[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118614-en":3,"doc-seo-118614-105":30,"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":4,"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":27,"seo_description":14,"update_tm":28,"read_time":29},118614,687197207919,"Theodora","https://ap-avatar.wpscdn.com/avatar/a000253d6f5f7c60be?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779446848396160552",8,"Research & Report","Artificial intelligence and machine learning generated conjectures with TxGraffiti","TxGraffiti is a machine learning and heuristic-driven artificial intelligence that automates conjecturing in mathematics. Since its development, it has produced many surprising conjectures that reached publication in reputable mathematical journals. The paper details the machine-learning and heuristic components implemented in TxGraffiti, summarizes its contributions to mathematical literature, and introduces a new online version of the program for exploring conjectures in graph theory.","arXiv :2407 .0273 1v 1 [ cs .AI] 3 Jul 2024  \nArtificial intelligence and machine learning generated conjectures with TxGraffiti  \n1 ,2 Randy Davila  \n1 Research and Development  \nRelationalAI  \nBerkeley, CA 94704, USA  \nEmail: randy.davila@relational .ai  \n2 Department of Computational Applied  \nMathematics & Operations Research Rice University  \nHouston, TX 77005, USA  \nEmail: [randy.r.davila@rice.edu](randy.r.davila@rice.edu)  \nAbstract  \nTxGraffiti is a machine learning and heuristic based artificial intelligence designed to automate the task of conjecturing in mathematics. Since its inception, TxGraffiti has generated many surprising conjectures leading to publication in respectable mathematical journals. In this paper we outline the machine learning and heuristic techniques implemented by TxGraffiti. We also recall its contributions to the mathematical literature and announce a new online version of the program available for anyone curious to explore conjectures in graph theory.  \nKeywords: Automated conjecturing; machine learned conjecturing; TxGraffiti.  \nAMS subject classification: 05C69  \n1 Introduction  \nThe ability of carefully designed computer programs to generate meaningful mathematical conjectures has been demonstrated since the late 1980s, notably by Fajtlowicz’s GRAFFITI program [23] . Indeed, this heuristic-based program was the first artificial intelligence to make significant conjectures in matrices, number theory, and graph theory, attracting the attention of renowned mathematicians like Paul Erd˝os, Ronald Graham, and Odile Favaron. Inspired by the pioneering work of Fajtlowicz, and by interactions with mathematicians who considered conjectures of GRAFFITI, we developed the TxGraffiti program, a modern conjecturing artificial intelligence named in homage to this rich history of conjectures made by GRAFFITI and now available as an interactive website. While our program TxGraffiti  \ndraws inspiration from GRAFFITI and its successor Graffiti.pc by DeLaVi˜na [19], it was developed independently and features several distinct design elements and conjecturing capabilities, which we detail in this paper.  \nWhen discussing computer-assisted conjecturing, we remark that it is easy for a computer to generate many plausible conjectures. For example, one might gather a set of mathematical objects and test various functions applied to these objects to identify potential relationships (inequalities) . If a relationship holds across all objects in the database, it becomes a plausible conjecture. For instance, given a database of graphs and the ability to compute various parameters on said graphs, a computer might quickly discover the relation:  \nα (G) ≤ n (G), (1)  \nwhere α(G) is the independence number (the cardinality of a maximum set of pairwise non-adjacent vertices in G) and n (G) is the order (the number of vertices in G) . A more refined bound for α (G) in nontrivial, connected graphs is:  \nα (G) ≤ n (G) − 1. (2)  \nBoth inequalities 1 and 2 hold under specific conditions, and TxGraffiti is designed to consider various hypotheses to form such conjectures. The mechanism for considering different hypotheses is a heuristic called Theo, detailed in Section 3 .  \nTo discover relationships like inequalities 1 and 2, TxGraffiti employs a machine learning, data-driven approach using linear optimization methods. This approach allows the program to find optimal parameters m, b ∈ R for example conjecturing on α (G) in terms of another graph invariant, say i (G), presenting conjectures in the form:  \nConjecture 1 . If G satisfies certain boolean conditions, then  \nα (G) ≤ m · i(G) + b,  \nwhere this bound is sharp.  \nBy integrating machine learning techniques with the Theo and Dalmation heuristics (see Section 2), TxGraffiti generates novel conjectures suitable for publication in mathematical journals. In Section 2, we discuss the historical development of AI-assisted conjecturing and relevant techniques. Section 3 details TxG","cbCaiqM5RbxG02y2","https://ap.wps.com/l/cbCaiqM5RbxG02y2","pdf",327215,1,10,"English","en",105,"# Introduction\n## Related Work\n## Implementation of TxGraffiti\n## TxGraffiti-generated conjectures and publications\n## Concluding remarks","[{\"question\":\"What is TxGraffiti designed to do?\",\"answer\":\"TxGraffiti is designed to automate conjecturing in mathematics by combining machine learning with heuristic methods.\"},{\"question\":\"Which techniques does the paper describe for TxGraffiti?\",\"answer\":\"The paper outlines machine learning and heuristic techniques, including a heuristic mechanism called Theo and references to Dalmation heuristics.\"},{\"question\":\"How has TxGraffiti contributed to mathematical research?\",\"answer\":\"TxGraffiti has generated surprising conjectures that have been published in mathematical journals, and the paper also announces a new online version for exploring graph-theory conjectures.\"}]","Artificial intelligence and machine learning generated conjectures with TxGraffiti | PDF",1785684518,25,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"artificial-intelligence-and-machine-learning-generated-conjectures-with-txgraffiti","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/artificial-intelligence-and-machine-learning-generated-conjectures-with-txgraffiti/118614/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-02",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is TxGraffiti designed to do?","Question",{"text":75,"@type":76},"TxGraffiti is designed to automate conjecturing in mathematics by combining machine learning with heuristic methods.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Which techniques does the paper describe for TxGraffiti?",{"text":80,"@type":76},"The paper outlines machine learning and heuristic techniques, including a heuristic mechanism called Theo and references to Dalmation heuristics.",{"name":82,"@type":73,"acceptedAnswer":83},"How has TxGraffiti contributed to mathematical research?",{"text":84,"@type":76},"TxGraffiti has generated surprising conjectures that have been published in mathematical journals, and the paper also announces a new online version for exploring graph-theory conjectures.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,134],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":21,"slug":133},"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]