{"id":"https://openalex.org/W7212936348","doi":"https://doi.org/10.48550/arxiv.2609.12024","title":"Learning the Geometry of Collider Events with Metric-Aware Deep Sets","display_name":"Learning the Geometry of Collider Events with Metric-Aware Deep Sets","publication_year":2026,"publication_date":"2026-09-10","ids":{"openalex":"https://openalex.org/W7212936348","doi":"https://doi.org/10.48550/arxiv.2609.12024"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.12024","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12024","pdf_url":"https://arxiv.org/pdf/2609.12024","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.12024","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5105510388","display_name":"L. Hay","orcid":"https://orcid.org/0000-0002-7086-7641","observed_orcids":["https://orcid.org/0000-0002-7086-7641"]},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]},{"id":"https://openalex.org/I4210160315","display_name":"The NSF AI Institute for Artificial Intelligence and Fundamental Interactions","ror":"https://ror.org/04pvzz946","country_code":"US","type":"facility","lineage":["https://openalex.org/I121934306","https://openalex.org/I12912129","https://openalex.org/I136199984","https://openalex.org/I4210160315","https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hay, Lauren","raw_affiliation_strings":["Brown University / IAIFI"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Brown University / IAIFI","institution_ids":["https://openalex.org/I27804330","https://openalex.org/I4210160315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5151673767","display_name":"Rishabh Jain","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jain, Rishabh","raw_affiliation_strings":["Brown University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Brown University","institution_ids":["https://openalex.org/I27804330"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035695436","display_name":"M. LeBlanc","orcid":"https://orcid.org/0000-0001-5977-6418","observed_orcids":["https://orcid.org/0000-0001-5977-6418"]},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]},{"id":"https://openalex.org/I4210160315","display_name":"The NSF AI Institute for Artificial Intelligence and Fundamental Interactions","ror":"https://ror.org/04pvzz946","country_code":"US","type":"facility","lineage":["https://openalex.org/I121934306","https://openalex.org/I12912129","https://openalex.org/I136199984","https://openalex.org/I4210160315","https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"LeBlanc, Matt","raw_affiliation_strings":["Brown University / IAIFI"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Brown University / IAIFI","institution_ids":["https://openalex.org/I27804330","https://openalex.org/I4210160315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5106125289","display_name":"J. Roloff","orcid":"https://orcid.org/0000-0001-6479-3079","observed_orcids":["https://orcid.org/0000-0001-6479-3079"]},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Roloff, Jennifer","raw_affiliation_strings":["Brown University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Brown University","institution_ids":["https://openalex.org/I27804330"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.4255000054836273,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.4255000054836273,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.13619999587535858,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.06840000301599503,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/optimal-transport","display_name":"optimal transport","score":0.8889999985694885},{"id":"https://openalex.org/keywords/deep-sets","display_name":"Deep Sets","score":0.6579999923706055},{"id":"https://openalex.org/keywords/triangle-inequality","display_name":"triangle inequality","score":0.6320000290870667},{"id":"https://openalex.org/keywords/particle-physics","display_name":"particle physics","score":0.4650000035762787},{"id":"https://openalex.org/keywords/neural-network-surrogate-model","display_name":"neural network surrogate model","score":0.6100000143051147},{"id":"https://openalex.org/keywords/inductive-bias","display_name":"inductive bias","score":0.6380000114440918}],"concepts":[{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6553999781608582},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.5751000046730042},{"id":"https://openalex.org/C182964748","wikidata":"https://www.wikidata.org/wiki/Q208216","display_name":"Triangle inequality","level":2,"score":0.574999988079071},{"id":"https://openalex.org/C152290109","wikidata":"https://www.wikidata.org/wiki/Q2033879","display_name":"Collider","level":2,"score":0.5701000094413757},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.5235000252723694},{"id":"https://openalex.org/C2779662365","wikidata":"https://www.wikidata.org/wiki/Q5416694","display_name":"Event (particle physics)","level":2,"score":0.51419997215271},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5059999823570251},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.48809999227523804},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48669999837875366},{"id":"https://openalex.org/C165696696","wikidata":"https://www.wikidata.org/wiki/Q11287","display_name":"Exploit","level":2,"score":0.4578000009059906},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4108999967575073},{"id":"https://openalex.org/C157764524","wikidata":"https://www.wikidata.org/wiki/Q1383412","display_name":"Throughput","level":3,"score":0.4081000089645386},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.40400001406669617},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.400299996137619},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3562000095844269},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3458999991416931},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.34200000762939453},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.32499998807907104},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.30660000443458557},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.30300000309944153},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.29829999804496765},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.29660001397132874},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.2906999886035919},{"id":"https://openalex.org/C2778517922","wikidata":"https://www.wikidata.org/wiki/Q7140482","display_name":"Particle (ecology)","level":2,"score":0.2874000072479248},{"id":"https://openalex.org/C68767595","wikidata":"https://www.wikidata.org/wiki/Q1677999","display_name":"Contiguity","level":2,"score":0.28110000491142273},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.27489998936653137},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.2696000039577484},{"id":"https://openalex.org/C32946077","wikidata":"https://www.wikidata.org/wiki/Q618079","display_name":"Network analysis","level":2,"score":0.2671999931335449},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.2621000111103058},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.2597000002861023},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.257999986410141},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25529998540878296},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.2540000081062317},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2515000104904175}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.12024","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12024","pdf_url":"https://arxiv.org/pdf/2609.12024","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.12024","doi":"https://doi.org/10.48550/arxiv.2609.12024","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.12024","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.12024","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12024","pdf_url":"https://arxiv.org/pdf/2609.12024","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3509299210","display_name":"AI Institute: AI Research Institute for Fundamental Interactions","funder_award_id":"2019786","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5851783697","display_name":null,"funder_award_id":"DE-SC0026285","funder_id":"https://openalex.org/F4320337511","funder_display_name":"High Energy Physics"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320309070","display_name":"Brown University","ror":"https://ror.org/05gq02987"},{"id":"https://openalex.org/F4320332359","display_name":"Office of Science","ror":"https://ror.org/00mmn6b08"},{"id":"https://openalex.org/F4320337511","display_name":"High Energy Physics","ror":"https://ror.org/035m6g344"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212936348.pdf","grobid_xml":"https://content.openalex.org/works/W7212936348.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W2000443531","https://openalex.org/W2005900119","https://openalex.org/W2019106840","https://openalex.org/W2029241756","https://openalex.org/W2084823023","https://openalex.org/W2154904230","https://openalex.org/W2895846750","https://openalex.org/W2911264653","https://openalex.org/W2939653360","https://openalex.org/W3015829700","https://openalex.org/W3017153206","https://openalex.org/W3045102472","https://openalex.org/W3072271437","https://openalex.org/W3130159758","https://openalex.org/W4299457904","https://openalex.org/W4378718267","https://openalex.org/W4383047164","https://openalex.org/W4384199957","https://openalex.org/W4389901936","https://openalex.org/W4398781580","https://openalex.org/W4403754990","https://openalex.org/W4417212658","https://openalex.org/W7167901997","https://openalex.org/W7203938138"],"related_works":["https://openalex.org/W4300980652","https://openalex.org/W3101501459","https://openalex.org/W4311552631","https://openalex.org/W6940912062","https://openalex.org/W6982572629","https://openalex.org/W4388127866","https://openalex.org/W4404884866","https://openalex.org/W7133238702","https://openalex.org/W4416395563","https://openalex.org/W4403754990"],"abstract_inverted_index":{"Optimal":[0],"transport":[1],"gives":[2],"structured":[3],"data":[4],"a":[5,34,68,119],"geometry,":[6],"but":[7,25],"exact":[8,90],"evaluation":[9],"is":[10],"costly":[11],"in":[12,67],"large":[13],"pairwise":[14],"analyses":[15],"that":[16,45,103,136],"exploit":[17],"relationships":[18],"among":[19],"distances.":[20],"Learned":[21],"surrogates":[22,144],"are":[23,98,104],"faster,":[24],"need":[26],"not":[27,105],"preserve":[28],"this":[29],"metric":[30],"structure.":[31],"We":[32],"develop":[33],"Deep":[35],"Sets":[36],"surrogate":[37],"for":[38,118],"OT":[39],"between":[40,64],"variable-size":[41],"weighted":[42],"point":[43],"clouds":[44],"enforces":[46],"non-negativity,":[47],"exchange":[48],"symmetry,":[49],"and":[50,91,125],"zero":[51],"self-distance,":[52],"leaving":[53],"the":[54,60,72,126],"triangle":[55],"inequality":[56],"unconstrained.":[57],"Applied":[58],"to":[59,100,123,130],"Energy":[61],"Mover's":[62],"Distance":[63],"collider":[65],"events":[66],"particle":[69],"physics":[70],"application,":[71],"Metric-Aware":[73],"Particle":[74],"Flow":[75],"Network":[76],"achieves":[77],"percent-level":[78],"mean":[79],"absolute":[80],"percentage":[81],"error":[82],"while":[83],"significantly":[84],"improving":[85],"inference":[86],"throughput":[87],"over":[88],"other":[89],"approximate":[92],"methods":[93],"surveyed.":[94],"The":[95],"architectural":[96],"constraints":[97],"found":[99],"improve":[101],"properties":[102],"explicitly":[106],"enforced:":[107],"across":[108],"$10^6$":[109],"held-out":[110],"event":[111],"triplets,":[112],"triangle-inequality":[113],"violations":[114],"fall":[115],"from":[116,128],"199":[117],"matched":[120],"unconstrained":[121],"network":[122],"2,":[124],"maximum":[127],"149.5":[129],"5.8":[131],"GeV.":[132],"These":[133],"results":[134],"demonstrate":[135],"targeted":[137],"inductive":[138],"biases":[139],"can":[140],"yield":[141],"fast":[142],"neural":[143],"with":[145],"substantially":[146],"improved":[147],"geometric":[148],"fidelity.":[149]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-15T00:00:00"}