Evaluating Uncertainty Quantification Methods in Argumentative Large Language Models (2025)

Abstract: Research in uncertainty quantification (UQ) for large language models (LLMs) is increasingly important towards guaranteeing the reliability of this groundbreaking technology. We explore the integration of LLM UQ methods in argumentative LLMs (ArgLLMs), an explainable LLM framework for decision-making based on computational argumentation in which UQ plays a critical role. We conduct experiments to evaluate ArgLLMs’ performance on claim verification tasks when using different LLM UQ methods, inherently performing an assessment of the UQ methods’ effectiveness. Moreover, the experimental procedure itself is a novel way of evaluating the effectiveness of UQ methods, especially when intricate and potentially contentious statements are present. Our results demonstrate that, despite its simplicity, direct prompting is an effective UQ strategy in ArgLLMs, outperforming considerably more complex approaches.

## introduction large language models (llms) have demonstrated impressive capabilities across a range of tasks, such as coding, reasoning, and speech recognition @xcite . however, they also often generate hallucinated answers @xcite , with no clear indication of the uncertainty which caused them. still, many users are prone to blindly trusting llms' responses @xcite , which is especially risky in areas such as healthcare where llms are being applied @xcite . in these settings, the ability to reliably retrieve an llm's uncertainty would be immensely impactful, highlighting the importance of uncertainty quantification (uq) research in the development of trustworthy ai systems. recent research has shown that llms exhibit strong performance in automated decisionmaking @xcite , but that they also here, the input claim is derived from the truthfulqa dataset @xcite , arguments are generated by llama 3.1 @xcite , and a default base score 0.50 is used for the input claim. face challenges such as the inability to faithfully explain their decisions @xcite and reliably correct mistakes based on user feedback @xcite . towards addressing these challenges, @xcite introduce argumentative llms (argllms), which leverage computational argumentation to improve explainability and contestability for decisionmaking tasks such as claim verification. for a given statement, argllms generate an argumentation framework of supporting and attacking arguments, quantify argument uncertainty, and aggregate these components using gradual semantics @xcite , a form of formal reasoning, to determine whether a statement is true (see figure 1 for an example of an argllm evaluating a claim). argllms demonstrate comparable performance in claim verification against prompt-ing methods such as direct questioning and chainof-thought @xcite while also providing faithful explanations through the argumentative structure. it can be seen from figure 1 that in argllms, the estimated confidence in the generated arguments, and thus the chosen uq method, is pivotal in the claim verification task itself. for example, if (unlike in figure 1 ) the confidence in the attacking argument(s) was stronger than that in the supporting argument(s), we would expect the final determination to be false. 1 thus, argllms are an appealing evaluation setting for uq methods. since the confidence scores from the used uq method directly feed into the final predictions, ar-gllms enable evaluation of these scores without requiring access to the ground-truth labels for the arguments, as they only require the label for the top-level claim. for instance, arguments in favor of an incorrect prediction can generally be expected to be less convincing, and should thus be less certain. in this setting, uq methods can be seen as a proxy for downstream factuality and output reliability, which is a common use-case. additionally, argllms involve long and potentially contentious arguments, and the generation of supporting and attacking arguments for each claim ensures a strong diversity of statements to evaluate, making for a challenging, realistic, and wide-ranging setting. various uq methods exist in the literature, from directly prompting the model for an uncertainty estimate (also known as verbalized uq), which have proven effective and at times well-calibrated @xcite , to more complex methods involving token logits or semantic similarity @xcite . it is thus unclear which uq method would be ideal in the context of ar-gllms, which use direct prompting in @xcite . this is especially true since verbalized uq can sometimes have issues arising from llms being overconfident and biased when evaluating their own answers @xcite . in this paper, we aim to shed light on this problem by experimenting with a set of llm uq methods and examining their effect on the performance of ar-gllms in the claim verification task. concretely, our contributions are as follows: ## experiments we evaluate the performance of argllms on the claim verification task when using different llm uq methods as the uncertainty estimator for the arguments. for the experiments, we build upon the publicly released code provided by @xcite . 3 we also employ the same prompts as @xcite except for a minor change to argument generation (see appendix b). ## results and discussion in some cases, the advantage of direct prompting was substantial, such as in the strategyclaim gemma-2 0.5 bs (@xmath1.130 higher accuracy than the next best method. in contrast, the most direct prompting is ever outperformed is 0.028 by luq in the strategyclaim, llama 3.1, 0.5 bs, and @xmath2. we assessed the statistical significance of the accuracy results by conducting bootstrap tests with 5000 resamples to obtain 95% confidence intervals for the pairwise accuracy differences between the methods. these confidence intervals are used to determine the statistical significance of the best performances per configuration in in addition to accuracy, we also measured the brier scores for all experiments, which computes the mean squared difference between the predicted probability and the true label. in our case, the final argllm score is used as the predicted probability, and the label is 1 if the topic claim is true and 0 if it is false. the full table of brier scores is presented in appendix e. in summary, direct prompting scored the best in 18 instances, the most of any method, followed by luq with 9, semantic entropy with 7, and eccentricity with 2. overall, these results support the notion that verbalized confidence scores from direct prompting can be well-calibrated @xcite and represent the model's internal knowledge well with effective prompting @xcite . moreover, direct prompting likely outperforms the other methods due to the nature of longform contentious generations in argumentation. sampling-based methods such as semantic entropy require the capture of semantic consistency among multiple arguments, which can lead to degraded performance as the length of texts grows. as shown in figure 1 , argllms have long generations which can sometimes be contentious, unlike more definitive true or false statements. in this situation, direct prompting is often better suited to estimate a reasonable uncertainty level based on the llm's self-knowledge. also, it does not rely on an additional normalization step to map the uq outputs to suitable confidence scores, which can be prone to noise and introduces further estimation compounded with the existing estimation task. on top of its superior performance, the advantage of direct prompting is further amplified by its lower resource requirements. many of the other high-performing llm uq methods, including all three tested in this paper, require a separate nli model and multiple generations per instance, increasing both memory and time complexity. while not outperforming direct prompting overall, luq's relatively strong performance and high frequency of performing the best are intriguing. for example, when using llama 3.1 with strategy-claim, luq is the best in all four settings, illustrating the potential for a uq method to perform the best in a specific setup. in total, as seen in luq's capabilities in these experiments are also consistent with its strong performance in factuality tasks @xcite . while sentence splitting is not included in the luq implementation we use, computing uncertainty more directly from the entailment and contradiction logits between responses is another potential advantage which could have contributed to the stronger performance. all in all, the experiments demonstrate that argllms offer a compelling benchmark for llm uq methods. the qbaf structure of supporting and attacking arguments poses challenges distinct from those in existing benchmarks. at the same time, certain features that enhance performance on other tasks can also improve argllm claim verification performance as in the case of luq, lending further credibility to argllms as an evaluation environment. ## conclusion our work integrates commonly used and highperforming llm uq methods into argllms and assesses their performance on claim verification. we find that direct prompting leads to notably better performance than the other uq methods. among the latter, the lm-polygraph implementation of luq performs better than semantic entropy and eccentricity, reflecting luq's advantages seen in other tasks. overall, the experiments affirm the role of verbalized confidence prompting in eliciting confidence scores in argllms and suggest that prompt-based methods offer benefits for llm uq with long-form and potentially contentious statements. our research also presents and highlights the value of evaluating llm uq methods in argumentative settings and faithfully explainable frameworks such as argllms.