarios. In this work, we explore how conformal prediction can be used to provide uncertainty quantification in language models for the specific task of multiple-choice question-answering. We find that the uncertainty estimates from conformal prediction are tightly correlated with prediction accuracy. This observation can be useful for downstream applications such as selective classification and filtering out low-quality predictions. We also investigate the exchangeability assumption required by conformal prediction to out-of-subject questions, which may be a more realistic scenario for many practical applications. Our work contributes towards more trustworthy and reliable usage of large language models in safety-critical situations, where robust guarantees of error rate are required.

Leveraging human preferences for steering the behavior of Large Language Models (LLMs) has demonstrated notable success in recent years. Nonetheless, data selection and labeling are still a bottleneck for these systems, particularly at large scale. Hence, selecting the most informative points for acquiring human feedback may considerably reduce the cost of preference labeling and unleash the further development of LLMs. Bayesian Active Learning provides a principled framework for addressing this challenge and has demonstrated remarkable success in diverse settings. However, previous attempts to employ it for Preference Modeling did not meet such expectations. In this work, we identify that naive epistemic uncertainty estimation leads to the acquisition of redundant samples. We address this by proposing the Bayesian Active Learner for Preference Modeling (BAL-PM), a novel stochastic acquisition policy that not only targets points of high epistemic uncertainty according to the preference model but also seeks to maximize the entropy of the acquired prompt distribution in the feature space spanned by the employed LLM. Notably, our experiments demonstrate that BAL-PM requires 33% to 68% fewer preference labels in two popular human preference datasets and exceeds previous stochastic Bayesian acquisition policies.

In question-answering tasks, determining when to trust the outputs is crucial to the alignment of large language models (LLMs). Kuhn et al. (2023) introduces semantic entropy as a measure of uncertainty, by incorporating linguistic invariances from the same meaning. It primarily relies on setting threshold to measure the level of semantic equivalence relation. We propose a more nuanced framework that extends beyond such thresholding by developing a Shapley-based uncertainty metric that captures the continuous nature of semantic relationships. We establish three fundamental properties that characterize valid uncertainty metrics and prove that our Shapley uncertainty satisfies these criteria. Through extensive experiments, we demonstrate that our Shapley uncertainty more accurately predicts LLM performance in question-answering and other datasets, compared to similar baseline measures.

Estimating the uncertainty of responses of Large Language Models~(LLMs) remains a critical challenge. While recent Bayesian methods have demonstrated effectiveness in quantifying uncertainty through low-rank weight updates, they typically require complex fine-tuning or post-training procedures. In this paper, we propose Training-Free Bayesianization~(TFB), a novel framework that transforms existing off-the-shelf trained LoRA adapters into Bayesian ones without additional training. TFB systematically searches for the maximally acceptable level of variance in the weight posterior, constrained within a family of low-rank isotropic Gaussian distributions. We theoretically demonstrate that under mild conditions, this search process is equivalent to variational inference for the weights. Through comprehensive experiments, we show that TFB achieves superior uncertainty estimation and generalization compared to existing methods while eliminating the need for complex training procedures. Code will be available at https://github.com/Wang-ML-Lab/bayesian-peft.

As instruction-tuned large language models (LLMs) evolve, aligning pretrained foundation models presents increasing challenges. Existing alignment strategies, which typically leverage diverse and high-quality data sources, often overlook the intrinsic uncertainty of tasks, learning all data samples equally. This may lead to suboptimal data efficiency and model performance. In response, we propose uncertainty-aware learning (UAL) to improve the model alignment of different task scenarios, by introducing the sample uncertainty (elicited from more capable LLMs). We implement UAL in a simple fashion -- adaptively setting the label smoothing value of training according to the uncertainty of individual samples. Analysis shows that our UAL indeed facilitates better token clustering in the feature space, validating our hypothesis. Extensive experiments on widely used benchmarks demonstrate that our UAL significantly and consistently outperforms standard supervised fine-tuning. Notably, LLMs aligned in a mixed scenario have achieved an average improvement of 10.62\% on high-entropy tasks (i.e., AlpacaEval leaderboard), and 1.81\% on complex low-entropy tasks (i.e., MetaMath and GSM8K).

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) often suffer from overconfidence during inference, particularly when adapted to downstream domain-specific tasks with limited data. Previous work addresses this issue by employing approximate Bayesian estimation after the LLMs are trained, enabling them to quantify uncertainty. However, such post-training approaches' performance is severely limited by the parameters learned during training. In this paper, we go beyond post-training Bayesianization and propose Bayesian Low-Rank Adaptation by Backpropagation (BLoB), an algorithm that continuously and jointly adjusts both the mean and covariance of LLM parameters throughout the whole fine-tuning process. Our empirical results verify the effectiveness of BLoB in terms of generalization and uncertainty estimation, when evaluated on both in-distribution and out-of-distribution data.

Vision-language models (VLMs) embed aligned image-text pairs into a joint space but often rely on deterministic embeddings, assuming a one-to-one correspondence between images and texts. This oversimplifies real-world relationships, which are inherently many-to-many, with multiple captions describing a single image and vice versa. We introduce Probabilistic Language-Image Pre-training (ProLIP), the first probabilistic VLM pre-trained on a billion-scale image-text dataset using only probabilistic objectives, achieving a strong zero-shot capability (e.g., 74.6% ImageNet zero-shot accuracy with ViT-B/16). ProLIP efficiently estimates uncertainty by an "uncertainty token" without extra parameters. We also introduce a novel inclusion loss that enforces distributional inclusion relationships between image-text pairs and between original and masked inputs. Experiments demonstrate that, by leveraging uncertainty estimates, ProLIP benefits downstream tasks and aligns with intuitive notions of uncertainty, e.g., shorter texts being more uncertain and more general inputs including specific ones. Utilizing text uncertainties, we further improve ImageNet accuracy from 74.6% to 75.8% (under a few-shot setting), supporting the practical advantages of our probabilistic approach. The code is available at https://github.com/naver-ai/prolip

Large language models (LLMs) have demonstrated remarkable performance across diverse tasks by encoding vast amounts of factual knowledge. However, they are still prone to hallucinations, generating incorrect or misleading information, often accompanied by high uncertainty. Existing methods for hallucination detection primarily focus on quantifying internal uncertainty, which arises from missing or conflicting knowledge within the model. However, hallucinations can also stem from external uncertainty, where ambiguous user queries lead to multiple possible interpretations. In this work, we introduce Semantic Volume, a novel mathematical measure for quantifying both external and internal uncertainty in LLMs. Our approach perturbs queries and responses, embeds them in a semantic space, and computes the determinant of the Gram matrix of the embedding vectors, capturing their dispersion as a measure of uncertainty. Our framework provides a generalizable and unsupervised uncertainty detection method without requiring white-box access to LLMs. We conduct extensive experiments on both external and internal uncertainty detection, demonstrating that our Semantic Volume method consistently outperforms existing baselines in both tasks. Additionally, we provide theoretical insights linking our measure to differential entropy, unifying and extending previous sampling-based uncertainty measures such as the semantic entropy. Semantic Volume is shown to be a robust and interpretable approach to improving the reliability of LLMs by systematically detecting uncertainty in both user queries and model responses.

Eliciting information to reduce uncertainty about a latent entity is a critical task in many application domains, e.g., assessing individual student learning outcomes, diagnosing underlying diseases, or learning user preferences. Though natural language is a powerful medium for this purpose, large language models (LLMs) and existing fine-tuning algorithms lack mechanisms for strategically gathering information to refine their own understanding of the latent entity. To harness the generalization power and world knowledge of LLMs in developing effective information-gathering strategies, we propose an adaptive elicitation framework that actively reduces uncertainty on the latent entity. Since probabilistic modeling of an abstract latent entity is difficult, our framework adopts a predictive view of uncertainty, using a meta-learned language model to simulate future observations and enable scalable uncertainty quantification over complex natural language. Through autoregressive forward simulation, our model quantifies how new questions reduce epistemic uncertainty, enabling the development of sophisticated information-gathering strategies to choose the most informative next queries. In experiments on the 20 questions game, dynamic opinion polling, and adaptive student assessment, our method consistently outperforms baselines in identifying critical unknowns and improving downstream predictions, illustrating the promise of strategic information gathering in natural language settings.

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

Recently, Large Language Models (LLMs) have demonstrated significant potential for data annotation, markedly reducing the labor costs associated with downstream applications. However, existing methods mostly adopt an aggressive strategy by prompting LLM to determine a single gold label for each unlabeled sample. Due to the inherent uncertainty within LLMs, they often produce incorrect labels for difficult samples, severely compromising the data quality for downstream applications. Motivated by ambiguity aversion in human behaviors, we propose a novel candidate annotation paradigm wherein large language models are encouraged to output all possible labels when incurring uncertainty. To ensure unique labels are provided for downstream tasks, we develop a teacher-student framework CanDist that distills candidate annotations with a Small Language Model (SLM). We further provide a rigorous justification demonstrating that distilling candidate annotations from the teacher LLM offers superior theoretical guarantees compared to directly using single annotations. Extensive experiments across six text classification tasks validate the effectiveness of our proposed method. The source code is available at https://github.com/MingxuanXia/CanDist.

Vision-language models (VLMs), such as CLIP and SigLIP, have found remarkable success in classification, retrieval, and generative tasks. For this, VLMs deterministically map images and text descriptions to a joint latent space in which their similarity is assessed using the cosine similarity. However, a deterministic mapping of inputs fails to capture uncertainties over concepts arising from domain shifts when used in downstream tasks. In this work, we propose post-hoc uncertainty estimation in VLMs that does not require additional training. Our method leverages a Bayesian posterior approximation over the last layers in VLMs and analytically quantifies uncertainties over cosine similarities. We demonstrate its effectiveness for uncertainty quantification and support set selection in active learning. Compared to baselines, we obtain improved and well-calibrated predictive uncertainties, interpretable uncertainty estimates, and sample-efficient active learning. Our results show promise for safety-critical applications of large-scale models.

Uncertainty quantification (UQ) for open-ended language generation remains a critical yet underexplored challenge, especially under black-box constraints where internal model signals are inaccessible. In this paper, we introduce Token-Entropy Conformal Prediction (TECP), a novel framework that leverages token-level entropy as a logit-free, reference-free uncertainty measure and integrates it into a split conformal prediction (CP) pipeline to construct prediction sets with formal coverage guarantees. Unlike existing approaches that rely on semantic consistency heuristics or white-box features, TECP directly estimates epistemic uncertainty from the token entropy structure of sampled generations and calibrates uncertainty thresholds via CP quantiles to ensure provable error control. Empirical evaluations across six large language models and two benchmarks (CoQA and TriviaQA) demonstrate that TECP consistently achieves reliable coverage and compact prediction sets, outperforming prior self-consistency-based UQ methods. Our method provides a principled and efficient solution for trustworthy generation in black-box LLM settings.

Reward models (RM) play a critical role in aligning generations of large language models (LLM) to human expectations. However, prevailing RMs fail to capture the stochasticity within human preferences and cannot effectively evaluate the reliability of reward predictions. To address these issues, we propose Uncertain-aware RM (URM) and Uncertain-aware RM Ensemble (URME) to incorporate and manage uncertainty in reward modeling. URM can model the distribution of disentangled attributes within human preferences, while URME quantifies uncertainty through discrepancies in the ensemble, thereby identifying potential lack of knowledge during reward evaluation. Experiment results indicate that the proposed URM achieves state-of-the-art performance compared to models with the same size, demonstrating the effectiveness of modeling uncertainty within human preferences. Furthermore, empirical results show that through uncertainty quantification, URM and URME can identify unreliable predictions to improve the quality of reward evaluations.

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

Comprehensive evaluation of Large Language Models (LLMs) is an open research problem. Existing evaluations rely on deterministic point estimates generated via greedy decoding. However, we find that deterministic evaluations fail to capture the whole output distribution of a model, yielding inaccurate estimations of model capabilities. This is particularly problematic in critical contexts such as unlearning and alignment, where precise model evaluations are crucial. To remedy this, we introduce the first formal probabilistic evaluation framework for LLMs. Namely, we propose novel metrics with high probability guarantees concerning the output distribution of a model. Our metrics are application-independent and allow practitioners to make more reliable estimates about model capabilities before deployment. Our experimental analysis reveals that deterministic evaluations falsely indicate successful unlearning and alignment, whereas our probabilistic evaluations better capture model capabilities. We show how to overcome challenges associated with probabilistic outputs in a case study on unlearning by introducing (1) a novel loss based on entropy optimization, and (2) adaptive temperature scaling. We demonstrate that our approach significantly enhances unlearning in probabilistic settings on recent benchmarks. Overall, our proposed shift from point estimates to probabilistic evaluations of output distributions represents an important step toward comprehensive evaluations of LLMs. Code available at https://www.cs.cit.tum.de/daml/probabilistic-unlearning/.

Being probabilistic models, during inference large language models (LLMs) display rare events: behaviour that is far from typical but highly significant. By definition all rare events are hard to see, but the enormous scale of LLM usage means that events completely unobserved during development are likely to become prominent in deployment. Here we present an end-to-end framework for the systematic analysis of rare events in LLMs. We provide a practical implementation spanning theory, efficient generation strategies, probability estimation and error analysis, which we illustrate with concrete examples. We outline extensions and applications to other models and contexts, highlighting the generality of the concepts and techniques presented here.

In many applications of LLMs, natural language responses often have an underlying structure such as representing discrete labels, numerical values, or graphs. Yet, existing decoding and uncertainty estimation methods operate only in language space and largely disregard structural information. We address this by modeling LLM outputs directly in a task-dependent latent structure. By equipping this structure with a dissimilarity measure, we can compute Bayes-optimal responses. These are not selected from sampled generations but are newly synthesized by combining individual responses in the latent space. Across different tasks, Bayes-optimal responses consistently outperform standard decoding methods like beam search. Moreover, quantifying uncertainty via the induced Bayesian risk captures variations in terms of the latent structure and improves alignment with output quality and correctness. Our decision-theoretic framework is applicable to any problem that admits a latent response structure and enables reliable task-aware LLM predictions.

Uncertainty quantification (UQ) is an important technique for ensuring the trustworthiness of LLMs, given their tendency to hallucinate. Existing state-of-the-art UQ approaches for free-form generation rely heavily on sampling, which incurs high computational cost and variance. In this work, we propose the first gradient-based UQ method for free-form generation, SemGrad, which is sampling-free and computationally efficient. Unlike prior gradient-based methods developed for classification tasks that operates in parameter space, we propose to consider gradients in semantic space. Our method builds on the key intuition that a confident LLM should maintain stable output distributions under semantically equivalent input perturbations. We interpret the stability as the gradients in semantic space and introduce a Semantic Preservation Score (SPS) to identify embeddings that best capture semantics, with respect to which gradients are computed. We further propose HybridGrad, which combines the strengths of SemGrad and parameter gradients. Experiments demonstrate that both of our methods provide efficient and effective uncertainty estimates, achieving superior performance than state-of-the-art methods, particularly in settings with multiple valid responses.

This paper investigates the capabilities of Large Language Models (LLMs) in the context of understanding their own knowledge and measuring their uncertainty. We argue this is an important feature for mitigating hallucinations. Specifically, we focus on addressing known-unknown questions, characterized by high uncertainty due to the absence of definitive answers. To facilitate our study, we collect a dataset with new Known-Unknown Questions (KUQ) and propose a novel categorization scheme to elucidate the sources of uncertainty. Subsequently, we assess the LLMs' ability to differentiate between known and unknown questions and classify them accordingly. Moreover, we evaluate the quality of their answers in an Open-Ended QA setting. To quantify the uncertainty expressed in the answers, we create a semantic evaluation method that measures the model's accuracy in expressing uncertainty between known vs unknown questions.

As large language models (LLMs) are increasingly integrated into high-stakes decision-making, the ability to reliably quantify uncertainty has become a critical requirement for safety and trust. However, current uncertainty quantification methods primarily operate at the output level, often failing to distinguish whether uncertainty arises from the model's lack of knowledge or from ambiguity in the user's input. While input-centric uncertainty quantification has recently emerged as a promising direction, it remains relatively underexplored and typically relies on coarse, input-level information. Consequently, users are provided with scalar uncertainty scores that offer little actionable guidance on which parts of the input should be clarified to improve reliability. To address this limitation, we propose Shapley-based input uncertainty Quantification (ShaQ), a framework for span-level attribution of input-induced uncertainty. Our approach models ambiguous spans in the input as players in a cooperative game and quantifies their contributions using Shapley values, defined via the weighted average of marginal reductions in conditional entropy obtained by clarifying each span coalition. Unlike existing input-level approaches, our formulation captures complex interactions among spans and provides a principled decomposition in which individual attributions sum exactly to the total input-induced uncertainty. We evaluate ShaQ on the AmbigQA and AmbiEnt benchmarks, where it achieves state-of-the-art performance in ambiguity detection. We further demonstrate its utility on MediTOD, showing that ShaQ can localize under-specified clinical utterances and facilitate human-AI collaboration in high-stakes settings. Overall, ShaQ improves uncertainty estimation and provides actionable insights for targeted input clarification.

Large language models (LLMs) have demonstrated remarkable capabilities across various tasks but still face challenges such as hallucinations. One potential reason for hallucinations is the lack of relevant knowledge or context. Thus, a promising solution to mitigate this issue involves instructing LLMs to respond with "I do not know" when a question falls outside their knowledge domain or the provided context. However, in this work, we observed that LLMs struggle to admit their lack of knowledge, primarily due to existing instruction datasets designed to encourage specific answers. To improve large language models' capability to recognize the boundaries of their knowledge, we propose a novel approach called uncertainty-sensitive tuning. This method involves two-stage training designed for uncertainty recognition and prompt-sensitive activation. In the first stage, we guide the LLM to reject unknown questions. In the second stage, we recover the decreased performance in QA tasks by incorporating designed causal instructions. By leveraging this method, we aim to enhance the model's ability to identify areas of uncertainty. The experimental results demonstrate that our proposed uncertainty-sensitive tuning method significantly improves the performance of the Llama2-chat-7B model. Specifically, it achieves a substantial 34.7% improvement in handling questions involving knowledge gaps compared to the original model. Moreover, our approach outperforms GPT-4, exhibiting a 9.4% increase in overall performance. We open-source the model and code on GitHub.

The proliferation of open-source Large Language Models (LLMs) from various institutions has highlighted the urgent need for comprehensive evaluation methods. However, current evaluation platforms, such as the widely recognized HuggingFace open LLM leaderboard, neglect a crucial aspect -- uncertainty, which is vital for thoroughly assessing LLMs. To bridge this gap, we introduce a new benchmarking approach for LLMs that integrates uncertainty quantification. Our examination involves eight LLMs (LLM series) spanning five representative natural language processing tasks. Additionally, we introduce an uncertainty-aware evaluation metric, UAcc, which takes into account both prediction accuracy and prediction uncertainty. Our findings reveal that: I) LLMs with higher accuracy may exhibit lower certainty; II) Larger-scale LLMs may display greater uncertainty compared to their smaller counterparts; and III) Instruction-finetuning tends to increase the uncertainty of LLMs. By taking uncertainty into account, our new UAcc metric can either amplify or diminish the relative improvement of one LLM over another and may even change the relative ranking of two LLMs. These results underscore the significance of incorporating uncertainty in the evaluation of LLMs.

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

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

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.

Several neural-based metrics have been recently proposed to evaluate machine translation quality. However, all of them resort to point estimates, which provide limited information at segment level. This is made worse as they are trained on noisy, biased and scarce human judgements, often resulting in unreliable quality predictions. In this paper, we introduce uncertainty-aware MT evaluation and analyze the trustworthiness of the predicted quality. We combine the COMET framework with two uncertainty estimation methods, Monte Carlo dropout and deep ensembles, to obtain quality scores along with confidence intervals. We compare the performance of our uncertainty-aware MT evaluation methods across multiple language pairs from the QT21 dataset and the WMT20 metrics task, augmented with MQM annotations. We experiment with varying numbers of references and further discuss the usefulness of uncertainty-aware quality estimation (without references) to flag possibly critical translation mistakes.

Text embeddings are essential components in modern NLP pipelines. While numerous embedding models have been proposed, their performance varies across domains. This variability motivates the use of ensemble techniques to combine complementary strengths. However, most existing ensemble methods operate on deterministic embeddings and fail to account for model-specific uncertainty, limiting their robustness and reliability in downstream applications. To address these limitations, we propose Uncertainty-driven Embedding Convolution (UEC). UEC first transforms deterministic embeddings into probabilistic ones in a post-hoc manner. It then computes adaptive ensemble weights based on embedding uncertainty, grounded in a Bayes-optimal solution under a surrogate loss. Additionally, UEC employs an uncertainty-aware similarity function that directly incorporates uncertainty into the similarity scoring, providing a theoretically grounded and efficient surrogate to distributional distances. Extensive experiments on diverse benchmarks demonstrate that UEC consistently improves both performance and robustness by leveraging principled uncertainty modeling.

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.

With the widespread application of Large Language Models (LLMs) to various domains, concerns regarding the trustworthiness of LLMs in safety-critical scenarios have been raised, due to their unpredictable tendency to hallucinate and generate misinformation. Existing LLMs do not have an inherent functionality to provide the users with an uncertainty/confidence metric for each response it generates, making it difficult to evaluate trustworthiness. Although several studies aim to develop uncertainty quantification methods for LLMs, they have fundamental limitations, such as being restricted to classification tasks, requiring additional training and data, considering only lexical instead of semantic information, and being prompt-wise but not response-wise. A new framework is proposed in this paper to address these issues. Semantic density extracts uncertainty/confidence information for each response from a probability distribution perspective in semantic space. It has no restriction on task types and is "off-the-shelf" for new models and tasks. Experiments on seven state-of-the-art LLMs, including the latest Llama 3 and Mixtral-8x22B models, on four free-form question-answering benchmarks demonstrate the superior performance and robustness of semantic density compared to prior approaches.

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

Uncertainty Quantification (UQ) in Language Models (LMs) is crucial for improving their safety and reliability. Evaluations often use performance metrics like AUROC to assess how well UQ methods (e.g., negative sequence probabilities) correlate with task correctness functions (e.g., ROUGE-L). In this paper, we show that commonly used correctness functions bias UQ evaluations by inflating the performance of certain UQ methods. We evaluate 7 correctness functions -- from lexical-based and embedding-based metrics to LLM-as-a-judge approaches -- across 4 datasets x 4 models x 6 UQ methods. Our analysis reveals that length biases in the errors of these correctness functions distort UQ assessments by interacting with length biases in UQ methods. We identify LLM-as-a-judge approaches as among the least length-biased choices and hence a potential solution to mitigate these biases.

Effective interlocutors account for the uncertain goals, beliefs, and emotions of others. But even the best human conversationalist cannot perfectly anticipate the trajectory of a dialogue. How well can language models represent inherent uncertainty in conversations? We propose FortUne Dial, an expansion of the long-standing "conversation forecasting" task: instead of just accuracy, evaluation is conducted with uncertainty-aware metrics, effectively enabling abstention on individual instances. We study two ways in which language models potentially represent outcome uncertainty (internally, using scores and directly, using tokens) and propose fine-tuning strategies to improve calibration of both representations. Experiments on eight difficult negotiation corpora demonstrate that our proposed fine-tuning strategies (a traditional supervision strategy and an off-policy reinforcement learning strategy) can calibrate smaller open-source models to compete with pre-trained models 10x their size.

Large language models (LLMs) can suffer from hallucinations when generating text. These hallucinations impede various applications in society and industry by making LLMs untrustworthy. Current LLMs generate text in an autoregressive fashion by predicting and appending text tokens. When an LLM is uncertain about the semantic meaning of the next tokens to generate, it is likely to start hallucinating. Thus, it has been suggested that hallucinations stem from predictive uncertainty. We introduce Semantically Diverse Language Generation (SDLG) to quantify predictive uncertainty in LLMs. SDLG steers the LLM to generate semantically diverse yet likely alternatives for an initially generated text. This approach provides a precise measure of aleatoric semantic uncertainty, detecting whether the initial text is likely to be hallucinated. Experiments on question-answering tasks demonstrate that SDLG consistently outperforms existing methods while being the most computationally efficient, setting a new standard for uncertainty estimation in LLMs.

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

Uncertainty quantification (UQ) is a perspective approach to detecting Large Language Model (LLM) hallucinations and low quality output. In this work, we address one of the challenges of UQ in generation tasks that arises from the conditional dependency between the generation steps of an LLM. We propose to learn this dependency from data. We train a regression model, which target variable is the gap between the conditional and the unconditional generation confidence. During LLM inference, we use this learned conditional dependency model to modulate the uncertainty of the current generation step based on the uncertainty of the previous step. Our experimental evaluation on nine datasets and three LLMs shows that the proposed method is highly effective for uncertainty quantification, achieving substantial improvements over rivaling approaches.

Today's probabilistic language generators fall short when it comes to producing coherent and fluent text despite the fact that the underlying models perform well under standard metrics, e.g., perplexity. This discrepancy has puzzled the language generation community for the last few years. In this work, we posit that the abstraction of natural language generation as a discrete stochastic process--which allows for an information-theoretic analysis--can provide new insights into the behavior of probabilistic language generators, e.g., why high-probability texts can be dull or repetitive. Humans use language as a means of communicating information, aiming to do so in a simultaneously efficient and error-minimizing manner; in fact, psycholinguistics research suggests humans choose each word in a string with this subconscious goal in mind. We formally define the set of strings that meet this criterion: those for which each word has an information content close to the expected information content, i.e., the conditional entropy of our model. We then propose a simple and efficient procedure for enforcing this criterion when generating from probabilistic models, which we call locally typical sampling. Automatic and human evaluations show that, in comparison to nucleus and top-k sampling, locally typical sampling offers competitive performance (in both abstractive summarization and story generation) in terms of quality while consistently reducing degenerate repetitions.

We present UncertaintyRAG, a novel approach for long-context Retrieval-Augmented Generation (RAG) that utilizes Signal-to-Noise Ratio (SNR)-based span uncertainty to estimate similarity between text chunks. This span uncertainty enhances model calibration, improving robustness and mitigating semantic inconsistencies introduced by random chunking. Leveraging this insight, we propose an efficient unsupervised learning technique to train the retrieval model, alongside an effective data sampling and scaling strategy. UncertaintyRAG outperforms baselines by 2.03% on LLaMA-2-7B, achieving state-of-the-art results while using only 4% of the training data compared to other advanced open-source retrieval models under distribution shift settings. Our method demonstrates strong calibration through span uncertainty, leading to improved generalization and robustness in long-context RAG tasks. Additionally, UncertaintyRAG provides a lightweight retrieval model that can be integrated into any large language model with varying context window lengths, without the need for fine-tuning, showcasing the flexibility of our approach.

Uncertainty quantification (UQ) for large language models (LLMs) is a key building block for safety guardrails of daily LLM applications. Yet, even as LLM agents are increasingly deployed in highly complex tasks, most UQ research still centers on single-turn question-answering. We argue that UQ research must shift to realistic settings with interactive agents, and that a new principled framework for agent UQ is needed. This paper presents the first general formulation of agent UQ that subsumes broad classes of existing UQ setups. Under this formulation, we show that prior works implicitly treat LLM UQ as an uncertainty accumulation process, a viewpoint that breaks down for interactive agents in an open world. In contrast, we propose a novel perspective, a conditional uncertainty reduction process, that explicitly models reducible uncertainty over an agent's trajectory by highlighting "interactivity" of actions. From this perspective, we outline a conceptual framework to provide actionable guidance for designing UQ in LLM agent setups. Finally, we conclude with practical implications of the agent UQ in frontier LLM development and domain-specific applications, as well as open remaining problems.

We propose semantic entropy probes (SEPs), a cheap and reliable method for uncertainty quantification in Large Language Models (LLMs). Hallucinations, which are plausible-sounding but factually incorrect and arbitrary model generations, present a major challenge to the practical adoption of LLMs. Recent work by Farquhar et al. (2024) proposes semantic entropy (SE), which can detect hallucinations by estimating uncertainty in the space semantic meaning for a set of model generations. However, the 5-to-10-fold increase in computation cost associated with SE computation hinders practical adoption. To address this, we propose SEPs, which directly approximate SE from the hidden states of a single generation. SEPs are simple to train and do not require sampling multiple model generations at test time, reducing the overhead of semantic uncertainty quantification to almost zero. We show that SEPs retain high performance for hallucination detection and generalize better to out-of-distribution data than previous probing methods that directly predict model accuracy. Our results across models and tasks suggest that model hidden states capture SE, and our ablation studies give further insights into the token positions and model layers for which this is the case.

Trainable evaluation metrics for machine translation (MT) exhibit strong correlation with human judgements, but they are often hard to interpret and might produce unreliable scores under noisy or out-of-domain data. Recent work has attempted to mitigate this with simple uncertainty quantification techniques (Monte Carlo dropout and deep ensembles), however these techniques (as we show) are limited in several ways -- for example, they are unable to distinguish between different kinds of uncertainty, and they are time and memory consuming. In this paper, we propose more powerful and efficient uncertainty predictors for MT evaluation, and we assess their ability to target different sources of aleatoric and epistemic uncertainty. To this end, we develop and compare training objectives for the COMET metric to enhance it with an uncertainty prediction output, including heteroscedastic regression, divergence minimization, and direct uncertainty prediction. Our experiments show improved results on uncertainty prediction for the WMT metrics task datasets, with a substantial reduction in computational costs. Moreover, they demonstrate the ability of these predictors to address specific uncertainty causes in MT evaluation, such as low quality references and out-of-domain data.

We propose LoRA-MCL, a training scheme that extends next-token prediction in language models with a method designed to decode diverse, plausible sentence continuations at inference time. Traditional language modeling is an intrinsically ill-posed problem: given a context, multiple futures may be equally plausible. Our approach leverages Multiple Choice Learning (MCL) and the Winner-Takes-All (WTA) loss to efficiently handle ambiguity through Low-Rank Adaptation (LoRA). We provide a theoretical interpretation of applying Multiple Choice Learning to Language Modeling, assuming the data is generated from a mixture of distributions. To illustrate the proposed approach, we use data sampled from mixtures of Markov chains. We then demonstrate with extensive experiments on real-world visual and audio captioning tasks that our method achieves high diversity and relevance in generated outputs.

Large Language Models (LLMs) have recently been successfully applied to regression tasks -- such as time series forecasting and tabular prediction -- by leveraging their in-context learning abilities. However, their autoregressive decoding process may be ill-suited to continuous-valued outputs, where obtaining predictive distributions over numerical targets requires repeated sampling, leading to high computational cost and inference time. In this work, we investigate whether distributional properties of LLM predictions can be recovered without explicit autoregressive generation. To this end, we study a set of regression probes trained to predict statistical functionals (e.g., mean, median, quantiles) of the LLM's numerical output distribution directly from its internal representations. Our results suggest that LLM embeddings carry informative signals about summary statistics of their predictive distributions, including the numerical uncertainty. This investigation opens up new questions about how LLMs internally encode uncertainty in numerical tasks, and about the feasibility of lightweight alternatives to sampling-based approaches for uncertainty-aware numerical predictions.

We present evidence of substantial benefit from efficient exploration in gathering human feedback to improve large language models. In our experiments, an agent sequentially generates queries while fitting a reward model to the feedback received. Our best-performing agent generates queries using double Thompson sampling, with uncertainty represented by an epistemic neural network. Our results demonstrate that efficient exploration enables high levels of performance with far fewer queries. Further, both uncertainty estimation and the choice of exploration scheme play critical roles.

Hallucination in large language models (LLMs) can be detected by assessing the uncertainty of model outputs, typically measured using entropy. Semantic entropy (SE) enhances traditional entropy estimation by quantifying uncertainty at the semantic cluster level. However, as modern LLMs generate longer one-sentence responses, SE becomes less effective because it overlooks two crucial factors: intra-cluster similarity (the spread within a cluster) and inter-cluster similarity (the distance between clusters). To address these limitations, we propose a simple black-box uncertainty quantification method inspired by nearest neighbor estimates of entropy. Our approach can also be easily extended to white-box settings by incorporating token probabilities. Additionally, we provide theoretical results showing that our method generalizes semantic entropy. Extensive empirical results demonstrate its effectiveness compared to semantic entropy across two recent LLMs (Phi3 and Llama3) and three common text generation tasks: question answering, text summarization, and machine translation. Our code is available at https://github.com/BigML-CS-UCLA/SNNE.

Large language models (LLMs) now exhibit strong multi-step reasoning abilities, but existing inference-time scaling methods remain computationally expensive, often relying on extensive sampling or external evaluators. We propose a principled strategy that frames reasoning as uncertainty minimisation and operates at the level of individual thoughts rather than tokens. Our method selects, at each reasoning step, the continuation that maximizes the model's self-certainty, a metric computed from its internal predictive distribution. This approach achieves significant improvement with a small number of samples, relies exclusively on model-internal signals, and applies to open-ended questions as opposed to methods like majority voting. Experiments on MATH500 and GSM8K across multiple model sizes demonstrate that thought-level self-certainty maximization consistently outperforms greedy decoding and matches or exceeds self-consistency under comparable token budgets. Cross-linguistic evaluations further indicate that the method transfers robustly beyond high-resource languages. Furthermore, analysis of self-certainty dynamics reveals that correct reasoning trajectories converge early to stable paths, suggesting that early decisions, likely associated with the planning of the reasoning process, are predictive of final accuracy. Building on this result, we show that self-certainty maximisation applied to the early steps can explain most of the performance gain and provide a simple yet efficient inference-time scaling method.

We present a probabilistic language model for time-stamped text data which tracks the semantic evolution of individual words over time. The model represents words and contexts by latent trajectories in an embedding space. At each moment in time, the embedding vectors are inferred from a probabilistic version of word2vec [Mikolov et al., 2013]. These embedding vectors are connected in time through a latent diffusion process. We describe two scalable variational inference algorithms--skip-gram smoothing and skip-gram filtering--that allow us to train the model jointly over all times; thus learning on all data while simultaneously allowing word and context vectors to drift. Experimental results on three different corpora demonstrate that our dynamic model infers word embedding trajectories that are more interpretable and lead to higher predictive likelihoods than competing methods that are based on static models trained separately on time slices.

The recent proliferation of research into transformer based natural language processing has led to a number of studies which attempt to detect the presence of human-like cognitive behavior in the models. We contend that, as is true of human psychology, the investigation of cognitive behavior in language models must be conducted in an appropriate population of an appropriate size for the results to be meaningful. We leverage work in uncertainty estimation in a novel approach to efficiently construct experimental populations. The resultant tool, PopulationLM, has been made open source. We provide theoretical grounding in the uncertainty estimation literature and motivation from current cognitive work regarding language models. We discuss the methodological lessons from other scientific communities and attempt to demonstrate their application to two artificial population studies. Through population based experimentation we find that language models exhibit behavior consistent with typicality effects among categories highly represented in training. However, we find that language models don't tend to exhibit structural priming effects. Generally, our results show that single models tend to over estimate the presence of cognitive behaviors in neural models.

State-of-the-art supervised NLP models achieve high accuracy but are also susceptible to failures on inputs from low-data regimes, such as domains that are not represented in training data. As an approximation to collecting ground-truth labels for the specific domain, we study the use of large language models (LLMs) for annotating inputs and improving the generalization of NLP models. Specifically, given a budget for LLM annotations, we present an algorithm for sampling the most informative inputs to annotate and retrain the NLP model. We find that popular active learning strategies such as uncertainty-based sampling do not work well. Instead, we propose a sampling strategy based on the difference in prediction scores between the base model and the finetuned NLP model, utilizing the fact that most NLP models are finetuned from a base model. Experiments with classification (semantic similarity) and ranking (semantic search) tasks show that our sampling strategy leads to significant gains in accuracy for both the training and target domains.

Deploying large language models (LLMs) for long-context inference remains challenging due to their substantial memory and computational demands. While techniques such as Key-Value (KV) cache compression are designed to reduce memory usage, they often neglect the structured sparsity inherent in the relationship between hidden states and their corresponding KV cache. In this work, we explore the role of uncertainty as a potential indicator of sparsity within LLMs. We propose UNComp, an uncertainty-aware framework that leverages truncated matrix entropy to identify areas of low information content, thereby revealing sparsity patterns that can be used for adaptive compression. Unlike traditional methods that apply uniform compression, UNComp dynamically adjusts its approach to compression, guided by uncertainty measures that reflect the importance of various model components. Our analysis shows that sparsity patterns, when derived from uncertainty estimates, can be exploited to reveal special long-range dependencies, such as retrieval heads and retrieval layers. This perspective not only enhances our understanding of how compression can be optimized but also provides new insights into the inherent sparsity of LLMs during long-context inference. By focusing on uncertainty to analyze the sparsity pattern in detail, UNComp reduces the KV cache size to 4.74% of the original, achieves a 6% prefill speedup, and improves throughput by 6.4x - not only delivering strong lossless compression performance, but also validating the effectiveness of the underlying theoretical tool. We release the code at https://github.com/menik1126/UNComp.

Large Language Models (LLMs) have shown strong capabilities in document re-ranking, a key component in modern Information Retrieval (IR) systems. However, existing LLM-based approaches face notable limitations, including ranking uncertainty, unstable top-k recovery, and high token cost due to token-intensive prompting. To effectively address these limitations, we propose REALM, an uncertainty-aware re-ranking framework that models LLM-derived relevance as Gaussian distributions and refines them through recursive Bayesian updates. By explicitly capturing uncertainty and minimizing redundant queries, REALM achieves better rankings more efficiently. Experimental results demonstrate that our REALM surpasses state-of-the-art re-rankers while significantly reducing token usage and latency, improving NDCG@10 by 0.7-11.9 and simultaneously reducing the number of LLM inferences by 23.4-84.4%, promoting it as the next-generation re-ranker for modern IR systems.

As large language models (LLMs) are pretrained on massive web corpora, careful selection of data becomes essential to ensure effective and efficient learning. While perplexity (PPL)-based filtering has shown strong performance, it suffers from drawbacks: substantial time costs and inherent unreliability of the model when handling noisy or out-of-distribution samples. In this work, we propose a simple yet powerful alternative: a prior-based data filtering method that estimates token priors using corpus-level term frequency statistics, inspired by linguistic insights on word roles and lexical density. Our approach filters documents based on the mean and standard deviation of token priors, serving as a fast proxy to PPL while requiring no model inference. Despite its simplicity, the prior-based filter achieves the highest average performance across 20 downstream benchmarks, while reducing time cost by over 1000x compared to PPL-based filtering. We further demonstrate its applicability to symbolic languages such as code and math, and its dynamic adaptability to multilingual corpora without supervision

Large language models (LLMs) have proven to be remarkably efficient, both across a wide range of natural language processing tasks and well beyond them. However, a comprehensive theoretical analysis of the origins of their impressive performance remains elusive. In this paper, we approach this challenging task by drawing an equivalence between generic autoregressive language models with vocabulary of size T and context window of size K and Markov chains defined on a finite state space of size O(T^K). We derive several surprising findings related to the existence of a stationary distribution of Markov chains that capture the inference power of LLMs, their speed of convergence to it, and the influence of the temperature on the latter. We then prove pre-training and in-context generalization bounds and show how the drawn equivalence allows us to enrich their interpretation. Finally, we illustrate our theoretical guarantees with experiments on several recent LLMs to highlight how they capture the behavior observed in practice.

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

Predictive models often need to work with incomplete information in real-world tasks. Consequently, they must provide reliable probability or confidence estimation, especially in large-scale decision-making and planning tasks. Current large language models (LLMs) are insufficient for accurate estimations, but they can generate relevant factors that may affect the probabilities, produce coarse-grained probabilities when the information is more complete, and help determine which factors are relevant to specific downstream contexts. In this paper, we make use of these capabilities of LLMs to provide a significantly more accurate probabilistic estimation. We propose BIRD, a novel probabilistic inference framework that aligns a Bayesian network with LLM abductions and then estimates more accurate probabilities in a deduction step. We show BIRD provides reliable probability estimations that are 30% better than those provided directly by LLM baselines. These estimates further contribute to better and more trustworthy decision making.

Recently, the emergence of pre-trained models (PTMs) has brought natural language processing (NLP) to a new era. In this survey, we provide a comprehensive review of PTMs for NLP. We first briefly introduce language representation learning and its research progress. Then we systematically categorize existing PTMs based on a taxonomy with four perspectives. Next, we describe how to adapt the knowledge of PTMs to the downstream tasks. Finally, we outline some potential directions of PTMs for future research. This survey is purposed to be a hands-on guide for understanding, using, and developing PTMs for various NLP tasks.

Probabilistic models of language understanding are valuable tools for investigating human language use. However, they need to be hand-designed for a particular domain. In contrast, large language models (LLMs) are trained on text that spans a wide array of domains, but they lack the structure and interpretability of probabilistic models. In this paper, we use chain-of-thought prompts to introduce structures from probabilistic models into LLMs. We explore this approach in the case of metaphor understanding. Our chain-of-thought prompts lead language models to infer latent variables and reason about their relationships in order to choose appropriate paraphrases for metaphors. The latent variables and relationships chosen are informed by theories of metaphor understanding from cognitive psychology. We apply these prompts to the two largest versions of GPT-3 and show that they can improve performance in a paraphrase selection task.

We address two challenges of probabilistic topic modelling in order to better estimate the probability of a word in a given context, i.e., P(word|context): (1) No Language Structure in Context: Probabilistic topic models ignore word order by summarizing a given context as a "bag-of-word" and consequently the semantics of words in the context is lost. The LSTM-LM learns a vector-space representation of each word by accounting for word order in local collocation patterns and models complex characteristics of language (e.g., syntax and semantics), while the TM simultaneously learns a latent representation from the entire document and discovers the underlying thematic structure. We unite two complementary paradigms of learning the meaning of word occurrences by combining a TM (e.g., DocNADE) and a LM in a unified probabilistic framework, named as ctx-DocNADE. (2) Limited Context and/or Smaller training corpus of documents: In settings with a small number of word occurrences (i.e., lack of context) in short text or data sparsity in a corpus of few documents, the application of TMs is challenging. We address this challenge by incorporating external knowledge into neural autoregressive topic models via a language modelling approach: we use word embeddings as input of a LSTM-LM with the aim to improve the word-topic mapping on a smaller and/or short-text corpus. The proposed DocNADE extension is named as ctx-DocNADEe. We present novel neural autoregressive topic model variants coupled with neural LMs and embeddings priors that consistently outperform state-of-the-art generative TMs in terms of generalization (perplexity), interpretability (topic coherence) and applicability (retrieval and classification) over 6 long-text and 8 short-text datasets from diverse domains.

Large language models demonstrate remarkable in-context learning capabilities, adapting to new tasks without parameter updates. While this phenomenon has been successfully modeled as implicit Bayesian inference, recent empirical findings reveal a fundamental contradiction: transformers systematically violate the martingale property, a cornerstone requirement of Bayesian updating on exchangeable data. This violation challenges the theoretical foundations underlying uncertainty quantification in critical applications. Our theoretical analysis establishes four key results: (1) positional encodings induce martingale violations of order Theta(log n / n); (2) transformers achieve information-theoretic optimality with excess risk O(n^{-1/2}) in expectation over orderings; (3) the implicit posterior representation converges to the true Bayesian posterior in the space of sufficient statistics; and (4) we derive the optimal chain-of-thought length as k^* = Theta(nlog(1/varepsilon)) with explicit constants, providing a principled approach to reduce inference costs while maintaining performance. Empirical validation on GPT-3 confirms predictions (1)-(3), with transformers reaching 99\% of theoretical entropy limits within 20 examples. Our framework provides practical methods for extracting calibrated uncertainty estimates from position-aware architectures and optimizing computational efficiency in deployment.

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

We introduce a novel approach for building language models based on a systematic, recursive exploration of skip n-gram models which are interpolated using modified Kneser-Ney smoothing. Our approach generalizes language models as it contains the classical interpolation with lower order models as a special case. In this paper we motivate, formalize and present our approach. In an extensive empirical experiment over English text corpora we demonstrate that our generalized language models lead to a substantial reduction of perplexity between 3.1% and 12.7% in comparison to traditional language models using modified Kneser-Ney smoothing. Furthermore, we investigate the behaviour over three other languages and a domain specific corpus where we observed consistent improvements. Finally, we also show that the strength of our approach lies in its ability to cope in particular with sparse training data. Using a very small training data set of only 736 KB text we yield improvements of even 25.7% reduction of perplexity.

We propose a new benchmark corpus to be used for measuring progress in statistical language modeling. With almost one billion words of training data, we hope this benchmark will be useful to quickly evaluate novel language modeling techniques, and to compare their contribution when combined with other advanced techniques. We show performance of several well-known types of language models, with the best results achieved with a recurrent neural network based language model. The baseline unpruned Kneser-Ney 5-gram model achieves perplexity 67.6; a combination of techniques leads to 35% reduction in perplexity, or 10% reduction in cross-entropy (bits), over that baseline. The benchmark is available as a code.google.com project; besides the scripts needed to rebuild the training/held-out data, it also makes available log-probability values for each word in each of ten held-out data sets, for each of the baseline n-gram models.

Large language models (LLMs), while transformative for NLP, come with significant computational demands, underlining the need for efficient, training-free compression. Notably, the reliability of perplexity as a benchmark for compressed model efficacy is in question, as our tests using LLaMA-7B and OPT-6.7b reveal a significant performance drop in several realistic downstream tasks, underscoring the disparity between perplexity as a performance indicator and real-world performance. Investigation into the trade-off between resource-intensive post-compression re-training highlights the prospect of prompt-driven recovery as a lightweight adaption tool. However, existing studies, confined mainly to perplexity evaluations and simple tasks, fail to offer unequivocal confidence in the scalability and generalizability of prompting. We tackle this uncertainty in two key ways. First, we uncover the vulnerability of naive prompts in LLM compression as an over-reliance on a singular prompt per input. In response, we propose inference-time dynamic prompting (IDP), a mechanism that autonomously chooses from a set of curated prompts based on the context of each individual input. Second, we delve into a scientific understanding of why ``prompting might be all you need post-LLM compression". Our findings suggest that compression doesn't irretrievably erase LLM model knowledge but displace it, necessitating a new inference path. IDP effectively redirects this path, enabling the model to tap into its inherent yet displaced knowledge and thereby recover performance. Empirical tests affirm the value of IDP, demonstrating an average performance improvement of 1.24% across nine varied tasks spanning multiple knowledge domains.

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

Large Language Models (LLMs) are prone to hallucination, particularly in long-form generations. A promising direction to mitigate hallucination is to teach LLMs to express uncertainty explicitly when they lack sufficient knowledge. However, existing work lacks direct and fair evaluation of LLMs' ability to express uncertainty effectively in long-form generation. To address this gap, we first introduce UNCLE, a benchmark designed to evaluate uncertainty expression in both long- and short-form question answering (QA). UNCLE spans five domains and comprises 4k long-form QA instances and over 20k short-form QA pairs. Our dataset is the first to directly bridge short- and long-form QA with paired questions and gold-standard answers. Along with the benchmark, we propose a suite of new metrics to assess the models' capabilities to selectively express uncertainty. Using UNCLE, we then demonstrate that current models fail to convey uncertainty appropriately in long-form generation. We further explore both prompt-based and training-based methods to improve models' performance, with the training-based methods yielding greater gains. Further analysis of alignment gaps between short- and long-form uncertainty expression highlights promising directions for future research using UNCLE.

Open Information Extraction (OIE) task aims at extracting structured facts from unstructured text, typically in the form of (subject, relation, object) triples. Despite the potential of large language models (LLMs) like ChatGPT as a general task solver, they lag behind state-of-the-art (supervised) methods in OIE tasks due to two key issues. First, LLMs struggle to distinguish irrelevant context from relevant relations and generate structured output due to the restrictions on fine-tuning the model. Second, LLMs generates responses autoregressively based on probability, which makes the predicted relations lack confidence. In this paper, we assess the capabilities of LLMs in improving the OIE task. Particularly, we propose various in-context learning strategies to enhance LLM's instruction-following ability and a demonstration uncertainty quantification module to enhance the confidence of the generated relations. Our experiments on three OIE benchmark datasets show that our approach holds its own against established supervised methods, both quantitatively and qualitatively.

Large language models (LLMs) are notorious for hallucinating, i.e., producing erroneous claims in their output. Such hallucinations can be dangerous, as occasional factual inaccuracies in the generated text might be obscured by the rest of the output being generally factual, making it extremely hard for the users to spot them. Current services that leverage LLMs usually do not provide any means for detecting unreliable generations. Here, we aim to bridge this gap. In particular, we propose a novel fact-checking and hallucination detection pipeline based on token-level uncertainty quantification. Uncertainty scores leverage information encapsulated in the output of a neural network or its layers to detect unreliable predictions, and we show that they can be used to fact-check the atomic claims in the LLM output. Moreover, we present a novel token-level uncertainty quantification method that removes the impact of uncertainty about what claim to generate on the current step and what surface form to use. Our method Claim Conditioned Probability (CCP) measures only the uncertainty of particular claim value expressed by the model. Experiments on the task of biography generation demonstrate strong improvements for CCP compared to the baselines for six different LLMs and three languages. Human evaluation reveals that the fact-checking pipeline based on uncertainty quantification is competitive with a fact-checking tool that leverages external knowledge.

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

Annotating training data for sequence tagging of texts is usually very time-consuming. Recent advances in transfer learning for natural language processing in conjunction with active learning open the possibility to significantly reduce the necessary annotation budget. We are the first to thoroughly investigate this powerful combination for the sequence tagging task. We conduct an extensive empirical study of various Bayesian uncertainty estimation methods and Monte Carlo dropout options for deep pre-trained models in the active learning framework and find the best combinations for different types of models. Besides, we also demonstrate that to acquire instances during active learning, a full-size Transformer can be substituted with a distilled version, which yields better computational performance and reduces obstacles for applying deep active learning in practice.

Claim-level Uncertainty Quantification (UQ) is a promising approach to mitigate the lack of reliability in Large Language Models (LLMs). We introduce MUCH, the first claim-level UQ benchmark designed for fair and reproducible evaluation of future methods under realistic conditions. It includes 4,873 samples across four European languages (English, French, Spanish, and German) and four instruction-tuned open-weight LLMs. Unlike prior claim-level benchmarks, we release 24 generation logits per token, facilitating the development of future white-box methods without re-generating data. Moreover, in contrast to previous benchmarks that rely on manual or LLM-based segmentation, we propose a new deterministic algorithm capable of segmenting claims using as little as 0.2% of the LLM generation time. This makes our segmentation approach suitable for real-time monitoring of LLM outputs, ensuring that MUCH evaluates UQ methods under realistic deployment constraints. Finally, our evaluations show that current methods still have substantial room for improvement in both performance and efficiency.

Retrieval-Augmented Generation equips large language models with the capability to retrieve external knowledge, thereby mitigating hallucinations by incorporating information beyond the model's intrinsic abilities. However, most prior works have focused on invoking retrieval deterministically, which makes it unsuitable for tasks such as long-form question answering. Instead, dynamically performing retrieval by invoking it only when the underlying LLM lacks the required knowledge can be more efficient. In this context, we delve deeper into the question, "To Retrieve or Not to Retrieve?" by exploring multiple uncertainty detection methods. We evaluate these methods for the task of long-form question answering, employing dynamic retrieval, and present our comparisons. Our findings suggest that uncertainty detection metrics, such as Degree Matrix Jaccard and Eccentricity, can reduce the number of retrieval calls by almost half, with only a slight reduction in question-answering accuracy.

Modeling semantic plausibility requires commonsense knowledge about the world and has been used as a testbed for exploring various knowledge representations. Previous work has focused specifically on modeling physical plausibility and shown that distributional methods fail when tested in a supervised setting. At the same time, distributional models, namely large pretrained language models, have led to improved results for many natural language understanding tasks. In this work, we show that these pretrained language models are in fact effective at modeling physical plausibility in the supervised setting. We therefore present the more difficult problem of learning to model physical plausibility directly from text. We create a training set by extracting attested events from a large corpus, and we provide a baseline for training on these attested events in a self-supervised manner and testing on a physical plausibility task. We believe results could be further improved by injecting explicit commonsense knowledge into a distributional model.

Words of estimative probability (WEP) are expressions of a statement's plausibility (probably, maybe, likely, doubt, likely, unlikely, impossible...). Multiple surveys demonstrate the agreement of human evaluators when assigning numerical probability levels to WEP. For example, highly likely corresponds to a median chance of 0.90+-0.08 in Fagen-Ulmschneider (2015)'s survey. In this work, we measure the ability of neural language processing models to capture the consensual probability level associated to each WEP. Firstly, we use the UNLI dataset (Chen et al., 2020) which associates premises and hypotheses with their perceived joint probability p, to construct prompts, e.g. "[PREMISE]. [WEP], [HYPOTHESIS]." and assess whether language models can predict whether the WEP consensual probability level is close to p. Secondly, we construct a dataset of WEP-based probabilistic reasoning, to test whether language models can reason with WEP compositions. When prompted "[EVENTA] is likely. [EVENTB] is impossible.", a causal language model should not express that [EVENTA&B] is likely. We show that both tasks are unsolved by off-the-shelf English language models, but that fine-tuning leads to transferable improvement.

Ambiguity remains a fundamental challenge in Natural Language Processing (NLP) due to the inherent complexity and flexibility of human language. With the advent of Large Language Models (LLMs), addressing ambiguity has become even more critical due to their expanded capabilities and applications. In the context of Conversational Question Answering (CQA), this paper explores the definition, forms, and implications of ambiguity for language driven systems, particularly in the context of LLMs. We define key terms and concepts, categorize various disambiguation approaches enabled by LLMs, and provide a comparative analysis of their advantages and disadvantages. We also explore publicly available datasets for benchmarking ambiguity detection and resolution techniques and highlight their relevance for ongoing research. Finally, we identify open problems and future research directions, proposing areas for further investigation. By offering a comprehensive review of current research on ambiguities and disambiguation with LLMs, we aim to contribute to the development of more robust and reliable language systems.

We introduce a variational reasoning framework for language models that treats thinking traces as latent variables and optimizes them through variational inference. Starting from the evidence lower bound (ELBO), we extend it to a multi-trace objective for tighter bounds and propose a forward-KL formulation that stabilizes the training of the variational posterior. We further show that rejection sampling finetuning and binary-reward RL, including GRPO, can be interpreted as local forward-KL objectives, where an implicit weighting by model accuracy naturally arises from the derivation and reveals a previously unnoticed bias toward easier questions. We empirically validate our method on the Qwen 2.5 and Qwen 3 model families across a wide range of reasoning tasks. Overall, our work provides a principled probabilistic perspective that unifies variational inference with RL-style methods and yields stable objectives for improving the reasoning ability of language models. Our code is available at https://github.com/sail-sg/variational-reasoning.

Despite their widespread applications, Large Language Models (LLMs) often struggle to express uncertainty, posing a challenge for reliable deployment in high stakes and safety critical domains like clinical diagnostics. Existing standard baseline methods such as model logits and elicited probabilities produce overconfident and poorly calibrated estimates. In this work, we propose Approximate Bayesian Computation (ABC), a likelihood-free Bayesian inference, based approach that treats LLMs as a stochastic simulator to infer posterior distributions over predictive probabilities. We evaluate our ABC approach on two clinically relevant benchmarks: a synthetic oral lesion diagnosis dataset and the publicly available GretelAI symptom-to-diagnosis dataset. Compared to standard baselines, our approach improves accuracy by up to 46.9\%, reduces Brier scores by 74.4\%, and enhances calibration as measured by Expected Calibration Error (ECE) and predictive entropy.

Recent work has sought to quantify large language model uncertainty to facilitate model control and modulate user trust. Previous works focus on measures of uncertainty that are theoretically grounded or reflect the average overt behavior of the model. In this work, we investigate a variety of uncertainty measures, in order to identify measures that correlate with human group-level uncertainty. We find that Bayesian measures and a variation on entropy measures, top-k entropy, tend to agree with human behavior as a function of model size. We find that some strong measures decrease in human-similarity with model size, but, by multiple linear regression, we find that combining multiple uncertainty measures provide comparable human-alignment with reduced size-dependency.

We propose a Distributional Approach for addressing Controlled Text Generation from pre-trained Language Models (LMs). This approach permits to specify, in a single formal framework, both "pointwise" and "distributional" constraints over the target LM -- to our knowledge, the first model with such generality -- while minimizing KL divergence from the initial LM distribution. The optimal target distribution is then uniquely determined as an explicit EBM (Energy-Based Model) representation. From that optimal representation we then train a target controlled Autoregressive LM through an adaptive distributional variant of Policy Gradient. We conduct a first set of experiments over pointwise constraints showing the advantages of our approach over a set of baselines, in terms of obtaining a controlled LM balancing constraint satisfaction with divergence from the initial LM. We then perform experiments over distributional constraints, a unique feature of our approach, demonstrating its potential as a remedy to the problem of Bias in Language Models. Through an ablation study, we show the effectiveness of our adaptive technique for obtaining faster convergence. (Code available at https://github.com/naver/gdc)

Plenty of existing work has analyzed the abilities of the transformer architecture by describing its representational capacity with formal models of computation. However, the focus so far has been on analyzing the architecture in terms of language acceptance. We contend that this is an ill-suited problem in the study of language models (LMs), which are definitionally probability distributions over strings. In this paper, we focus on the relationship between transformer LMs and n-gram LMs, a simple and historically relevant class of language models. We show that transformer LMs using the hard or sparse attention mechanisms can exactly represent any n-gram LM, giving us a concrete lower bound on their probabilistic representational capacity. This provides a first step towards understanding the mechanisms that transformer LMs can use to represent probability distributions over strings.

Large Language Models (LLMs) have attracted extensive attention due to their remarkable performance across various tasks. However, the substantial computational and memory requirements of LLM inference pose challenges for deployment in resource-constrained scenarios. Efforts within the field have been directed towards developing techniques aimed at enhancing the efficiency of LLM inference. This paper presents a comprehensive survey of the existing literature on efficient LLM inference. We start by analyzing the primary causes of the inefficient LLM inference, i.e., the large model size, the quadratic-complexity attention operation, and the auto-regressive decoding approach. Then, we introduce a comprehensive taxonomy that organizes the current literature into data-level, model-level, and system-level optimization. Moreover, the paper includes comparative experiments on representative methods within critical sub-fields to provide quantitative insights. Last but not least, we provide some knowledge summary and discuss future research directions.

Large Language Models~(LLMs) are prone to hallucinations, and Retrieval-Augmented Generation (RAG) helps mitigate this, but at a high computational cost while risking misinformation. Adaptive retrieval aims to retrieve only when necessary, but existing approaches rely on LLM-based uncertainty estimation, which remain inefficient and impractical. In this study, we introduce lightweight LLM-independent adaptive retrieval methods based on external information. We investigated 27 features, organized into 7 groups, and their hybrid combinations. We evaluated these methods on 6 QA datasets, assessing the QA performance and efficiency. The results show that our approach matches the performance of complex LLM-based methods while achieving significant efficiency gains, demonstrating the potential of external information for adaptive retrieval.

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

Inference-time scaling has emerged as a powerful technique for enhancing the reasoning performance of Large Language Models (LLMs). However, existing approaches often rely on heuristic strategies for parallel sampling, lacking a principled foundation. To address this gap, we propose a probabilistic framework that formalizes the optimality of inference-time scaling under the assumption that parallel samples are independently and identically distributed (i.i.d.), and where the Best-of-N selection strategy follows a probability distribution that can be estimated. Within this framework, we derive a theoretical lower bound on the required number of samples to achieve a target performance level, providing the first principled guidance for compute-efficient scaling. Leveraging this insight, we develop OptScale, a practical algorithm that dynamically determines the optimal number of sampled responses. OptScale employs a language model-based predictor to estimate probabilistic prior parameters, enabling the decision of the minimal number of samples needed that satisfy predefined performance thresholds and confidence levels. Extensive experiments on representative reasoning benchmarks (including MATH-500, GSM8K, AIME, and AMC) demonstrate that OptScale significantly reduces sampling overhead while remaining better or on par with state-of-the-art reasoning performance. Our work offers both a theoretical foundation and a practical solution for principled inference-time scaling, addressing a critical gap in the efficient deployment of LLMs for complex reasoning.

Despite the frequent challenges posed by ambiguity when representing meaning via natural language, it is often ignored or deliberately removed in tasks mapping language to formally-designed representations, which generally assume a one-to-one mapping between linguistic and formal representations. We attempt to address this shortcoming by introducing AmP, a framework, dataset, and challenge for translating ambiguous natural language to formal representations like logic and code. We define templates and generate data for five well-documented linguistic ambiguities. Using AmP, we investigate how several few-shot text-to-code systems handle ambiguity, introducing three new metrics. We find that large pre-trained models perform poorly at capturing the distribution of possible meanings without deliberate instruction. However, models are able to capture the distribution well when ambiguity is attested in their inputs. These results motivate a call for including ambiguity explicitly in datasets and promote considering the distribution of possible outputs when evaluating systems. Data and code: https://github.com/esteng/ambiguous_parsing

Retrieval Augmented Generation (RAG) improves correctness of Question Answering (QA) and addresses hallucinations in Large Language Models (LLMs), yet greatly increase computational costs. Besides, RAG is not always needed as may introduce irrelevant information. Recent adaptive retrieval methods integrate LLMs' intrinsic knowledge with external information appealing to LLM self-knowledge, but they often neglect efficiency evaluations and comparisons with uncertainty estimation techniques. We bridge this gap by conducting a comprehensive analysis of 35 adaptive retrieval methods, including 8 recent approaches and 27 uncertainty estimation techniques, across 6 datasets using 10 metrics for QA performance, self-knowledge, and efficiency. Our findings show that uncertainty estimation techniques often outperform complex pipelines in terms of efficiency and self-knowledge, while maintaining comparable QA performance.

We show that a GPT-3 model can learn to express uncertainty about its own answers in natural language -- without use of model logits. When given a question, the model generates both an answer and a level of confidence (e.g. "90% confidence" or "high confidence"). These levels map to probabilities that are well calibrated. The model also remains moderately calibrated under distribution shift, and is sensitive to uncertainty in its own answers, rather than imitating human examples. To our knowledge, this is the first time a model has been shown to express calibrated uncertainty about its own answers in natural language. For testing calibration, we introduce the CalibratedMath suite of tasks. We compare the calibration of uncertainty expressed in words ("verbalized probability") to uncertainty extracted from model logits. Both kinds of uncertainty are capable of generalizing calibration under distribution shift. We also provide evidence that GPT-3's ability to generalize calibration depends on pre-trained latent representations that correlate with epistemic uncertainty over its answers.

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.

Languages are not created randomly but rather to communicate information. There is a strong association between languages and their underlying meanings, resulting in a sparse joint distribution that is heavily peaked according to their correlations. Moreover, these peak values happen to match with the marginal distribution of languages due to the sparsity. With the advent of LLMs trained on big data and large models, we can now precisely assess the marginal distribution of languages, providing a convenient means of exploring the sparse structures in the joint distribution for effective inferences. In this paper, we categorize languages as either unambiguous or {\epsilon}-ambiguous and present quantitative results to demonstrate that the emergent abilities of LLMs, such as language understanding, in-context learning, chain-of-thought prompting, and effective instruction fine-tuning, can all be attributed to Bayesian inference on the sparse joint distribution of languages.

In this paper, we cast the problem of task underspecification in causal terms, and develop a method for empirical measurement of spurious associations between gender and gender-neutral entities for unmodified large language models, detecting previously unreported spurious correlations. We then describe a lightweight method to exploit the resulting spurious associations for prediction task uncertainty classification, achieving over 90% accuracy on a Winogender Schemas challenge set. Finally, we generalize our approach to address a wider range of prediction tasks and provide open-source demos for each method described here.

In this paper, we focus on inferring whether the given user command is clear, ambiguous, or infeasible in the context of interactive robotic agents utilizing large language models (LLMs). To tackle this problem, we first present an uncertainty estimation method for LLMs to classify whether the command is certain (i.e., clear) or not (i.e., ambiguous or infeasible). Once the command is classified as uncertain, we further distinguish it between ambiguous or infeasible commands leveraging LLMs with situational aware context in a zero-shot manner. For ambiguous commands, we disambiguate the command by interacting with users via question generation with LLMs. We believe that proper recognition of the given commands could lead to a decrease in malfunction and undesired actions of the robot, enhancing the reliability of interactive robot agents. We present a dataset for robotic situational awareness, consisting pair of high-level commands, scene descriptions, and labels of command type (i.e., clear, ambiguous, or infeasible). We validate the proposed method on the collected dataset, pick-and-place tabletop simulation. Finally, we demonstrate the proposed approach in real-world human-robot interaction experiments, i.e., handover scenarios.

Large Language Models (LLMs) have demonstrated remarkable capabilities across various applications, fundamentally reshaping the landscape of natural language processing (NLP) research. However, recent evaluation frameworks often rely on the output probabilities of LLMs for predictions, primarily due to computational constraints, diverging from real-world LLM usage scenarios. While widely employed, the efficacy of these probability-based evaluation strategies remains an open research question. This study aims to scrutinize the validity of such probability-based evaluation methods within the context of using LLMs for Multiple Choice Questions (MCQs), highlighting their inherent limitations. Our empirical investigation reveals that the prevalent probability-based evaluation method inadequately aligns with generation-based prediction. Furthermore, current evaluation frameworks typically assess LLMs through predictive tasks based on output probabilities rather than directly generating responses, owing to computational limitations. We illustrate that these probability-based approaches do not effectively correspond with generative predictions. The outcomes of our study can enhance the understanding of LLM evaluation methodologies and provide insights for future research in this domain.

Large language models (LLMs) are increasingly deployed as multi-step decision-making agents, where effective reward design is essential for guiding learning. Although recent work explores various forms of reward shaping and step-level credit assignment, a key signal remains largely overlooked: the intrinsic uncertainty of LLMs. Uncertainty reflects model confidence, reveals where exploration is needed, and offers valuable learning cues even in failed trajectories. We introduce SELAUR: Self Evolving LLM Agent via Uncertainty-aware Rewards, a reinforcement learning framework that incorporates uncertainty directly into the reward design. SELAUR integrates entropy-, least-confidence-, and margin-based metrics into a combined token-level uncertainty estimate, providing dense confidence-aligned supervision, and employs a failure-aware reward reshaping mechanism that injects these uncertainty signals into step- and trajectory-level rewards to improve exploration efficiency and learning stability. Experiments on two benchmarks, ALFWorld and WebShop, show that our method consistently improves success rates over strong baselines. Ablation studies further demonstrate how uncertainty signals enhance exploration and robustness.

Neural language models are probabilistic models of human text. They are predominantly trained using maximum likelihood estimation (MLE), which is equivalent to minimizing the forward cross-entropy between the empirical data distribution and the model distribution. However, various degeneration phenomena are still widely observed when decoding from the distributions learned by such models. We establish that the forward cross-entropy is suboptimal as a distance metric for aligning human and model distribution due to its (1) recall-prioritization (2) negative diversity ignorance and (3) train-test mismatch. In this paper, we propose Earth Mover Distance Optimization (EMO) for auto-regressive language modeling. EMO capitalizes on the inherent properties of earth mover distance to address the aforementioned challenges. Due to the high complexity of direct computation, we further introduce a feasible upper bound for EMO to ease end-to-end training. Upon extensive evaluation of language models trained using EMO and MLE. We find that EMO demonstrates a consistently better language modeling performance than MLE across domains. Moreover, EMO demonstrates noteworthy enhancements in downstream performance with minimal fine-tuning on merely 25,000 sentences. This highlights the tremendous potential of EMO as a lightweight calibration method for enhancing large-scale pre-trained language models.

Large Language Models (LLMs) suffer significant performance degradation in multi-turn conversations when information is presented incrementally. Given that multi-turn conversations characterize everyday interactions with LLMs, this degradation poses a severe challenge to real world usability. We hypothesize that abrupt increases in model uncertainty signal misalignment in multi-turn LLM interactions, and we exploit this insight to dynamically realign conversational context. We introduce ERGO (Entropy-guided Resetting for Generation Optimization), which continuously quantifies internal uncertainty via Shannon entropy over next token distributions and triggers adaptive prompt consolidation when a sharp spike in entropy is detected. By treating uncertainty as a first class signal rather than a nuisance to eliminate, ERGO embraces variability in language and modeling, representing and responding to uncertainty. In multi-turn tasks with incrementally revealed instructions, ERGO yields a 56.6% average performance gain over standard baselines, increases aptitude (peak performance capability) by 24.7%, and decreases unreliability (variability in performance) by 35.3%, demonstrating that uncertainty aware interventions can improve both accuracy and reliability in conversational AI.

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