[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82790-en":3,"doc-seo-82790-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},82790,137441390410,"Hazel","https://ap-avatar.wpscdn.com/avatar/2000252f4ab5702993?_k=1776741390130283984",8,"Research & Report","Language models guide symbolic equation discovery by controlling search","Scientific equation discovery requires combining broad domain priors with rigorous numerical verification. Symbolic regression grounds candidate formulas numerically but suffers from a rapidly growing combinatorial search space, while many language-model approaches generate or select equations directly. This work evaluates multiple role specifications for language models, including equation authorship, candidate deciding, and search control via LLM-PySR. Across 74 AI-Feynman equations and complex recovery tasks, search control balances accuracy, complexity, stability, and cost, and supports compact relations for cycle life.","Language models guide symbolic equation discovery by controlling search  \nZikai Xie 1,2,†, *, Wenmei Li 1,†, Man Luo 1, Jun Jiang 1,2,* and Linjiang Chen1,2,3,*  \n1 State Key Laboratory of Precision and Intelligent Chemistry, Hefei National Research Center for Physical Sciences at the Microscale, School of Chemistry and Materials Science, University of Science and Technology of China, Hefei, China.  \n2 Center for Scientific Intelligence Innovation, Hefei, China  \n3 School of Chemistry, School of Computer Science, University of Birmingham, Birmingham, UK † These authors contributed equally: Zikai Xie, Wenmei Li  \n* Corresponding authors: [linjiangchen@ustc.edu.cn](linjiangchen@ustc.edu.cn), [jiangj1@ustc.edu.cn](jiangj1@ustc.edu.cn), [zikaix@ustc.edu.cn](zikaix@ustc.edu.cn)  \nAbstract  \nScientific equation discovery must combine broad domain priors with strict numerical testing. Symbolic regression supplies numerical grounding but faces a combinatorial search space, whereas many languagemodel systems ask the model to propose or select formulas directly. We test a different division of labour. We compare role specifications in which the language model acts as equation author, candidate decider or search controller, alongside end-to-end language-model and purely numerical baselines. In the controller setting we propose here, implemented as LLM-PySR, language models specify variables, operators, transformations and search depth; symbolic regression enumerates and fits expressions; and deterministic metrics govern retention. Across 74 AI-Feynman equations and seven complex formula-recovery tasks, search control achieved the strongest observed balance of accuracy, complexity, stability and cost. On an independent battery dataset, LLM-PySR identified a compact piecewise-linear relation between early voltage-curve displacement and cycle life. The results suggest that language models should shape hypothesis exploration rather than decide which equations survive.  \nMain  \nInferring compact, mechanistically meaningful equations from data has long been a hallmark of scientific discovery, and is also a central goal of scientific machine learning.1 Unlike conventional machine-learning models that primarily optimize predictive accuracy, scientific equation discovery seeks compact analytical relations that can be inspected, tested and connected to mechanism.2 Symbolic regression (SR) is one of the main approaches to this problem: it searches over variables, operators and constants to identify closed-form expressions that explain observed data. This makes SR especially attractive in physics, chemistry, materials science and engineering, where an explicit formula can provide insight beyond numerical prediction.3–7 However, the same flexibility that makes SR powerful also makes it difficult: the space of possible expressions grows rapidly with the number of variables, operators and allowed expression computation complexity.8  \nRecent large-language-model (LLM) based SR methods have improved equation discovery by injecting scientific priors, semantic information and code-generation ability into the search process.9–12 Compared with traditional search-based approaches, these approaches provide a hybrid mechanism that couples semantic reasoning with symbolic search.13–18 A common strategy is agentification: to prompt an LLM with data summaries, variable names, scientific context and previous feedback, and ask it to generate candidate equation skeletons, which are then numerically fitted and evaluated.19 This paradigm has shown that LLMs can provide useful high-level priors for SR. However, in such skeleton-generation pipelines, the LLM does more than provide priors: it effectively pre-selects the structural search space by deciding which equation forms are passed to numerical fitting. Although numerical optimization can fit constants after a skeleton is proposed, the  \nstructural search itself remains limited by the LLM ’s prompt-level interpretati","cbCaiaqfbzWZFezL","https://ap.wps.com/l/cbCaiaqfbzWZFezL","pdf",2248260,1,119,"English","en",105,"# Abstract\n# Scientific equation discovery and symbolic regression\n# LLM-based methods and agentification pipelines\n# Proposed division of labour: semantic control vs numerical search\n# Role specifications and experimental evaluation","[{\"question\":\"What problem does the paper address in scientific equation discovery?\",\"answer\":\"The paper addresses how to infer compact, mechanistically meaningful equations from data reliably, despite the combinatorial growth of symbolic regression’s search space and the potential fragility of direct equation generation by language models.\"},{\"question\":\"How does the proposed approach differ from direct equation generation by LLMs?\",\"answer\":\"The approach restricts the LLM to controlling the search space—choosing variables, operators, transformations, and search depth—while a symbolic regression engine performs the combinatorial search and constant optimization, with deterministic numerical metrics governing retention.\"},{\"question\":\"What were the main experimental findings about role specifications for LLMs?\",\"answer\":\"Evaluating five role specifications shows that the search-controller configuration (LLM-PySR) yields the strongest observed balance of accuracy, complexity, stability, and cost, and reduces computational cost compared with end-to-end LLM search.\"}]",1784182950,300,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"language-models-guide-symbolic-equation-discovery-by-controlling-search","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/language-models-guide-symbolic-equation-discovery-by-controlling-search/82790/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does the paper address in scientific equation discovery?","Question",{"text":75,"@type":76},"The paper addresses how to infer compact, mechanistically meaningful equations from data reliably, despite the combinatorial growth of symbolic regression’s search space and the potential fragility of direct equation generation by language models.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed approach differ from direct equation generation by LLMs?",{"text":80,"@type":76},"The approach restricts the LLM to controlling the search space—choosing variables, operators, transformations, and search depth—while a symbolic regression engine performs the combinatorial search and constant optimization, with deterministic numerical metrics governing retention.",{"name":82,"@type":73,"acceptedAnswer":83},"What were the main experimental findings about role specifications for LLMs?",{"text":84,"@type":76},"Evaluating five role specifications shows that the 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