[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118540-en":3,"doc-seo-118540-105":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},118540,13056703019662,"Evangeline","https://ap-avatar.wpscdn.com/avatar/be000253a8e92610077?_k=1778726343310543188",8,"Research & Report","Tensor Networks in Machine Learning - Bachelor’s thesis","This bachelor’s thesis investigates tensor networks (TNs) as structured tools to mitigate the curse of dimensionality in machine learning. It builds a comprehensive theoretical foundation for tensors and tensor networks, combining mathematical perspectives with machine learning intuition. The work presents tensor operations and tensor diagram notation, then discusses structural properties of major decomposition formats. It applies TN-based supervised learning to classification tasks, with special focus on sweeping optimization, implements sweeping optimization for an MPS model in Julia, and evaluates results on Fashion-MNIST against traditional neural networks using performance, parameter count, and computational efficiency.","TENSOR NETWORKS IN MACHINE LEARNING  \nAdam Kalvoda  \nBachelor’s thesis  \nFaculty of Information Technology Czech Technical University in Prague Department of Applied Mathematics Study program: Informatics  \nSpecialisation: Artificial Intelligence  \nSupervisor: Ing. Tomáš Kalvoda, Ph.D.  \nMay 15, 2025  \nAssignment of bachelor’s thesis  \nTitle: Tensor Networks in Machine Learning  \nStudent: Adam Kalvoda  \nSupervisor: Ing. Tomáš Kalvoda, Ph. D.  \nStudy program: Informatics  \nBranch / specialization: Artificial Intelligence 2021  \nDepartment: Department of Applied Mathematics  \nValidity: until the end of summer semester 2025/2026  \nInstructions  \nThe aim of this thesis is to analyze applications of techniques based on tensor networks in machine learning and compare this approach with traditional neural networks.  \n1. Familiarize yourself with the theoretical description of tensor products using tensor networks [1] . Focus on the diagrammatic representation of these networks and summarize their possible applications in physics and machine learning.  \n2. Thoroughly study the use of tensor networks in supervised learning, focusing particularly on the \"sweeping\" optimization algorithm [2] .  \n3. Apply this technique to a supervised learning problem on selected dataset (e.g., Fashion-MNIST, CIFAR-10) using the Julia programming environment.  \n4. Compare the performance of your solution to traditional methods based on neural networks. Focusing on computational complexity and memory requirements of both approaches.  \n[1] J. C. Bridgeman, C. T. Chubb, Hand-waving and interpretive dance: an introductory course on tensor networks, J. Phys. A: Math. Theor. 50, 2017. [https://iopscience.iop.org/](https://iopscience.iop.org/)[ ](https://iopscience.iop.org/)article/10 . 1088/1751-8121/aa6dc3  \n[2] E. M. Stoudenmire, David J. Schwab, Supervised learning with tensor networks. Proceedings of the 30th International Conference on Neural Information Processing Systems (NIPS'16), 2016. [https://dl.acm.org/doi/abs/10.5555/3157382.3157634](https://dl.acm.org/doi/abs/10.5555/3157382.3157634)  \nElectronically approved by Ing. Magda Friedjungová, Ph.D. on 11 November 2024 in Prague.  \nCzech Technical University in Prague Faculty of Information Technology © 2025 Adam Kalvoda. All rights reserved.  \nThis thesis is school work as defined by Copyright Act of the Czech Republic. It has been submitted at Czech Technical University in Prague, Faculty of Information Technology. The thesis is protected by the Copyright Act and its usage without author’s permission is prohibited (with exceptions defined by the Copyright Act) .  \nCitation of this thesis: Kalvoda Adam. Tensor Networks in Machine Learning. Bachelor’s thesis. Czech Technical University in Prague, Faculty of Information Technology, 2025.  \nI would like to express my gratitude to my theis supervisor, Ing. Tomáš Kalvoda, Ph.D., for his invaluable guidance and pieces of advice throughout the course of this work. I also thank Jonáš Fuksa, M.Math, for suggesting this topic, which I might not have discovered otherwise. Last but not least, I am deeply grateful tomy family and my partner for their continuous support throughout my studies.  \nDeclaration  \nI hereby declare that the presented thesis is my own work and that I have cited all sources of information in accordance with the Guideline for adhering to ethical principles when elaborating an academic final thesis.  \nI acknowledge that my thesis is subject to the rights and obligations stipulated by the Act No. 121/2000 Coll., the Copyright Act, as amended, in particular that the Czech Technical University in Prague has the right to conclude a license agreement on the utilization of this thesis as a school work under the provisions of Article 60 (1) of the Act.  \nI declare that I have used AI tools during the preparation and writing of my thesis. I have verified the generated content. I confirm that I am aware that I am fully responsible for the content of the","cbCaibPp8l6HHKCu","https://ap.wps.com/l/cbCaibPp8l6HHKCu","pdf",1713060,1,86,"English","en",105,"# Assignment of bachelor’s thesis\n## Instructions\n# Abstract\n## Keywords","[{\"question\":\"What is the main objective of the thesis?\",\"answer\":\"To analyze applications of tensor network techniques in machine learning and compare them with traditional neural networks, especially for supervised learning classification.\"},{\"question\":\"Which supervised learning optimization method receives special emphasis?\",\"answer\":\"The sweeping optimization algorithm.\"},{\"question\":\"How is the implemented model evaluated and against what baseline?\",\"answer\":\"The sweeping optimization is implemented for an MPS-based classification model in Julia, applied to Fashion-MNIST, and compared with traditional neural networks using performance metrics, parameter/memory efficiency, and computational efficiency.\"}]","Tensor Networks in Machine Learning - Bachelor’s thesis | PDF",1785684056,217,{"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},"tensor-networks-in-machine-learning-bachelors-thesis","",{"@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/tensor-networks-in-machine-learning-bachelors-thesis/118540/",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 the main objective of the thesis?","Question",{"text":75,"@type":76},"To analyze applications of tensor network techniques in machine learning and compare them with traditional neural networks, especially for supervised learning classification.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Which supervised learning optimization method receives special emphasis?",{"text":80,"@type":76},"The sweeping optimization algorithm.",{"name":82,"@type":73,"acceptedAnswer":83},"How is the implemented model evaluated and against what baseline?",{"text":84,"@type":76},"The sweeping optimization is implemented for an MPS-based classification model in Julia, applied to Fashion-MNIST, and compared with traditional neural networks using performance metrics, parameter/memory efficiency, and computational efficiency.","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},[93,97,101,105,110,115,120,123,128,131,135],{"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":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]