{"paper":{"title":"Reasoning Models Don't Just Think Longer, They Move Differently","license":"http://creativecommons.org/licenses/by/4.0/","headline":"After length correction, reasoning models show distinct hidden-state trajectories on harder problems.","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.CL","authors_text":"Anders Gj{\\o}lbye, Lars Kai Hansen, Sanmi Koyejo","submitted_at":"2026-05-14T22:37:33Z","abstract_excerpt":"Reasoning-trained language models often spend more tokens on harder problems, but longer chains of thought do not show whether a model is merely computing for more steps or following a different internal trajectory. We study this distinction through hidden-state trajectories during chain-of-thought generation across competitive programming, mathematics, and Boolean satisfiability. Raw trajectory geometry is strongly shaped by generation length: longer generations mechanically alter path statistics, so difficulty-dependent comparisons are misleading without adjustment. After residualizing traje"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"After residualizing trajectory statistics on length, difficulty remains systematically coupled to corrected trajectory geometry across all domains studied. The clearest reasoning-specific separation appears in the code domain, where harder problems show more direct corrected trajectories and less heterogeneous local curvature in reasoning-trained models than in matched instruction-tuned baselines.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That residualizing raw trajectory statistics on generation length successfully removes all mechanical length-induced effects and leaves only the component attributable to reasoning strategy or internal computation.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"After length-correcting hidden-state trajectories during chain-of-thought, reasoning models show systematically different geometry on harder problems than baselines, strongest in competitive programming.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"After length correction, reasoning models show distinct hidden-state trajectories on harder problems.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"85f9268695eb2cfd6131799219a41f072b599757cd8b2ec8981df2744cae394f"},"source":{"id":"2605.15454","kind":"arxiv","version":1},"verdict":{"id":"7b502532-69c7-4d89-bdda-a77467dddae6","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T14:39:02.963239Z","strongest_claim":"After residualizing trajectory statistics on length, difficulty remains systematically coupled to corrected trajectory geometry across all domains studied. The clearest reasoning-specific separation appears in the code domain, where harder problems show more direct corrected trajectories and less heterogeneous local curvature in reasoning-trained models than in matched instruction-tuned baselines.","one_line_summary":"After length-correcting hidden-state trajectories during chain-of-thought, reasoning models show systematically different geometry on harder problems than baselines, strongest in competitive programming.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That residualizing raw trajectory statistics on generation length successfully removes all mechanical length-induced effects and leaves only the component attributable to reasoning strategy or internal computation.","pith_extraction_headline":"After length correction, reasoning models show distinct hidden-state trajectories on harder problems."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15454/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"cited_work_retraction","ran_at":"2026-05-19T15:51:55.289286Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"citation_quote_validity","ran_at":"2026-05-19T15:49:52.204121Z","status":"completed","version":"0.1.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T15:01:17.612094Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T14:50:17.313748Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T14:21:54.106172Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T13:33:22.675294Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"0f17cfab8e6dac1d12ecc3804fe9e585399e81eacf7ed7ab52ad8cdf7f746b79"},"references":{"count":14,"sample":[{"doi":"","year":null,"title":"Mitigating overthinking in large reasoning models via manifold steering","work_id":"f8c2a7ce-0438-463d-8985-cfd021da58cb","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2065,"title":"Jolliffe and Jorge Cadima","work_id":"5b863ffc-2076-49ed-889b-81ecc3cf2f65","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Probing the difficulty perception mechanism of large language models","work_id":"b131cbd5-0794-4a78-a1db-5d7f274ea2fb","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"LLMs encode how difficult problems are.arXiv preprint arXiv:2510.18147,","work_id":"6948d73b-e278-4096-8f01-0856a18ca1ba","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters","work_id":"a8d50b24-bdf5-46ed-bc4f-2927dfd81f1d","ref_index":5,"cited_arxiv_id":"2408.03314","is_internal_anchor":true}],"resolved_work":14,"snapshot_sha256":"d8e12ec78efbfd91823462f19e54c49c88ddef77fd875e4bb3bf612409b65a30","internal_anchors":2},"formal_canon":{"evidence_count":2,"snapshot_sha256":"a92230f44cfaf3190036fd61fcc4d094ec508df946b5ca722110c1747436e564"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}