Logical Graphs Improve LLM Uncertainty Quantification

Large Language Models (LLMs) frequently produce outputs that, despite being confidently stated, are unreliable, posing significant risks in critical applications. Current methods for quantifying LLM uncertainty, such as semantic entropy, primarily assess agreement based on semantic equivalence. This approach often overlooks the underlying logical connections between different answers, leading to an overestimation of uncertainty and incorrectly flagging hallucinations when responses are diverse in form but logically consistent (e.g., varying in specificity or granularity). To address this, a new framework called Logical Graph Uncertainty (LGU) has been developed. LGU explicitly models the implication and incompatibility relationships among generated answers. It aggregates probability mass along chains of entailment, calculates entropy over logically maximal hypotheses, and penalizes mutually incompatible responses. Across several question-answering benchmarks, LGU consistently demonstrates superior uncertainty estimation compared to existing methods, showing notable improvements in metrics like AUROC and AUARC, thereby offering a more accurate assessment of LLM reliability.