[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118582-en":3,"doc-seo-118582-105":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},118582,1374391974564,"Clementine","https://ap-avatar.wpscdn.com/avatar/14000253aa45c000a9e?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779874745381141002",8,"Research & Report","Forceful Functors - A Categorical Approach to Constraint Monitoring in Machine Learning Models","This thesis addresses how heuristic design choices in machine learning—such as training methods, model depth/width, activation functions, and error functions—create algorithm variants with different strengths and trade-offs. It applies category theory to provide a formal language that describes how hyperparameters change machine learning model structure. A focused construction explains how regularization affects model structure, followed by an inventory of hyperparameters with corresponding categorical interpretations. The work argues that categorification can specify constraints early in the design process and track them through final implementation.","University of North Dakota  \nUND Scholarly Commons  \n\n| Theses and Dissertations | Theses, Dissertations, and Senior Projects |\n| --- | --- |\n\nJanuary 2025  \nForceful Functors: A Categorical Approach To Constraint Monitoring In Machine Learning Models  \nJonathan Wirkkala  \nHow does access to this work benefit you? Let us know!  \nFollow this and additional works at: [https://commons.und.edu/theses](https://commons.und.edu/theses)  \nRecommended Citation  \nWirkkala, Jonathan, \"Forceful Functors: A Categorical Approach To Constraint Monitoring In Machine Learning Models\" (2025) . Theses and Dissertations. 7165.  \n[https://commons.und.edu/theses/7165](https://commons.und.edu/theses/7165)  \nThis Thesis is brought to you for free and open access by the Theses, Dissertations, and Senior Projects at UND Scholarly Commons. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of UND Scholarly Commons. For more information, please contact [und.commons@library.und.edu](und.commons@library.und.edu).  \nForceful Functors: A Categorical Approach to Constraint Monitoring in Machine Learning Models  \nby  \nJonathan Wirkkala  \nBachelor of Science, University of North Dakota, Grand Forks, ND, 2022  \nA thesis  \nsubmitted to the Graduate Faculty  \nof the  \nUniversity of North Dakota  \nIn partial fulfillment of the requirements  \nfor the degree of  \nMaster of Science  \nGrand Forks, North Dakota  \nMay  \n©2025 –Jonathan Wirkkala  \nall rights reserved.  \nii  \nName:  Jonathan Wirkkala   \nDegree:  Master of Science   \nThis document, submitted in partial fulfillment of the requirements for the degree from the University of North Dakota, has been read by the Faculty Advisory Committee under whom the work has been done and is hereby approved.  \nBryce Christopherson  \n| Anthony Bevelacqua\u003Cbr> |\n| --- |\n| Ryan Zerr |\n\n____________________________________  \n____________________________________  \nThis document is being submitted by the appointed advisory committee as having met all the requirements of the School of Graduate Studies at the University of North Dakota and is hereby approved.  \nJeff Holm  \nActing Dean of the School of Graduate Studies 5/5/2025  \nDate  \nPERMISSION  \nTitle: Forceful Functors: A Categorical Approach to Constraint Monitoring in Machine Learning Models  \nDepartment: Department of Mathematics and Statistics  \nDegree: Master of Science  \nIn presenting this document in partial fulfillment of the requirements for a graduate degree from the University of North Dakota , I agree that the library of this University shall make it freely available for inspection. I further agree that permission for extensive copying for scholarly purposes maybe granted by the professor who supervised my dissertation work or, in their absence, by the Chairperson of the department or the Dean of the Graduate School. It is understood that any copying or publication or other use of this dissertation or part thereof for financial gain shall not be allowed without my written permission. It is also understood that due recognition shall be given to me and to the University of North Dakota in any scholarly use which may be made of any material in my dissertation.  \nJonathan Wirkkala May 01, 2025  \nDedicated to my friends. Who all kept asking how my research was going, despite  \nknowing how long my response would be.  \nAbstract  \nOften times in machine learning there are several heuristic choices that one makes during model selection, training, and validation. These choices include the type of training used, the width and depth of the model, type activation function and many more. These choices are general rules of thumb and best practices when creating a machine learning algorithm to achieve acceptable results. For example, in the case of image processing, this may mean determining whether or not a given image contains a tumor. Decisions made during the design process create several variations of machine learning algorithms, all with","cbCainyKIZhOsB2n","https://ap.wps.com/l/cbCainyKIZhOsB2n","pdf",1273427,1,49,"English","en",105,"# Introduction\n## Artificial Intelligence and Machine Learning\n## The Math of Machine Learning\n### The Artificial Neuron\n### Networks of Artificial Neurons\n### Training a Neural Network\n### Methods of Training: Gradient Descent\n### Backpropagation\n### Regularization\n### Hyperparameters\n# Category Theory\n## What is a Category?\n## Functors\n## Natural Transformations\n## Diagrams\n## Categories With More","[{\"question\":\"What problem does the thesis target in machine learning model design?\",\"answer\":\"It targets the challenge of documenting and relating the many heuristic choices made during model selection, training, and validation, especially how those choices affect model structure and behavior.\"},{\"question\":\"How does the thesis use category theory in machine learning?\",\"answer\":\"It uses category theory to describe the structure of machine learning algorithms and to formalize how hyperparameters induce changes in that structure.\"},{\"question\":\"What is the thesis’s specific focus regarding regularization?\",\"answer\":\"It presents a categorical example showing how regularization changes the structure of machine learning models, and then connects other hyperparameters to categorical constructions.\"}]","Forceful Functors - 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