{"paper":{"title":"Where Does Reasoning Break? Step-Level Hallucination Detection via Hidden-State Transport Geometry","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Hidden-state trajectories expose the exact step where LLM reasoning first breaks via transport geometry.","cross_cats":["cs.AI"],"primary_cat":"cs.CL","authors_text":"Ali Baheri, Tyler Alvarez","submitted_at":"2026-05-13T16:48:48Z","abstract_excerpt":"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"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that the first error creates a positive transport margin over preceding correct transitions (stated in the abstract) and that a stable manifold of locally coherent transitions exists for correct reasoning.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Hallucination is detected as a transport-cost excursion in hidden-state trajectories, localized via contrastive PCA in a teacher model and distilled to a BiLSTM student.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Hidden-state trajectories expose the exact step where LLM reasoning first breaks via transport geometry.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"efa85fefcb1c98e682359bfe75e56e9bc0a0f08ed1b87ed356da560e42600c2f"},"source":{"id":"2605.13772","kind":"arxiv","version":1},"verdict":{"id":"e4ea1508-098a-4573-822e-54e52dc27c96","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T19:11:26.310867Z","strongest_claim":"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.","one_line_summary":"Hallucination is detected as a transport-cost excursion in hidden-state trajectories, localized via contrastive PCA in a teacher model and distilled to a BiLSTM student.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that the first error creates a positive transport margin over preceding correct transitions (stated in the abstract) and that a stable manifold of locally coherent transitions exists for correct reasoning.","pith_extraction_headline":"Hidden-state trajectories expose the exact step where LLM reasoning first breaks via transport geometry."},"references":{"count":27,"sample":[{"doi":"","year":2018,"title":"Abid, A., Zhang, M. J., Bagaria, V . K., and Zou, J. Exploring patterns enriched in a dataset with contrastive principal component analysis.Nature Communications, 9(1):2134, 2018. doi: 10.1038/ s41467","work_id":"08a3108f-0520-4001-82e3-74d6f866aa0a","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.48550/arxiv.2602.16015","year":2026,"title":"Geometry-aware uncertainty quantification via conformal prediction on man- ifolds","work_id":"77604c07-4e88-4584-8c33-e349b35787b7","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"Azaria, A. and Mitchell, T. The internal state of an LLM knows when it’s lying. InFindings of the Asso- ciation for Computational Linguistics: EMNLP 2023, pp. 967–976, Singapore, 2023","work_id":"d8c63f53-f165-4631-a2d0-64fb0195b233","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.48550/arxiv.2602","year":2026,"title":"Merlean: An agentic framework for autoformalization in quantum computation","work_id":"2c62ea97-8f54-46ed-ab36-91703f30ac87","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"Baheri, A. and Alm, C. O. LLMs-augmented contex- tual bandit. InNeurIPS 2023 Workshop on Foundation Models for Decision Making, 2023. FMDM@NeurIPS 2023","work_id":"c7296444-dffa-43dc-8460-5108a6ecd4ff","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":27,"snapshot_sha256":"e6d4ed96f98c7adfb813d40d01a1d4605af1d3bd8f6408fc203703241b15df0d","internal_anchors":5},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}