[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118616-en":3,"doc-seo-118616-105":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},118616,687197207919,"Theodora","https://ap-avatar.wpscdn.com/avatar/a000253d6f5f7c60be?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779446848396160552",8,"Research & Report","A Theory of Machine Learning","The paper critically reviews three foundational theories of machine learning—possible worlds, recognition, and operation—and argues that each faces significant limitations. It introduces a new learning framework in which machines learn a function when they successfully compute it, not when they recover probabilistic truth or converge to it. The work shows that this perspective undermines common assumptions in statistical and computational learning theories. It further examines implications through brief case studies in natural language processing and macroeconomics.","arXiv :2407 .05520v 1 [ cs .LG] 7 Jul 2024  \nA Theory of Machine Learning  \nJinsook Kim∗  \nUnderwood International College Yonsei University Seoul, Korea 03722 [jki76364@gmail.com](jki76364@gmail.com)  \nJinho Kang  \nEmeritus, Seoul National University Seoul, Korea 08826 [jhkang@snu.ac.kr](jhkang@snu.ac.kr)  \nAbstract  \nWe critically review three major theories of machine learning and provide a new theory according to which machines learn a function when the machines successfully compute it. We show that this theory challenges common assumptions in the statistical and the computational learning theories, for it implies that learning true probabilities is equivalent neither to obtaining a correct calculation of the true probabilities nor to obtaining an almost-sure convergence to them. We also brie􀀃y discuss some case studies from natural language processing and macroeconomics from the perspective of the new theory.  \n1 Introduction  \nIn this paper, we examine three major theories of machine learning. We will call them the possible worlds theory, the recognition theory, and the operation theory. Both the possible worlds theory and the recognition theory are based on what we will call the epistemic approach to machine learning, whereas the operation theory is based on what we will call the behavioral approach. We will prove that all three theories have important problems. We will then provide a new theory of machine learning according to which machines learn a function when machines successfully compute it. We will show that this theory challenges common assumptions in the statistical and the computational learning theories, for it implies that learning true probabilities is equivalent neither to obtaining a correct calculation of true probabilities nor to obtaining an almost-sure convergence to them. Lastly, we will discuss when machines can or cannot learn a probability function in the perspective of our new theory by considering two case studies, the 􀀂rst one from natural language processing and the second one from macroeconomics.  \n2 Two Theories of Machine Learning in the Epistemic Approach  \nThe epistemic approach to machine learning emphasizes that learning is the phenomenon of knowledge acquisition. In order for machines to learn a function, they must acquire knowledge of it. Given that what machines do is essentially computational, we can say that machines learn when they acquire knowledge through a computational method. There are two in􀀃uential theories of machine learning in the epistemic approach, the possible worlds theory and the recognition theory. Let us consider them in turn.  \n2.1 The Possible Worlds Theory  \nFirst, the possible worlds theory: two things are de􀀂ned here, (1) knowledge and (2) the process through which the learning algorithm returns the 􀀂nal knowledge from the completed task. For  \n􀀃 Use footnote for providing further information about author (webpage, alternative address)—not for acknowledging funding agencies.  \nPreprint. Under review.  \n(1), knowledge is de􀀂ned as truth in all epistemically possible worlds. Based on this de􀀂nition of knowledge, process is de􀀂ned as follows: extending some notions from Halpern et al. (1997, 2003), let us de􀀂ne a computer system or process by the set of possible runs. Here, a run is a description of the behavior of the system over time. Formally, a run is a function from time to state while each state encapsulates all the knowledge available to the system at that time. Now, this system may consist of either a single process or multiple processes. In the latter case, states can be further subdivided into local states and global states, and the system becomes a distributed system. It is worth noting here that time is discrete and does not need to be “real time.” To distinguish time from“real time”, we will call it a step. Now, except for the initial knowledge base given in the initial state s 1 , all the pieces of knowledge afterwards are internally provided at ea","cbCainhQ1FhaVdov","https://ap.wps.com/l/cbCainhQ1FhaVdov","pdf",291257,1,24,"English","en",105,"# Introduction\n# Two Theories of Machine Learning in the Epistemic Approach\n## The Possible Worlds Theory\n## The Recognition Theory","[{\"question\":\"What are the three major theories of machine learning discussed in the paper?\",\"answer\":\"The paper examines the possible worlds theory, the recognition theory, and the operation theory, grouped respectively by an epistemic or behavioral approach.\"},{\"question\":\"What is the key idea of the new machine learning theory proposed by the authors?\",\"answer\":\"Machines learn a function when they successfully compute it. This shifts the notion of learning away from recovering true probabilities.\"},{\"question\":\"How does the new theory challenge assumptions in statistical and computational learning theories?\",\"answer\":\"It implies that learning true probabilities is not equivalent to correctly calculating them or to almost-sure convergence to them, contradicting common assumptions in those areas.\"}]","A Theory of Machine Learning | PDF",1785684534,60,{"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},"a-theory-of-machine-learning","",{"@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/a-theory-of-machine-learning/118616/",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 are the three major theories of machine learning discussed in the paper?","Question",{"text":75,"@type":76},"The paper examines the possible worlds theory, the recognition theory, and the operation theory, grouped respectively by an epistemic or behavioral approach.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the key idea of the new machine learning theory proposed by the authors?",{"text":80,"@type":76},"Machines learn a function when they successfully compute it. This shifts the notion of learning away from recovering true probabilities.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the new theory challenge assumptions in statistical and computational learning theories?",{"text":84,"@type":76},"It implies that learning true probabilities is not equivalent to correctly calculating them or to almost-sure convergence to them, contradicting common assumptions in those areas.","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},[93,97,101,105,109,114,119,122,127,130,134],{"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":29,"slug":108},5,"Comic","comic",{"id":110,"doc_module":4,"doc_module_name":46,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]