[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-126797-en":3,"doc-seo-126797-105":30,"detail-sidebar-cat-0-en-105":83},{"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},126797,1099523882182,"Eliana","https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8",8,"Research & Report","Machine Learning models as Mathematics - Interpreting explainable AI in non-causal terms","Machine learning systems require explanations, yet typical accounts of “why” rely on philosophy of science and causal, often scientific, explanation models. The chapter argues that machine learning systems are best understood as non-causal mathematical objects, so their explainability should be interpreted through the analogy of mathematical explanations rather than causal ones. It keeps much of the theoretical apparatus while explaining the asymmetry of standard ML explanation methods by linking them to concrete implementations.","Machine Learning models as Mathematics: interpreting explainable AI in non-causal  \nterms Stefan Buijsman  \nForthcoming in Durn, J. & Pozzi, G. (eds.) Philosophy of Science for Machine Learning: Core Issues and New Perspectives. Springer Nature  \nAbstract  \nWe would like to have a wide range of explanations for the behaviour of machine learning systems. However, how should we understand these explanations? Typically, attempts to clarify what an explanations for questions such as ’why am I getting this output for these inputs?’ have been approached from the philosophy of science, through an analogy with scientific (and often causal) explanations. I show that ML systems are best thought of as noncausal, specifically mathematical objects. We should therefore interpret these explanations differently, through analogy with mathematical explanations. I show that this still allows us to use much of the same theoretical apparatus, and argue that the asymmetry of many of the standard ML explanations can be accounted for in virtue of the link these systems have with concrete implementations.  \n1 Introduction  \nMachine Learning (ML) systems are notorious for requiring explanations. We do not know why they give the outputs that they do, and we even do not know why machine learning systems are as accurate as they are. In response, a wide variety of tools has been developed to try to elucidate the outputs of ML systems (Das and Rad, 2020), and theories have been developed to explain the success of ML systems (Shwartz-Ziv and Tishby, 2017) . There are feature importance methods that calculate which input features were the most important for a particular output (e.g. Ribeiro et al., 2016; Lundberg and Lee, 2017), counterfactual methods that calculate the nearest alternative input for which the ML system returns a different (desired) output (Karimi et al., 2020) and much more. In turn, this has put forward the more philosophical issue of what it would mean to explain the behaviour (in a broad sense) of ML systems. This chapter focuses on that question, in particular in the light of the mathematical aspects  \nof machine learning systems. As discussed in section 2, we can understand ML systems as implementing mathematical functions. We use optimization procedures (typically stochastic gradient descent) to fit this function to the data set that is available, with the aim to then classify, predict or produce new instances. All of this suggests that ML systems are abstract objects. Moreover, this idea of an ML system being linked to a mathematical function is also relied on by some of the explainability methods just mentioned. For example, Simonyan et al.(2013) highlight pixels for which the gradient of the implemented function is particularly steep, thus directly using the mathematical function approximated by ML systems in the XAI method.  \nI will dive into this mathematical aspect of ML systems throughout the chapter. It is noteworthy, however, because most philosophical accounts atthe moment approach the interpretation of explanations of ML systems using theories of scientific explanation, leaving the abstract, mathematical, nature of machine learning aside. For example, the overview in (Beisbart and Rz, 2022, p.2) mentions for a sub-type of ML systems: ”DNNs are mathematical models” but includes no accounts of XAI in terms of mathematical explanations. More concretely, Buijsman (2022) and Watson and Floridi (2021) both use the causal interventionist framework from Halpern and Pearl (2005) and Woodward (2003) to present an account of explanations of ML systems. Erasmus et al. (2021) apply four different accounts of scientific explanation (deductivenomological, Inductive Statistical, Causal-Mechanical and New Mechanist) to the machine learning context. There is a strong tendency to appeal to accounts of explanation from the philosophy of science, even though these have been developed primarily for describing concrete phenomena.  \nAt the same time","cbCaigg4Tr97f8t2","https://ap.wps.com/l/cbCaigg4Tr97f8t2","pdf",131291,1,18,"English","en",105,"# Introduction\n## Explanations and the philosophical challenge\n## XAI methods and the causal explanation analogy\n# Abstraction and explanations of ML outputs\n## The status of ML systems\n## Interventions without causation\n# Accounting for asymmetry in ML explanations\n# Mathematical explanations and constraints","[{\"question\":\"How does the chapter explain the asymmetry found in many standard ML explanations?\",\"answer\":\"It argues that explanation asymmetry can be accounted for through the link between ML systems (as mathematical objects) and their concrete implementations, even without assuming strict causation.\"}]","Machine Learning models as Mathematics - Interpreting explainable AI in non-causal terms | PDF",1785934842,45,{"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":78,"head_meta":80,"extra_data":82,"updated_unix":28},"machine-learning-models-as-mathematics-interpreting-explainable-ai-in-non-causal-terms","",{"@graph":36,"@context":77},[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/machine-learning-models-as-mathematics-interpreting-explainable-ai-in-non-causal-terms/126797/",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","2026-08-05",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71],{"name":72,"@type":73,"acceptedAnswer":74},"How does the chapter explain the asymmetry found in many standard ML explanations?","Question",{"text":75,"@type":76},"It argues that explanation asymmetry can be accounted for through the link between ML systems (as mathematical objects) and their concrete implementations, even without assuming strict causation.","Answer","https://schema.org",{"og:url":52,"og:type":79,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":81,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":84},[85,89,93,97,102,107,112,115,120,123,127],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":86,"show_sort_weight":87,"slug":88},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":90,"show_sort_weight":91,"slug":92},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Exam",70,"exam",{"id":98,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},5,"Comic",60,"comic",{"id":103,"doc_module":4,"doc_module_name":46,"category_name":104,"show_sort_weight":105,"slug":106},6,"Technology",50,"technology",{"id":108,"doc_module":4,"doc_module_name":46,"category_name":109,"show_sort_weight":110,"slug":111},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":113,"slug":114},30,"research-report",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":46,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":98,"slug":130},19,"General","general"]