PhasePilot: Auditing and steering phase boundaries in budgeted in-context reasoning

PhasePilot: Auditing and steering phase boundaries in budgeted in-context reasoning | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article PhasePilot: Auditing and steering phase boundaries in budgeted in-context reasoning Rui Li, Shuang Cao, Ruihua Liu, Alexandre Duprey, Ziyao Wang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8912612/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Reasoning performance in in-context learning can change discontinuously as inference-time resources vary, even at fixed model size. We characterize this behavior with an operational framework that treats the prompt as a budgeted state space defined by context cap k, demonstration count N, and task depth D. We define an order parameter m (exact-match accuracy) and a sensitivity χ=∂m/∂logN; the peak of χ yields a critical example count Nc, complemented by transition width and plateau gap to make claims falsifiable. We validate this estimator against alternative threshold-detection methods and report stability and uncertainty via bootstrap. We introduce PhasePilot, a prompting protocol that steers phase boundaries under a strict 4096-token budget cap enforced by cap-based allocation (prompt cap + generation cap per call × calls). PhasePilot shifts Nc leftward by 2.6–4.1× on controlled tasks (median 3.4×) by reallocating budget into an explicit state scaffold (5–6 task-specific variables within a 4-block I/O schema: Input/State/Reasoning/Answer) and by suppressing distractor entropy. On 11 external benchmarks, PhasePilot achieves a median +25.9-point gain over CoT (IQR [22.3, 29.2]) across GSM8K, MATH L3–5, GPQA Diamond, BBH, AIME 2023–24, ARC-Challenge, HotpotQA, DROP, ProofWriter, LogiQA, and LongCtx-DQA; within BBH, per-configuration gains span +9.0 to +46.2, exposing strong task-structure heterogeneity. Per-instance gain distributions, realized-token diagnostics, and output audits support that improvements reflect reasoning quality rather than extraction artifacts. Under the same cap, PhasePilot lies on the empirical compute frontier on the controlled suite (94.8% accuracy with one call versus 75.1% for ToT(b=4) with 12 calls). Mechanistic probing with pre-registered head selection and randomized controls provides supporting evidence linking the boundary shift to a sparse mid-layer head set, with patching effects 5.8× larger than random-head baselines. Physical sciences/Mathematics and computing/Computer science Physical sciences/Mathematics and computing/Statistics Full Text Additional Declarations There is NO Competing Interest. Supplementary Files nmisupplementary.pdf Supplementary File Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8912612","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":593960765,"identity":"4d3ad442-2c37-4580-9a9b-372f06d0913a","order_by":0,"name":"Rui Li","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA20lEQVRIiWNgGAWjYFACxgaGBwY2CWzszA1QER4gNiCgJcEgLYGNmZFoLUCQwHA4gQFVCx5gPiMZaEvB+Tw+Zsa2Dx/+2Mibt589wPCjALcWmRuJIIfdLgY6rHnmzLY0wzln8hIYe/A4TEICoiWxDaiFmbfhMOMMCR4DBh7CWs5BtPz5898epIXxD2EtByBaGNgOJIK0MOO1hedhw4EEg2SwFsbetuTkGTw5Bodl8GlhT3/44MMfu8T57c2HGX78sbOdwX7G8OGbP7i1gMABIkRGwSgYBaNgFJAEAJ6MSocllulrAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0009-0007-6857-2127","institution":"Hill Research","correspondingAuthor":true,"prefix":"","firstName":"Rui","middleName":"","lastName":"Li","suffix":""},{"id":593960766,"identity":"4a8d6968-4776-4ca9-a6d9-c0cc7b85068b","order_by":1,"name":"Shuang Cao","email":"","orcid":"","institution":"Hill Research","correspondingAuthor":false,"prefix":"","firstName":"Shuang","middleName":"","lastName":"Cao","suffix":""},{"id":593960767,"identity":"f907d6dc-cdb4-4270-b73f-f7bdaf3bdf78","order_by":2,"name":"Ruihua Liu","email":"","orcid":"","institution":"Hill Research","correspondingAuthor":false,"prefix":"","firstName":"Ruihua","middleName":"","lastName":"Liu","suffix":""},{"id":593960768,"identity":"d546c8c8-68b1-47d2-85c4-1ca831083b62","order_by":3,"name":"Alexandre Duprey","email":"","orcid":"","institution":"Hill Research","correspondingAuthor":false,"prefix":"","firstName":"Alexandre","middleName":"","lastName":"Duprey","suffix":""},{"id":593960769,"identity":"e348177c-ad63-46c9-a355-eba8b2649fc4","order_by":4,"name":"Ziyao Wang","email":"","orcid":"","institution":"Hill Research","correspondingAuthor":false,"prefix":"","firstName":"Ziyao","middleName":"","lastName":"Wang","suffix":""}],"badges":[],"createdAt":"2026-02-18 22:26:01","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8912612/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8912612/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":103057731,"identity":"867bcab8-2b9a-4e84-b4b1-d403e4c29535","added_by":"auto","created_at":"2026-02-20 09:32:46","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":340105,"visible":true,"origin":"","legend":"Article File","description":"","filename":"nmi.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8912612/v1_covered_63089692-63ed-410f-a66d-9f189ef49991.pdf"},{"id":103038235,"identity":"80aaaa39-85ec-4923-bfe5-6ce46d1887c0","added_by":"auto","created_at":"2026-02-20 02:55:09","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":1132512,"visible":true,"origin":"","legend":"Supplementary File","description":"","filename":"nmisupplementary.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8912612/v1/380a8b49bbf328c3e908bb8f.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"PhasePilot: Auditing and steering phase boundaries in budgeted in-context reasoning","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8912612/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8912612/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Reasoning performance in in-context learning can change discontinuously as inference-time resources vary, even at fixed model size. We characterize this behavior with an operational framework that treats the prompt as a budgeted state space defined by context cap k, demonstration count N, and task depth D. We define an order parameter m (exact-match accuracy) and a sensitivity χ=∂m/∂logN; the peak of χ yields a critical example count Nc, complemented by transition width and plateau gap to make claims falsifiable. We validate this estimator against alternative threshold-detection methods and report stability and uncertainty via bootstrap.\r\nWe introduce PhasePilot, a prompting protocol that steers phase boundaries under a strict 4096-token budget cap enforced by cap-based allocation (prompt cap + generation cap per call × calls). PhasePilot shifts Nc leftward by 2.6–4.1× on controlled tasks (median 3.4×) by reallocating budget into an explicit state scaffold (5–6 task-specific variables within a 4-block I/O schema: Input/State/Reasoning/Answer) and by suppressing distractor entropy. On 11 external benchmarks, PhasePilot achieves a median +25.9-point gain over CoT (IQR [22.3, 29.2]) across GSM8K, MATH L3–5, GPQA Diamond, BBH, AIME 2023–24, ARC-Challenge, HotpotQA, DROP, ProofWriter, LogiQA, and LongCtx-DQA; within BBH, per-configuration gains span +9.0 to +46.2, exposing strong task-structure heterogeneity. Per-instance gain distributions, realized-token diagnostics, and output audits support that improvements reflect reasoning quality rather than extraction artifacts. Under the same cap, PhasePilot lies on the empirical compute frontier on the controlled suite (94.8% accuracy with one call versus 75.1% for ToT(b=4) with 12 calls). Mechanistic probing with pre-registered head selection and randomized controls provides supporting evidence linking the boundary shift to a sparse mid-layer head set, with patching effects 5.8× larger than random-head baselines.","manuscriptTitle":"PhasePilot: Auditing and steering phase boundaries in budgeted in-context reasoning","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-20 02:55:05","doi":"10.21203/rs.3.rs-8912612/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"3db85637-f94e-4c82-aaad-520d73c18fe1","owner":[],"postedDate":"February 20th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":63206570,"name":"Physical sciences/Mathematics and computing/Computer science"},{"id":63206571,"name":"Physical sciences/Mathematics and computing/Statistics"}],"tags":[],"updatedAt":"2026-02-20T09:16:23+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-20 02:55:05","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8912612","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8912612","identity":"rs-8912612","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}