[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119800-en":3,"doc-seo-119800-105":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":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},119800,34359740700684,"Finn","https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487",8,"Research & Report","Precision-Machine Learning for the Matrix Element Method","The matrix element method (MEM) provides optimal LHC inference under limited statistics by using differential cross sections to compute event-wise likelihood ratios, requiring challenging integration over all parton-level configurations. This work introduces a dedicated machine learning framework combining efficient phase-space integration with learned acceptance and transfer functions. It leverages invertible networks and diffusion networks, plus a transformer architecture to resolve jet combinatorics, enabling near-optimal likelihood extraction from small event samples.","arXiv :2310 .07752v 3 [hep-ph] 3 Oct 2024  \nPrecision-Machine Learning for the Matrix Element Method  \nTheo Heimel1 , Nathan Huetsch1 , Ramon Winterhalder2 , Tilman Plehn1 , and Anja Butter1,3  \n1 Institut für Theoretische Physik, Universität Heidelberg, Germany  \n2 CP3, Université catholique de Louvain, Louvain-la-Neuve, Belgium  \n3 LPNHE, Sorbonne Université, Université Paris Cité, CNRS/IN2P3, Paris, France Abstract  \nThe matrix element method is the LHC inference method of choice for limited statistics.  \nWe present a dedicated machine learning framework, based on efficient phase-space integration, a learned acceptance and transfer function. It is based on a choice of INN and diffusion networks, and a transformer to solve jet combinatorics. We showcase this setup for the CP-phase of the top Yukawa coupling in associated Higgs and single-top production.  \n\n| Contents |  |\n| --- | --- |\n| 1 Introduction and reference process | 2 |\n| 2 ML-matrix element method | 3 |\n| 3 Two-network baseline | 6 |\n| 4 Acceptance classifier | 11 |\n| 5 Transfer diffusion | 12 |\n| 6 Combinatorics transformer | 13 |\n| 7 Outlook | 17 |\n| A Network hyperparameters | 20 |\n| B Variable jet number and permutation invariance | 21 |\n| C Evaluating on Herwig | 24 |\n| References | 27 |\n\n1 Introduction and reference process  \nOptimal analyses are the key challenge for the current and future LHC program, including specific model-based as well simulation-based search strategies. A classic method is the matrix element method (MEM), developed for the top physics program at the Tevatron [1, 2] . It derives its optimality from the Neyman-Pearson lemma and the fact that all information for a given hypothesis is encoded in the differential cross section. In the MEM, we compute likelihood ratios for individual events, such that the log-likelihood ratio of an event sample is the sum of the event-wise log-likelihood ratios. A combination of events to a kinematic distribution is not necessary [3] .  \nThe MEM was first used in the top mass measurement [4–7] and the discovery of the singletop production process [8] at the Tevatron. At the LHC, there exist several studies [9–15] and analysis applications [14, 16–19] . The critical challenge to MEM analyses is the integration over all possible parton-level configurations which could lead to the analyzed observed events. It can be solved by using modern machine learning (ML) for a fast and efficient combination of simulation and integration [20, 21] . A related ML approach to likelihood extraction is the classifier-based estimation of likelihood ratios [22] .  \nWe present a comprehensive simulation and integration framework for the MEM, based on modern machine learning [23, 24] . It makes extensive use of generative networks, which are transforming LHC simulations and analyses just like any other part of our lives. This starts with phase-space integration and sampling [25–30] and continues with more LHC-specific tasks like event subtraction [31], event unweighting [32, 33], loop integrations [34], or superresolution enhancement [35, 36] . At the LHC, generative networks generally work in interpretable physics phase spaces, for example scattering events [37–43], parton showers [44–51], and detector simulations [52–75] . These networks can be trained on first-principle simulationsand are easy to handle, efficient to ship, powerful in amplifying the training samples [76, 77], and — most importantly—precise [42, 78–80] . Conditional versions of these established generative networks then enable new analysis methods, like probabilistic unfolding [81–89], inference [21, 90], or anomaly detection [91–96] .  \nWe introduce a new MEM-ML-analysis framework in Sec. 2. It combines two generative network and one classifier network and pushes the precision beyond our conceptual study [21], towards an experimentally required level. For a fast and bi-directional evaluation we use the established cINNs with advanced coupling layers [42], updat","cbCaimANagKMzMW2","https://ap.wps.com/l/cbCaimANagKMzMW2","pdf",2097011,1,34,"English","en",105,"# 1 Introduction and reference process\n# 2 ML-matrix element method\n## Two-network baseline\n## Acceptance classifier\n## Transfer diffusion\n## Combinatorics transformer\n## Outlook\n# A Network hyperparameters\n# B Variable jet number and permutation invariance\n# C Evaluating on Herwig\n# References","[{\"question\":\"What problem does the matrix element method address at the LHC?\",\"answer\":\"It performs simulation-based inference by deriving likelihood ratios from differential cross sections. The key difficulty is integrating over all possible parton-level configurations compatible with observed events.\"},{\"question\":\"What machine learning components are proposed in the ML-MEM framework?\",\"answer\":\"The method combines learned acceptance and transfer functions using generative networks, including choices of invertible networks and diffusion networks, plus a transformer to handle jet combinatorics.\"},{\"question\":\"How is the approach validated or demonstrated in this study?\",\"answer\":\"It is showcased on the CP-phase of the top Yukawa coupling in associated Higgs and single-top production using a hadronic signature with the rare H→γγ decay channel to control backgrounds.\"}]","Precision-Machine Learning for the Matrix Element Method | PDF",1785726372,86,{"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},"precision-machine-learning-for-the-matrix-element-method","",{"@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/precision-machine-learning-for-the-matrix-element-method/119800/",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":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does the matrix element method address at the LHC?","Question",{"text":75,"@type":76},"It performs simulation-based inference by deriving likelihood ratios from differential cross sections. The key difficulty is integrating over all possible parton-level configurations compatible with observed events.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What machine learning components are proposed in the ML-MEM framework?",{"text":80,"@type":76},"The method combines learned acceptance and transfer functions using generative networks, including choices of invertible networks and diffusion networks, plus a transformer to handle jet combinatorics.",{"name":82,"@type":73,"acceptedAnswer":83},"How is the approach validated or demonstrated in this study?",{"text":84,"@type":76},"It is showcased on the CP-phase of the top Yukawa coupling in associated Higgs and single-top production using a hadronic signature with the rare H→γγ decay channel to control backgrounds.","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"]