{"id":"https://openalex.org/W7160514264","doi":"https://doi.org/10.48550/arxiv.2605.05024","title":"Hypergraph Generation via Structured Stochastic Diffusion","display_name":"Hypergraph Generation via Structured Stochastic Diffusion","publication_year":2026,"publication_date":"2026-05-06","ids":{"openalex":"https://openalex.org/W7160514264","doi":"https://doi.org/10.48550/arxiv.2605.05024"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.05024","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.05024","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.05024","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079845478","display_name":"Christopher Nemeth","orcid":"https://orcid.org/0000-0002-9084-3866"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nemeth, Christopher","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5079845478"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.39320001006126404,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.39320001006126404,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.29269999265670776,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T12303","display_name":"Tensor decomposition and applications","score":0.13189999759197235,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.8420000076293945},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.621999979019165},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5544999837875366},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4943000078201294},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4251999855041504},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.4237000048160553},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.39640000462532043},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.37380000948905945},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.3621000051498413}],"concepts":[{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.8420000076293945},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.621999979019165},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.593500018119812},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5544999837875366},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4943000078201294},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43970000743865967},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4251999855041504},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.4237000048160553},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.39640000462532043},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.37380000948905945},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3621000051498413},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.35910001397132874},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.33899998664855957},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33629998564720154},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.32100000977516174},{"id":"https://openalex.org/C79772020","wikidata":"https://www.wikidata.org/wiki/Q5159264","display_name":"Conditional independence","level":2,"score":0.3183000087738037},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.3140999972820282},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.30959999561309814},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.3019999861717224},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.29910001158714294},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29420000314712524},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.2924000024795532},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2922999858856201},{"id":"https://openalex.org/C85136909","wikidata":"https://www.wikidata.org/wiki/Q939272","display_name":"Incidence matrix","level":3,"score":0.28439998626708984},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2831000089645386},{"id":"https://openalex.org/C176809094","wikidata":"https://www.wikidata.org/wiki/Q15401496","display_name":"Traverse","level":2,"score":0.27300000190734863},{"id":"https://openalex.org/C2779530757","wikidata":"https://www.wikidata.org/wiki/Q1207505","display_name":"Quality (philosophy)","level":2,"score":0.26100000739097595},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.25679999589920044},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.2533000111579895}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.05024","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.05024","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.05024","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.05024","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"},"sustainable_development_goals":[{"score":0.7797783017158508,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Hypergraphs":[0],"model":[1,29],"higher-order":[2],"interactions,":[3],"but":[4],"realistic":[5],"hypergraph":[6,138],"generation":[7,139],"remains":[8],"difficult":[9],"because":[10],"incidence,":[11],"hyperedge-size":[12],"heterogeneity,":[13],"and":[14,82,107,134],"overlap":[15],"structure":[16],"are":[17,85],"not":[18],"faithfully":[19],"captured":[20],"by":[21,101,110],"pairwise":[22],"reductions.":[23],"We":[24,90,121],"propose":[25],"\\HEDGE,":[26],"a":[27,37,45,93,112],"generative":[28],"defined":[30],"directly":[31],"on":[32,68],"relaxed":[33],"incidence":[34,99],"matrices":[35],"via":[36],"structured":[38],"stochastic":[39],"diffusion.":[40],"The":[41],"forward":[42,73],"process":[43,74],"combines":[44],"hypergraph-specific":[46],"two-sided":[47],"heat":[48],"operator":[49],"with":[50,130],"an":[51,62,69],"Ornstein--Uhlenbeck":[52],"component,":[53],"preserving":[54],"structure-aware":[55],"noising":[56],"near":[57],"the":[58,117,125],"data":[59],"while":[60],"yielding":[61],"explicit":[63],"Gaussian":[64,118],"terminal":[65],"law.":[66,120],"Conditional":[67],"observed":[70],"hypergraph,":[71],"this":[72],"is":[75],"linear-Gaussian,":[76],"so":[77],"conditional":[78,105],"means,":[79],"covariances,":[80],"scores,":[81],"reverse-drift":[83,96],"targets":[84],"available":[86],"in":[87,98,124],"closed":[88],"form.":[89],"therefore":[91],"learn":[92],"permutation-equivariant":[94],"state-only":[95,127],"field":[97],"space":[100],"regressing":[102],"onto":[103],"exact":[104],"targets,":[106],"generate":[108],"samples":[109],"simulating":[111],"learned":[113],"reverse-time":[114],"SDE":[115],"from":[116],"base":[119],"establish":[122],"exactness":[123],"ideal":[126],"setting":[128],"together":[129],"finite-horizon":[131],"stability":[132],"guarantees,":[133],"empirically":[135],"show":[136],"improved":[137],"quality":[140],"relative":[141],"to":[142],"strong":[143],"baselines.":[144]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-08T00:00:00"}
