Beyond the Endpoint: Hallucination Detection via Predictive-Path Geometry

Large language models (LLMs) are increasingly deployed where factual reliability matters, making hallucination detection a pressing need. Existing detectors draw on output confidence, response consistency, and internal representations, yet the geometry of ordered intermediate predictions remains underexplored. We introduce Hierarchical Path Excess (HiPEx), a post-hoc white-box detector that characterizes predictive-path non-directness. HiPEx projects intermediate residual states into a shared vocabulary probability space and measures path excess—the two-step path length minus the direct endpoint distance. The same measure is applied across neighboring decoder blocks and within their attention–feed-forward transitions, yielding complementary layer-wise profiles. A lightweight probe scores these profiles, extracted in one teacher-forced pass through the frozen model without auxiliary generations. Across two instruction-tuned models and four question-answering benchmarks under BLEURT-20 labels, HiPEx outperforms all eight baselines in AUROC in every setting, with an average gain of 2.32 percentage points over the strongest baseline in each setting. Controlled ablations demonstrate the benefits of subtracting endpoint distance and combining both scales. Cross-benchmark transfer and alternative-label evaluations further support its robustness. These results highlight the value of predictive-path geometry for hallucination detection: the route to a prediction matters alongside its endpoint.