Fact-Checking with Large Language Models via Probabilistic Certainty and Consistency

TL;DR

The paper tackles the persistent factuality problem in large language models by moving beyond blanket retrieval to an adaptive fact-checking framework. It introduces Probabilistic Certainty and Consistency (PCC), which jointly models internal certainty $\tau(c)$ and reasoning consistency $\gamma(c)$ to route verification via thresholds $\alpha,\beta$ into direct answering, deep search, or targeted search strategies. Empirical results on SciFact, HoVER, and FeLMW show PCC improves calibration (lower $\text{ECE}$) and macro-F1 across multiple model families, with notable gains on challenging or false claims, and demonstrates robust generalization to both proprietary and open models. The work highlights practical benefits in reducing unnecessary retrieval while maintaining reliability, offering a scalable approach to fact-checking that can adapt to model capability and task difficulty, with future directions toward adaptive policies and multimodal extensions.

Abstract

Large language models (LLMs) are increasingly used in applications requiring factual accuracy, yet their outputs often contain hallucinated responses. While fact-checking can mitigate these errors, existing methods typically retrieve external evidence indiscriminately, overlooking the model's internal knowledge and potentially introducing irrelevant noise. Moreover, current systems lack targeted mechanisms to resolve specific uncertainties in the model's reasoning. Inspired by how humans fact-check, we argue that LLMs should adaptively decide whether to rely on internal knowledge or initiate retrieval based on their confidence in a given claim. We introduce Probabilistic Certainty and Consistency (PCC), a framework that estimates factual confidence by jointly modeling an LLM's probabilistic certainty and reasoning consistency. These confidence signals enable an adaptive verification strategy: the model answers directly when confident, triggers targeted retrieval when uncertain or inconsistent, and escalates to deep search when ambiguity is high. Our confidence-guided routing mechanism ensures that retrieval is invoked only when necessary, improving both efficiency and reliability. Extensive experiments across three challenging benchmarks show that PCC achieves better uncertainty quantification than verbalized confidence and consistently outperforms strong LLM-based fact-checking baselines. Furthermore, we demonstrate that PCC generalizes well across various LLMs.

Figures (13)

• Figure 1: Illustration of how Probabilistic Certainty and Consistency (PCC) estimates an LLM’s factual confidence along two dimensions: internal certainty and reasoning consistency. Each claim is assigned to a distinct quadrant, and a tailored verification strategy is used accordingly.
• Figure 2: Illustration of Probabilistic Certainty and Consistency (PCC) framework. Internal certainty reflects the model’s probabilistic confidence in its predicted verdict, while reasoning consistency quantifies the logical coherence of its explanations across counterfactual reasoning.
• Figure 3: Expected Calibration Error (ECE) of PCC versus verbal confidence on SciFact, FeLMWk, and HoVer. Lower ECE indicates better-calibrated factual confidence. PCC consistently achieves superior calibration across all datasets and model families compared to verbal confidence.
• Figure 4: Macro-F$_1$ comparison of PCC versus verbal confidence on FactoolQA, FeLMWk, and SciFact. PCC uses the same search module as FIRE, differing only in the confidence signal used to trigger retrieval.
• Figure 5: Kernel density estimation (KDE) plots of score distributions for correct (green) and incorrect (red) predictions across datasets. PCC yields the clearest separation, reducing overlap in the overconfident region.