Where Does Reasoning Break? Step-Level Hallucination Detection via Hidden-State Transport Geometry

• URL: http://arxiv.org/abs/2605.13772v1
• Date: Wed, 13 May 2026 16:48:48 GMT
• Title: Where Does Reasoning Break? Step-Level Hallucination Detection via Hidden-State Transport Geometry
• Abstract summary: Large language models hallucinate during multi-step reasoning, but most existing detectors operate at the trace level.<n>We operationalize this view with a label-conditioned teacher that builds a trace-specific contrastive PCA lens.<n>We prove that contrastive PCA is the optimal projection for a transport-separation objective between first error and correct states.
• Score: 3.2848713528308817
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Large language models hallucinate during multi-step reasoning, but most existing detectors operate at the trace level: they assign one confidence score to a full output, fail to localize the first error, and often require multiple sampled completions. We frame hallucination instead as a property of the hidden-state trajectory produced during a single forward pass. Correct reasoning moves through a stable manifold of locally coherent transitions; a first error appears as a localized excursion in transport cost away from this manifold. We operationalize this view with a label-conditioned teacher that builds a trace-specific contrastive PCA lens and scores each step with seven geometric transition features, and a deployable BiLSTM student distilled from the teacher that operates on raw hidden states without inference-time labels. We prove that contrastive PCA is the optimal projection for a transport-separation objective between first error and correct states, and that single-pass first error localization holds whenever the first error creates a positive transport margin over preceding correct transitions. On ProcessBench, PRM800K, HaluEval, and TruthfulQA, both models outperform entropy-based, probing-based, and attention-based baselines in-domain; the teacher transfers stably across language models and datasets, while the student collapses under shift, a gap our distillation theory predicts. These results recast step-level hallucination detection as a problem of trajectory dynamics and identify the central obstacle to deployment: preserving the contrastive transport margin under distribution shift.

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