[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-139102-105":3,"doc-detail-139102-en":81,"detail-sidebar-cat-0-en-105":98},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","knowledge-centered-dual-process-reasoning-for-math-word-problems-with-large-language-models-research-on-knos-and-eknos-framework","Knowledge-Centered Dual-Process Reasoning for Math Word Problems With Large Language Models - Research on KNOS and EKNOS Framework","","Math word problem (MWP) evaluation tests both text understanding and mathematical knowledge mastery in AI models. Although large language models (LLMs) achieve strong results, they still frequently produce logical errors due to insufficient step-by-step knowledge-grounded reasoning. This paper introduces a Knowledge-guided Solver (KNOS) using dual-process cooperation: a knowledge system for invoking relevant knowledge and an inference system with verification and injection to guide interpretable symbolic deduction. An open-book variant, EKNOS, adds knowledge selectors to extract commonsense and formulas each step. Experiments on GPT3, ChatGPT, and GPT4 show improved reasoning accuracy.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/knowledge-centered-dual-process-reasoning-for-math-word-problems-with-large-language-models-research-on-knos-and-eknos-framework/139102/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/knowledge-centered-dual-process-reasoning-for-math-word-problems-with-large-language-models-research-on-knos-and-eknos-framework/139102.png","ImageObject",300,407,{"name":42,"@type":43},"\tCallum ","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-09-20","2026-08-23",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",9,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What problem does the paper address in LLM-based math word problem solving?","Question",{"text":63,"@type":64},"LLMs often generate logical errors and reasoning steps that are not fully grounded in the needed mathematical knowledge, even when they produce step-by-step chains.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How does KNOS improve step-by-step mathematical reasoning?",{"text":68,"@type":64},"KNOS uses an Invoke-Verify-Inject mechanism: it invokes relevant knowledge, verifies its rationality, and injects it to guide symbolic deduction in an interpretable way.",{"name":70,"@type":61,"acceptedAnswer":71},"What additional capability does EKNOS add to handle limited math-specific knowledge in LLMs?",{"text":72,"@type":64},"EKNOS assumes an open-book setting and designs knowledge selectors to extract the most relevant commonsense and math formulas from external sources for each reasoning step.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},139102,1787498210,{"code":4,"msg":82,"data":83},"success",{"doc_id":79,"user_id":84,"nickname":42,"user_avatar":85,"doc_module":4,"category_id":86,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":87,"file_id":88,"file_url":89,"file_type":90,"file_size":91,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":92,"language":93,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":94,"faqs":95,"seo_title":96,"seo_description":12,"update_tm":80,"read_time":97},137451211410,"https://ap-avatar.wpscdn.com/avatar/2000bb0a9246f588df?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786362646172706240",8,"Knowledge-Centered Dual-Process Reasoning for Math Word Problems With Large Language Models  \nJiayu Liu , Zhenya Huang , Member, IEEE, Qi Liu, Member, IEEE, Zhiyuan Ma, Chengxiang Zhai,  \nand Enhong Chen , Fellow, IEEE  \nAbstract—Math word problem (MWP) serves as a critical milestone for assessing the text mining ability and knowledge mastery level of models. Recent advancements have witnessed large language models (LLMs) showcasing remarkable performance on MWP. However, current LLMs still frequently exhibit logical errors, which highlights their inability to fully grasp the knowledge required for genuine step-by-step mathematical reasoning. To this end, in this paper, we propose a novel Knowledge-guided Solver (KNOS) framework that empowers LLMs to simulate human mathematical reasoning, whose core idea is to Invoke-Verify-Inject necessary knowledge to solve MWP. We draw inspiration from the dual-process theory to construct two cooperative systems: a Knowledge System and an Inference System. Specifically, the Knowledge System employs LLMs as the knowledge base and develops a novel knowledge invoker that can elicit their relevant knowledge to support the strict step-level mathematical reasoning. In the Inference System, we propose a knowledge verifier and a knowledge injector to evaluate the knowledge rationality and further guide the step-wise symbolic deduction in an interpretable manner based on human cognitive mechanism, respectively. Moreover, to tackle the potential scarcity issue of mathematics-specific knowledge in LLMs, we consider an open-book exam scenario and propose an improved version of KNOS called EKNOS. In EKNOS, we meticulously designknowledgeselectors to extract the most relevant commonsense and math formulas from external knowledge sources for each reasoning step. This knowledge is utilized to assist the knowledge invoker in better stimulating LLMs’ reasoning abilities. Both KNOS and EKNOS are flexible to empower different LLMs. Our experiments with GPT3, ChatGPT, and GPT4 not only demonstrate their reasoning accuracy improvement but also show  \nReceived 14 June 2024; revised 7 March 2025; accepted 22 March 2025 . Date of publication 1 April 2025; date of current version 1 May 2025 . This research was partially supported in part by the National Key Research and Development Program of China under Grant 2021YFF0901005, in part by the Key Technologies R&D Program of Anhui Province under Grant 202423k09020039, in part by the National Natural Science Foundation of China under Grant 62477044 and Grant 62337001, and in part by the Fundamental Research Funds for the Central Universities under Grant WK2150110038 . The work of Zhenya Huang was supported by the Young Elite Scientists Sponsorship Program by CAST under Grant 2024QNRC001. Recommended for acceptance by W. Ding.(Corresponding author: Zhenya Huang.)  \nJiayu Liu and Qi Liu are with the School ofData Science, State Key Laboratory of Cognitive Intelligence, University of Science and Technology of China, Hefei 230000, China (e-mail: [jy251198@mail.ustc.edu.cn](jy251198@mail.ustc.edu.cn); [qiliuql@ustc.edu.cn](qiliuql@ustc.edu.cn)).  \nZhenya Huang, Zhiyuan Ma, and Enhong Chen are with the School of Computer Science and Technology, State Key Laboratory of Cognitive Intelligence, University of Science and Technology of China, Hefei 230000, China (e-mail: [huangzhy@ustc.edu.cn](huangzhy@ustc.edu.cn); [zhyma@mail.ustc.edu.cn](zhyma@mail.ustc.edu.cn); [cheneh@ustc.edu.cn](cheneh@ustc.edu.cn)).  \nChengxiang Zhai is with the Department of Computer Science, University of Illinois at Urbana-Champaign, Champaign, IL 61820 USA (e-mail: [czhai@illinois.edu](czhai@illinois.edu)) .  \nThis article has supplementary downloadable material available at [https://doi.org/10.1109/TKDE.2025.3556367](https://doi.org/10.1109/TKDE.2025.3556367), provided by the authors.  \nDigital Object Identifier 10.1109/TKDE.2025.3556367  \nhow they bring the strict step-wise interpretability of mathematica","cbCairJr23pja5AR","https://ap.wps.com/l/cbCairJr23pja5AR","pdf",2782603,15,"English","# Introduction\n## Problem and limitations of current LLM reasoning\n## Dual-process motivation\n# Proposed framework: KNOS\n## Knowledge system and knowledge invoker\n## Inference system: knowledge verifier and injector\n# Open-book extension: EKNOS\n## Knowledge selectors from external sources\n## Step-wise enhancement of reasoning\n# Experiments\n## GPT3, ChatGPT, GPT4 evaluation\n## Accuracy improvements and analysis","[{\"question\":\"What problem does the paper address in LLM-based math word problem solving?\",\"answer\":\"LLMs often generate logical errors and reasoning steps that are not fully grounded in the needed mathematical knowledge, even when they produce step-by-step chains.\"},{\"question\":\"How does KNOS improve step-by-step mathematical reasoning?\",\"answer\":\"KNOS uses an Invoke-Verify-Inject mechanism: it invokes relevant knowledge, verifies its rationality, and injects it to guide symbolic deduction in an interpretable way.\"},{\"question\":\"What additional capability does EKNOS add to handle limited math-specific knowledge in LLMs?\",\"answer\":\"EKNOS assumes an open-book setting and designs knowledge selectors to extract the most relevant commonsense and math formulas from external sources for each reasoning step.\"}]","Knowledge-Centered Dual-Process Reasoning for Math Word Problems With Large Language Models - Research on KNOS and EKNOS Framework | PDF",38,{"code":4,"msg":82,"data":99},[100,104,108,112,117,122,127,130,134,137,141],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":105,"show_sort_weight":106,"slug":107},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":109,"show_sort_weight":110,"slug":111},"Exam",70,"exam",{"id":113,"doc_module":4,"doc_module_name":25,"category_name":114,"show_sort_weight":115,"slug":116},5,"Comic",60,"comic",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":119,"show_sort_weight":120,"slug":121},6,"Technology",50,"technology",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":125,"slug":126},7,"Healthcare",40,"healthcare",{"id":86,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":128,"slug":129},30,"research-report",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":131,"show_sort_weight":132,"slug":133},"Religion & Spirituality",20,"religion-spirituality",{"id":132,"doc_module":4,"doc_module_name":25,"category_name":135,"show_sort_weight":132,"slug":136},"World Cup","world-cup",{"id":138,"doc_module":4,"doc_module_name":25,"category_name":139,"show_sort_weight":138,"slug":140},10,"Lifestyle","lifestyle",{"id":142,"doc_module":4,"doc_module_name":25,"category_name":143,"show_sort_weight":113,"slug":144},19,"General","general"]