Significance-Gain Pair Encoding for LLMs: A Statistical Alternative to Frequency-Based Subword Merging

Significance-Gain Pair Encoding for LLMs: A Statistical Alternative to Frequency-Based Subword Merging | 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 Research Article Significance-Gain Pair Encoding for LLMs: A Statistical Alternative to Frequency-Based Subword Merging Azam Nouri This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9077250/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 Subword tokenization is a key design choice for modern language models, including large language models (LLMs), with byte/character-level BPE serving as a widely used baseline. Standard BPE selects merges by raw pair frequency, which favors compression but can conflate true adjacency cohesion with pairs that are frequent due to high marginal counts. We introduce Significance-Gain BPE, a drop-in alternative merge criterion that measures cohesion via a z-statistic under an independence null model and combines it with an explicit compression-aware gain term. We evaluate Significance-Gain BPE on WikiText-103 (raw) character slices using a small causal Transformer language model and report both token-dependent perplexity and the tokenizer-invariant metric bits-per-character (BPC). At a representative operating point, Significance-Gain BPE reduces validation and test perplexity by 13% and 12%, respectively, and improves validation and test BPC by ∼0.9–1.0%. A vocabulary-size sweep further shows lower BPC in most closest-compression comparisons, suggesting that statistically grounded merge selection can improve predictive efficiency per unit of raw text across a range of compression regimes. Artificial Intelligence and Machine Learning Full Text Additional Declarations The authors declare no competing interests. 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. 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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-9077250","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":603417424,"identity":"52686992-ef01-4d99-b92d-daae4a1ecae1","order_by":0,"name":"Azam Nouri","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvklEQVRIiWNgGAWjYLCCBAYbGTYQ4wGUS4yWNB42hGJitDAwHOZBUkxAizl7j9mHBzXnefikmx8+SNxxmIGfPccArxbLnjPGMxKO3eZhkzlmbJB45jCDZM8b/FoMbuQYMySwAbVI5LBJJLYdBokQo+XfOYQWe6K0JLYdQLJFgpCWM8eKGRL7koFa0oB+aUvnkTjzrAC/luPNmxl/fLOTk5+R/PDBxzZrOf725A14tWAAHtKUj4JRMApGwSjACgCttD/xbcUqTQAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0009-0009-6844-5392","institution":"Lincoln University","correspondingAuthor":true,"prefix":"","firstName":"Azam","middleName":"","lastName":"Nouri","suffix":""}],"badges":[],"createdAt":"2026-03-09 23:04:40","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9077250/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9077250/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104421649,"identity":"2b5ee353-c8aa-4b09-9d71-13aa703c8c49","added_by":"auto","created_at":"2026-03-11 13:58:31","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":223607,"visible":true,"origin":"","legend":"","description":"","filename":"LLMP2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9077250/v1_covered_2b078e78-d920-4fa9-83b0-a5220b7cbeb3.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eSignificance-Gain Pair Encoding for LLMs: A Statistical Alternative to Frequency-Based Subword Merging\u003c/p\u003e","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-9077250/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9077250/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eSubword tokenization is a key design choice for modern language models, including large language models (LLMs), with byte/character-level BPE serving as a widely used baseline. 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