[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85443-en":3,"doc-seo-85443-105":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":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},85443,687197100911,"Himbo","https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1782698725881665579",8,"Research & Report","Forecasting Generative Amplification","Generative networks accelerate LHC simulations while producing event samples in regions beyond the training-set size, making statistical precision and uncertainty critical. The work introduces two complementary ways to estimate an amplification factor without relying on large holdout datasets: averaging amplification, which uses Bayesian networks or ensembling to infer amplification from integral precision over phase-space volumes, and differential amplification, which applies hypothesis testing to quantify amplification without resolution loss. Applied to modern event generators, both methods enable amplification assessment in specific phase-space regions.","arXiv :2509 .08048v4 [hep-ph] 12 Jul 2026  \nForecasting Generative Amplification  \nHenning Bahl1 , Sascha Diefenbacher2 , Nina Elmer1 , Tilman Plehn1,3 , and Jonas Spinner1  \n1 Institut für Theoretische Physik, Universität Heidelberg, Germany  \n2 Physics Division, Lawrence Berkeley National Laboratory, Berkeley, USA  \n3 Interdisciplinary Center for Scientific Computing (IWR), Universität Heidelberg, Germany July 14, 2026  \nAbstract  \nGenerative networks are perfect tools to enhance the speed and precision of LHC simulations. Especially when generating events beyond the size of the training dataset, it is important to understand their statistical precision. We present two complementary methods to estimate the amplification factor without large holdout datasets. Averaging amplification uses Bayesian networks or ensembling to estimate amplification from the precision of integrals over given phase-space volumes. Differential amplification uses hypothesis testing to quantify amplification without any resolution loss. Applied to state-of-the-art event generators, both methods indicate that amplification is already possible in specific regions of phase space.  \n\n| Contents\u003Cbr>1 Introduction\u003Cbr>2 Basics and toy datasets\u003Cbr>3 Averaging amplification factor\u003Cbr>3.1 Metric extrapolation and Bayesian networks\u003Cbr>3.2 1D Gaussian fit illustration\u003Cbr>3.3 Gaussian-ring toy data\u003Cbr>4 Differential amplification factor\u003Cbr>4.1 Kolmogorov-Smirnov test\u003Cbr>4.2 Gaussian-ring toy data\u003Cbr>5 Top pair production\u003Cbr>5.1 Averaging amplification\u003Cbr>5.2 Differential amplification\u003Cbr>6 Outlook\u003Cbr>A Differential amplification factors\u003Cbr>References | 2\u003Cbr>3\u003Cbr>4 4\u003Cbr>6 8\u003Cbr>10\u003Cbr>11\u003Cbr>12\u003Cbr>15\u003Cbr>16\u003Cbr>18\u003Cbr>19\u003Cbr>21\u003Cbr>22 |\n| --- | --- |\n\n1 Introduction  \nThe enormous amount of data at the Large Hadron Collider (LHC) allows us to explore the Standard Model with unprecedented precision. Over the next decade, the High Luminosity LHC (HL-LHC) will increase the amount of data by another order of magnitude, promising a significant jump in precision. To analyze this data will require a corresponding increase in the precision and the amount of simulated data.  \nLHC simulations rely on a comprehensive Monte Carlo event generation and detector simulation chain. It starts with the interaction of partons, from where the events are propagated through jet radiation and hadronization steps to the detector simulation. All steps are based on or informed by first principles, with a high level of precision. This link to proper physics models comes with significant computational costs. As a result, the need for HL-LHC simulations exceeds our computational budget by a significant factor.  \nTo solve this pressing problem, we need more efficient simulation methods. Modern machine learning (ML) provides such methods [1, 2], including generative networks that learn the underlying phase space densities from a controlled dataset. For instance, we can train a generative network on classical simulation and use it to generate extra simulation data significantly faster. Generative ultra-fast simulation rests on the assumption that samples drawn from the network can exceed the statistical limitations of the training data, the so-called amplification* . From a purely frequentist point of view, amplification is not possible without introducing additional assumptions. Amplification instead relies on the interpolation of the underlying density given the inductive bias of the generative network. It has been shown to work for synthetic data [3–5] and detector simulations [6] .  \nPotentially amplifying generative networks have been developed for phase-space sampling [7–16], end-to-end event generation [17–24], hadronization [25, 26], and detector simulators trained on full simulations [27–52] . Generative amplification is complemented with learned smooth amplitude surrogates [23, 53–66] and can be systematically benchmarked using trained classifiers [67] . To quantify the amount of amplification i","cbCaiqPwPuJQcjLM","https://ap.wps.com/l/cbCaiqPwPuJQcjLM","pdf",682808,3,1,27,"English","en",105,"# Introduction\n# Basics and toy datasets\n# Averaging amplification factor\n# Differential amplification factor\n# Top pair production\n# Outlook","[{\"question\":\"Why is quantifying generative amplification important for HL-LHC simulations?\",\"answer\":\"HL-LHC will increase data and require more precise simulations than available compute budgets. Generative networks can accelerate event generation, but their amplification must be quantified to understand statistical uncertainty and how the network should be used.\"},{\"question\":\"How does averaging amplification estimate the amplification factor without a large holdout set?\",\"answer\":\"Averaging amplification leverages Bayesian networks or ensembling to estimate amplification from the precision of integrals over specified phase-space volumes, avoiding the need to compare against the true distribution.\"},{\"question\":\"How does differential amplification quantify amplification and what testing is used?\",\"answer\":\"Differential amplification applies hypothesis testing to measure amplification without losing resolution, using statistical tools such as the Kolmogorov–Smirnov test and toy-data examples.\"}]",1784203564,68,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"forecasting-generative-amplification","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"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":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/forecasting-generative-amplification/85443/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-25","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why is quantifying generative amplification important for HL-LHC simulations?","Question",{"text":75,"@type":76},"HL-LHC will increase data and require more precise simulations than available compute budgets. Generative networks can accelerate event generation, but their amplification must be quantified to understand statistical uncertainty and how the network should be used.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does averaging amplification estimate the amplification factor without a large holdout set?",{"text":80,"@type":76},"Averaging amplification leverages Bayesian networks or ensembling to estimate amplification from the precision of integrals over specified phase-space volumes, avoiding the need to compare against the true distribution.",{"name":82,"@type":73,"acceptedAnswer":83},"How does differential amplification quantify amplification and what testing is used?",{"text":84,"@type":76},"Differential amplification applies hypothesis testing to measure amplification without losing resolution, using statistical tools such as the Kolmogorov–Smirnov test and toy-data examples.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":21,"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":52,"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"]