A Probabilistic Framework for LLM Hallucination Detection via Belief Tree Propagation (2025)

Abstract: We describe Belief Tree Propagation (BTProp), a probabilistic framework for LLM hallucination detection. To judge the truth of a statement, BTProp generates a belief tree by recursively expanding the initial statement into a set of logically related claims, then reasoning globally about the relationships between these claims. BTProp works by constructing a probabilistic model of the LM itself: it reasons jointly about logical relationships between claims and relationships between claim probabilities and LM factuality judgments via probabilistic inference in a “hidden Markov tree”. This method improves over state-of-the-art baselines by 3%-9% (evaluated by AUROC and AUC-PR) on multiple hallucination detection benchmarks.

## introduction current large language models (llms) often produce factually incorrect statements (sometimes referred to as "hallucinations"). one popular approach to detecting hallucinations is to prompt llms to assign probabilities to the correctness of their own outputs (sometimes referred to as model "beliefs"; @xcite @xcite . however, these beliefs are themselves frequently incorrect, miscalibrated, or inconsistent with each other. to improve the accuracy of lm factuality judgments, a large body of work adjusts the assessed probability of a target claim by reasoning about sets of related statements @xcite @xcite . these approaches typically involve two steps: first, the llm is prompted to generate an augmented set of statements that support or contradict the target statement, possibly with probabilities attached @xcite ; second, these claims are combined ⑤ the freezing point of water can be as low as -2°c at the top of mount everest. an example belief tree via logical or probabilistic inference. as a simple example, if an lm assigns high probability to a target statement, but even higher probability to a contradictory statement, it may be reasonably inferred that the target statement is actually incorrect. one key limitation of current methods is that they do not model noise or uncertainty in the lm generation process itself. llms' "beliefs" are often poorly calibrated -even statements that models judge to be true with 100% probability are sometimes false. how can we produce reliable judgments about sets of related statements when even their assessments of individual statements are unreliable? to do so, we propose belief tree propagation (btprop), a probabilistic method for improving the accuracy llm "beliefs" with applications to hallucination detection. specifically, given an initial statement generated by an llm, btprop first generates a belief tree of recursively generated claims that are logically related ot the initial statement. an example is shown in figure 1 , in which the root node of the belief tree is one sentence generated by the llm about the freezing point of water, and each child node supports or contradicts its parent. next, btprop interprets this belief tree as a directed graphical model (a "hidden markov tree"; @xcite in which the llm's confidence scores are modeled as observed variables, and the ground-truth truthfulness of the statements as the corresponding hidden variables. thus, the problem of assigning probabilities to statements can be reduced to probabilistic inference in a well-studied model family. here, inference makes it possible to integrate knowledge about the (logical) structure of related statements, and the (probabilistic) relationship between statements and noisy lm outputs. experiment results show that our method achieves state-of-the-art performance, improving the hallucination detection performance (auroc and auc-pr) by 3%-9% on felm-science @xcite and factcheckgpt @xcite datasets relative to state-of-the-art baselines. ## method given a statement v from the llm-generated text, e.g., a star's temperature is determined by the amount of mass and energy it has, and an llm, we aim to use the llm to gauge the correctness of the statement. many previous approaches use simple prompting techniques to directly elicit the llm's "belief", or assessed probability of the statement, as a confidence score in [0, 1]. for example, one approach is to directly query the llm for whether this is true. by sampling multiple answers from the llm, we can obtain the confidence score as the fraction of answers that say yes (or some paraphrase thereof). crucially, these scores may be wrong in several ways: in addition to be-stars with lower mass will have lower temperatures than more massive ones. external factors such as a surrounding nebula determines the temperature. a star's temperature is determined by the amount of mass and energy it has. ing factually incorrect, they may be miscalibrated (reflecting an inappropriate degree of certainty or uncertainty) or inconsistent (e.g., assigning high probability to mutually incompatible statements, or different probabilities to logically equivalent statements). below, we describe a method that addresses both categories of error by reasoning jointly about relationships between the truth values of related statements and llm confidence scores. ## experiments in this section, we conduct empirical evaluations on widely-used hallucination detection benchmarks. ## conclusion in this paper, we propose btprop, a method that leverages the model's intrinsic capability for hallucination detection. given a statement from the llm-generated texts, our method organizes the model's intrinsic beliefs on neighboring statements in a belief tree. by introducing the hidden markov tree model, we convert the the hallucination detection into a posterior probability estimation problem and propose corresponding solutions to solve it. experiment results have demonstrate the effectiveness of our method. the future direction would be how to further improve the belief tree construction method to make it more effective and efficient.