[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118110-en":3,"doc-seo-118110-105":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},118110,5909877438554,"Maeve","https://ap-avatar.wpscdn.com/avatar/5600025385ad2bf12a7?_k=1778553567797529272",8,"Research & Report","Understanding quantum machine learning also requires rethinking generalization","Quantum machine learning models can generalize well even with few training samples, yet a systematic randomization study shows that traditional explanations of generalization do not account for the observed behavior. Experiments demonstrate that state-of-the-art quantum neural networks can accurately fit random quantum states and random labelings. This memorization undermines assumptions behind small generalization error and renders common complexity-based guarantees, such as VC dimension and Rademacher complexity, unreliable. A supporting theoretical construction shows fitting arbitrary labels, challenging guarantees based solely on the model family.","Article [https://doi.org/10.1038/s41467-024-45882-z](https://doi.org/10.1038/s41467-024-45882-z)  \nUnderstanding quantum machine learning also requires rethinking generalization  \nReceived: 3 July 2023  \n\n| Accepted: 6 February 2024 |\n| --- |\n|  |\n| Check for updates |\n\nElies Gil-Fuster 1,2, Jens Eisert 1,2,3  & Carlos Bravo-Prieto 1   \nQuantum machine learning models have shown successful generalization performance even when trained with few data. In this work, through systematic randomization experiments, we show that traditional approaches to understanding generalization fail to explain the behavior of such quantum models. Our experiments reveal that state-of-the-art quantum neural networks accurately fit random states and random labeling of training data. This ability to memorize random data defies current notions of small generalization error, problematizing approaches that build on complexity measures such asthe VC dimension, the Rademacher complexity, and all their uniform relatives. We complement our empirical results with a theoretical construction showing that quantum neural networks can fit arbitrary labels to quantum states, hinting at their memorization ability. Our results do not preclude the possibility of good generalization with few training data but rather rule out any possible guarantees based only on the properties of the model family. These findings expose a fundamental challenge in the conventional understanding of generalization in quantum machine learning and highlight the need for a paradigm shift in the study of quantum models for machine learning tasks.  \nQuantum devices promise applications in solving computational problems beyond the capabilities of classical computers1–5. Given the paramount importance of machine learning in a wide variety of algorithmic applications that make predictions based on training data, it is a natural thought to investigate to what extent quantum computers may assist in tackling machine learning tasks. Indeed, such tasks are commonly listed among the most promising candidate applications for near-term quantum devices6–9. To date, within this emergent field of quantum machine learning (QML) a body of literature is available that heuristically explores the potential of improving learning algorithms by having access to quantum devices10–20. Among the models considered, parameterized quantum circuits (PQCs), also known as quantum neural networks (QNNs), take center stage in those considerations21–23. For fine-tuned problems in quantum machine learning, quantum advantages in computational complexity have been proven over classical computers24–27, but to date, such advantages rely on the availability of full-scale quantum computers, not being within reach for near-term  \narchitectures. While for PQCs such an advantage has not been shown yet, a growing body of literature is available that investigates their expressivity28–34, trainability35–44, and generalization45–60—basically aimed at understanding what to expect from such quantum models. Among those studies, the latter notions of generalization are particularly important since they are aimed at providing guarantees on the performance of QML models with unseen data after the training process.  \nThe importance of notions of generalization for PQCs is actually reflecting the development in classical machine learning: Vapnik’s contributions61 have laid the groundwork for the formal study of statistical learning systems. This methodology was considered standard in classical machine learning theory until roughly the last decade. However, the mindset put forth in this work has been disrupted by seminal work62 demonstrating that the conventional understanding of generalization is unable to explain the great success oflarge-scale deep convolutional neural networks. These networks, which display orders of magnitude more trainable parameters than the dimensions of the  \n1Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, Ber","cbCail5cnse0vwQF","https://ap.wps.com/l/cbCail5cnse0vwQF","pdf",1085541,1,12,"English","en",105,"# Overview\n## Experimental randomization evidence\n## Limits of complexity-based generalization bounds\n## Theoretical construction and implications","[{\"question\":\"What do the randomization experiments reveal about quantum machine learning generalization?\",\"answer\":\"They show that conventional theory fails to explain the generalization behavior, because quantum neural networks can fit random quantum states and random training labels.\"},{\"question\":\"How do VC dimension and Rademacher complexity relate to the paper’s conclusions?\",\"answer\":\"The study finds that complexity measures used to bound generalization do not provide reliable explanations in this quantum setting, with memorization breaking the assumptions behind small generalization error.\"},{\"question\":\"Do the results completely rule out good generalization with few training samples?\",\"answer\":\"No. The paper states that the findings do not preclude good generalization with limited data; instead, they rule out guarantees that rely only on properties of the model family.\"}]","Understanding quantum machine learning also requires rethinking generalization | PDF",1785681663,30,{"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},"understanding-quantum-machine-learning-also-requires-rethinking-generalization","",{"@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/understanding-quantum-machine-learning-also-requires-rethinking-generalization/118110/",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 do the randomization experiments reveal about quantum machine learning generalization?","Question",{"text":75,"@type":76},"They show that conventional theory fails to explain the generalization behavior, because quantum neural networks can fit random quantum states and random training labels.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How do VC dimension and Rademacher complexity relate to the paper’s conclusions?",{"text":80,"@type":76},"The study finds that complexity measures used to bound generalization do not provide reliable explanations in this quantum setting, with memorization breaking the assumptions behind small generalization error.",{"name":82,"@type":73,"acceptedAnswer":83},"Do the results completely rule out good generalization with few training samples?",{"text":84,"@type":76},"No. The paper states that the findings do not preclude good generalization with limited data; instead, they rule out guarantees that rely only on properties of the model family.","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},[93,97,101,105,110,115,120,122,127,130,134],{"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":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":29,"slug":121},"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"]