A Probabilistic Framework for LLM Hallucination Detection via Belief Tree Propagation

TL;DR

This work introduces Belief Tree Propagation (BTProp), a probabilistic framework for detecting LLM hallucinations by constructing a belief tree of logically related statements and interpreting it as a hidden Markov tree. By jointly modeling LLM confidence scores (emissions) and the logical relations among statements (transitions), BTProp infers the posterior truth of the target claim, addressing calibration and consistency issues in prior belief-based methods. Empirical results on FELM-Science and FactCheckGPT show 3%–9% improvements in AUROC and AUC-PR over strong baselines, with additional analyses on efficiency and ablations illustrating the benefit of combining multiple belief-generation strategies. The approach offers a principled, scalable way to leverage internal model beliefs for factuality assessment, with practical implications for improving the reliability of LLM-generated content.

Abstract

This paper focuses on the task of hallucination detection, which aims to determine the truthfulness of LLM-generated statements. To address this problem, a popular class of methods utilize the LLM's self-consistencies in its beliefs in a set of logically related augmented statements generated by the LLM, which does not require external knowledge databases and can work with both white-box and black-box LLMs. However, in many existing approaches, the augmented statements tend to be very monotone and unstructured, which makes it difficult to integrate meaningful information from the LLM beliefs in these statements. Also, many methods work with the binarized version of the LLM's belief, instead of the continuous version, which significantly loses information. To overcome these limitations, in this paper, we propose Belief Tree Propagation (BTProp), a probabilistic framework for LLM hallucination detection. BTProp introduces a belief tree of logically related statements by recursively decomposing a parent statement into child statements with three decomposition strategies, and builds a hidden Markov tree model to integrate the LLM's belief scores in these statements in a principled way. Experiment results show that our method improves baselines by 3%-9% (evaluated by AUROC and AUC-PR) on multiple hallucination detection benchmarks. Code is available at https://github.com/UCSB-NLP-Chang/BTProp.

Figures (19)

• Figure 1: An example constructed belief tree.
• Figure 2: Motivating example for the proposed method.
• Figure 3: An example hidden Markov tree model.
• Figure 4: Performance-efficiency comparison.
• Figure 5: Belief tree example.