[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-121171-en":3,"doc-seo-121171-105":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},121171,687197207639,"Asher","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Improving Gradient Methods via Coordinate Transformations - Applications to Quantum Machine Learning","Machine learning optimization relies heavily on gradient-based methods such as gradient descent, whose performance is limited by local minima and barren plateaus. These issues slow training and can lead to non-optimal solutions, causing high computational and energy costs. The paper proposes a generic acceleration strategy based on coordinate transformations that adds cost-dependent directions in parameter space to navigate the configuration landscape more efficiently, validated by boosting multiple quantum machine learning algorithms with significant gains.","arXiv :2304 .06768v1 [ quant-ph] 13 Apr 2023  \nImproving Gradient Methods via Coordinate Transformations: Applications to Quantum Machine Learning  \nPablo Bermejo, 1, 2 Borja Aizpurua, 1 and Rom􀀓an Or􀀓us 1, 2, 3  \n1 Multiverse Computing, Paseo de Miram􀀓on 170, E-20014 San Sebasti􀀓an, Spain  \n2 Donostia International Physics Center, Paseo Manuel de Lardizabal 4, E-20018 San Sebasti􀀓an, Spain  \n3 Ikerbasque Foundation for Science, Maria Diaz de Haro 3, E-48013 Bilbao, Spain  \nMachine learning algorithms, both in their classical and quantum versions, heavily rely on optimization algorithms based on gradients, such as gradient descent and alike. The overall performance is dependent on the appearance of local minima and barren plateaus, which slow-down calculations and lead to non-optimal solutions. In practice, this results in dramatic computational and energy costs for AI applications. In this paper we introduce a generic strategy to accelerate and improve the overall performance of such methods, allowing to alleviate the e􀀋ect of barren plateaus and local minima. Our method is based on coordinate transformations, somehow similar to variational rotations, adding extra directions in parameter space that depend on the cost function itself, and which allow to explore the con􀀌guration landscape more e􀀎ciently. The validity of our method is benchmarked by boosting a number of quantum machine learning algorithms, getting a very signi􀀌cant improvement in their performance.  \nI. INTRODUCTION  \nMachine learning is revolutionizing society. We have witnessed it recently with the advent of game-changing applications such as ChatGPT, where Large Language Models [1] allow for unprecedented human-computer interaction. Such systems have a neural structure at their roots, with weights that must be optimized so as to minimize some error cost function. This optimization is usually done via gradient methods such as gradient descent, stochastic gradient descent, adaptive moment estimation, and alike, which are not free from problems such as barren plateaus and local minima. One important consequence is that current arti􀀌cial intelligence (AI) systems su􀀋er from long and complex training procedures, amounting to dramatic and unsustainable computational and energy costs [2] . And given the increasingly-huge demand of AI systems, the situation is even worse: we are in big need of more e􀀎cient machine learning.  \nMathematically speaking, numerical algorithms used for optimization problems are mostly based on techniques that sweep the whole hyperspace of solutions. This landscape might present a tractable shape where the optimal solution can be easily found, as in convex problems. However, most interesting problems have an ill-de􀀌ned landscape of solutions, with non-predictable shapes plenty of complexities impeding analytical and numerical methods to properly act on them. Gradient methods explore this landscape by computing local gradients of the cost function and updating the parameters according to the computed local slopes. More complex optimization methods, such as the widely-used stochastic gradient descent and adam optimizer, are based on the same idea.  \nThe work that we present here addresses the two main caveats of employing gradient methods for optimization purposes: local minima and barren plateaus. These features emerge inherently due to the shape of the cost function. In fact, both limitations can be understood as com-  \ning from moving along certain directions in the landscape of solutions. Changes in the optimization variables are the result of changes in the cost function, as the variables are modi􀀌ed. This is evidently an obstacle when we 􀀌nda 􀀍at region in the landscape of the cost function.  \nIn this paper we propose an alternative way to navigate the landscape of solutions by introducing extra freedom in the directions of the parameters' update. This is done by using (i) changes of coordinates, and (ii) adding extra dimensions related","cbCaiaklvlAFb7Hd","https://ap.wps.com/l/cbCaiaklvlAFb7Hd","pdf",778997,1,9,"English","en",105,"# Introduction\n## Methodology\n## Benchmarks and validation\n## Conclusions and future directions","[{\"question\":\"How do coordinate changes help avoid barren plateaus and local minima?\",\"answer\":\"Changing coordinates (e.g., hyperspherical coordinate changes and frame rotations) can produce non-zero gradients in the new representation, enabling optimization to escape stalled regions when projected back to the original landscape.\"}]","Improving Gradient Methods via Coordinate Transformations - Applications to Quantum Machine Learning | PDF",1785734197,23,{"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},"improving-gradient-methods-via-coordinate-transformations-applications-to-quantum-machine-learning","",{"@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/improving-gradient-methods-via-coordinate-transformations-applications-to-quantum-machine-learning/121171/",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","2026-08-03",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71],{"name":72,"@type":73,"acceptedAnswer":74},"How do coordinate changes help avoid barren plateaus and local minima?","Question",{"text":75,"@type":76},"Changing coordinates (e.g., hyperspherical coordinate changes and frame rotations) can produce non-zero gradients in the new representation, enabling optimization to escape stalled regions when projected back to the original landscape.","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},[85,89,93,97,102,107,112,115,119,122,126],{"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":21,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":117,"slug":118},"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":46,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":98,"slug":129},19,"General","general"]