aiqbench analysis
This research introduces Divergent Token Confidence (DTC), a novel framework that quantifies LLM uncertainty by counting tokens where multiple models disagree during decoding rather than relying solely on token probabilities. The study demonstrates that this divergence count serves as a robust signal for calibration across various model families and mathematical benchmarks, significantly outperforming standard full-sequence confidence methods without requiring explicit training or altering the generation process. By addressing the unclear mechanisms behind current probability-based estimates, DTC offers a practical tool for improving the reliability of chain-of-thought reasoning in large language models.
Probability is Not Enough: Exploring and Counting Divergent Tokens for Reasoning Uncertainty Quantification in LLMs
arXiv:2609.38070v1 Announce Type: new Abstract: As the chain-of-thought reasoning capabilities of large language models improve, evaluating and calibrating their reasoning confidence is becoming increasingly important for quantifying the uncertainty of their answers. Current methods for estimating the confidence of large language models are generally based on probabilities of selected key tokens, but the underlying mechanism remains unclear. Our pilot study finds that replacing selected token probabilities with coarse substitutes can also improve calibration, motivating us to further explore effective signals of model confidence. We introduce Divergent Token Confidence (DTC), a framework that estimates confidence by counting tokens at which two models strongly disagree during decoding. DTC identifies these divergent tokens using the Jensen-Shannon divergence between next-token distributions evaluated along the same reasoning trajectory. We find that their count is almost negatively associated with answer accuracy, thereby serving as a simple yet effective signal for uncertainty quantification. DTC supports both white-box and black-box evaluation using auxiliary models, without explicit training and affecting the generation process. Experiments across multiple model families and six mathematical benchmarks demonstrate improved calibration over probability-based and verbalized baselines. Under white-box evaluation, the count-only estimator achieves an average expected calibration error of 13.0%, compared with 32.7%-42.4% for standard full-sequence confidence methods. In black-box settings, it also improves calibration over the original verbalized scores. For example, mean expected calibration error falls from 32.1%-40.2% to 13.7%-16.3% on DeepSeek-V3.2. These findings provide new insights for improving reasoning uncertainty quantification in large language models. The code is released at https://github.com/szu-tera/DTC.git.
Abstract:As the chain-of-thought reasoning capabilities of large language models improve, evaluating and calibrating their reasoning confidence is becoming increasingly important for quantifying the uncertainty of their answers. Current methods for estimating the confidence of large language models are generally based on probabilities of selected key tokens, but the underlying mechanism remains unclear. Our pilot study finds that replacing selected token probabilities with coarse substitutes can also improve calibration, motivating us to further explore effective signals of model confidence. We introduce Divergent Token Confidence (DTC), a framework that estimates confidence by counting tokens at which two models strongly disagree during decoding. DTC identifies these divergent tokens using the Jensen-Shannon divergence between next-token distributions evaluated along the same reasoning trajectory. We find that their count is almost negatively associated with answer accuracy, thereby serving as a simple yet effective signal for uncertainty quantification. DTC supports both white-box and black-box evaluation using auxiliary models, without explicit training and affecting the generation process. Experiments across multiple model families and six mathematical benchmarks demonstrate improved calibration over probability-based and verbalized baselines. Under white-box evaluation, the count-only estimator achieves an average expected calibration error of 13.0%, compared with 32.7%-42.4% for standard full-sequence confidence methods. In black-box settings, it also improves calibration over the original verbalized scores. For example, mean expected calibration error falls from 32.1%-40.2% to 13.7%-16.3% on DeepSeek-V3.2. These findings provide new insights for improving reasoning uncertainty quantification in large language models. The code is released at this https URL.
25 pages, 16 figures, 8 tables. Under peer review
Artificial Intelligence (cs.AI)
arXiv:2609.38070 [cs.AI]
(or arXiv:2609.38070v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2609.38070 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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