{"id":"https://openalex.org/W7140136431","doi":"https://doi.org/10.48550/arxiv.2603.19670","title":"Radial Load--Reserve Certificates for Wasserstein Propagation in Isotropic Diffusion Samplers","display_name":"Radial Load--Reserve Certificates for Wasserstein Propagation in Isotropic Diffusion Samplers","publication_year":2026,"publication_date":"2026-03-20","ids":{"openalex":"https://openalex.org/W7140136431","doi":"https://doi.org/10.48550/arxiv.2603.19670"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.19670","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.19670","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.19670","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051302583","display_name":"Zicheng Lyu","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lyu, Zicheng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5130364698","display_name":"Zengfeng Huang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huang, Zengfeng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5051302583"],"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.19089999794960022,"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"}},"topics":[{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.19089999794960022,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.18330000340938568,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.0949999988079071,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/wasserstein-metric","display_name":"Wasserstein metric","score":0.7106999754905701},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.6577000021934509},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.6470000147819519},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.5461000204086304},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4779999852180481},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.46480000019073486},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4417000114917755},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.42080000042915344}],"concepts":[{"id":"https://openalex.org/C2777634741","wikidata":"https://www.wikidata.org/wiki/Q768993","display_name":"Wasserstein metric","level":2,"score":0.7106999754905701},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6596999764442444},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.6577000021934509},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6470000147819519},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.5461000204086304},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5432000160217285},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.5372999906539917},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4779999852180481},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.46480000019073486},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4417000114917755},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.42080000042915344},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.40049999952316284},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.38370001316070557},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.38339999318122864},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.35040000081062317},{"id":"https://openalex.org/C141898687","wikidata":"https://www.wikidata.org/wiki/Q1501997","display_name":"Hausdorff distance","level":2,"score":0.3400999903678894},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.31850001215934753},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.28040000796318054},{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.2556999921798706},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2542000114917755}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.19670","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.19670","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.19670","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.19670","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Nonasymptotic":[0],"diffusion":[1],"analyses":[2],"often":[3],"decompose":[4],"sampling":[5],"error":[6,82,93],"into":[7,169,184],"score":[8],"estimation,":[9],"continuous":[10],"reverse-time":[11],"propagation,":[12,176],"discretization,":[13],"and":[14,64,78,84,95,138,151,188,215,231],"terminal":[15,29],"conversion.":[16],"We":[17,197],"isolate":[18],"a":[19,59,68,104,120],"conditional":[20],"propagation":[21],"module":[22],"on":[23],"certified":[24,181],"scalar-isotropic":[25],"reverse-SDE":[26],"windows,":[27],"with":[28,146,205],"quadratic-Wasserstein":[30],"reporting":[31],"as":[32,86],"the":[33,48,54,97,139,166,211],"goal.":[34],"The":[35,101,171],"propagated":[36],"object":[37],"is":[38,103],"not":[39,209],"$W_2^2$,":[40],"but":[41],"an":[42,106,134],"affine-tail":[43,136,167],"transportation":[44],"cost":[45,109,145],"adapted":[46,144],"to":[47,67,113,164],"learned":[49,55,225],"drift.":[50],"Reflection":[51],"coupling":[52],"exposes":[53],"reverse":[56],"drift":[57],"through":[58],"worst-case":[60],"pairwise":[61],"radial":[62,89,116,212],"profile":[63],"reduces":[65],"stability":[66,99],"one-dimensional":[69],"comparison.":[70],"This":[71],"reduction":[72],"separates":[73],"consistency":[74],"from":[75],"stability.":[76],"Score-modeling":[77],"solver":[79],"residuals":[80],"quantify":[81],"injection":[83],"enter":[85],"additive":[87],"forcing;":[88],"load--reserve":[90],"geometry":[91],"quantifies":[92],"amplification":[94],"supplies":[96],"adapted-Wasserstein":[98],"certificate.":[100],"obstruction":[102],"barrier:":[105],"increasing":[107],"concave":[108],"must":[110],"spend":[111],"slope":[112],"cross":[114],"adverse":[115,202],"load":[117,130],"before":[118,131],"exploiting":[119],"contractive":[121],"tail":[122],"reserve.":[123],"Hardy":[124,213],"capacity":[125],"measures":[126],"this":[127,143,217],"bottleneck,":[128],"finite":[129,185],"reserve":[132],"yields":[133],"explicit":[135],"cost,":[137],"main":[140],"theorem":[141],"propagates":[142],"separate":[147],"score,":[148],"solver,":[149],"geometry,":[150],"terminal-reporting":[152],"inputs.":[153],"Terminal":[154],"tails,":[155],"moments,":[156],"or":[157],"bounded":[158],"support":[159],"are":[160],"used":[161],"only":[162],"afterward":[163],"convert":[165],"bound":[168],"$W_2^2$.":[170],"framework":[172],"recovers":[173],"uniformly":[174],"dissipative":[175],"transfers":[177],"bounded-amplitude":[178],"perturbations":[179],"of":[180],"reference":[182],"drifts":[183],"inverse-radius":[186],"load,":[187],"gives":[189],"analytic":[190],"certificates":[191],"for":[192],"common-covariance":[193],"Gaussian-mixture":[194],"smoothing":[195],"windows.":[196],"also":[198],"prove":[199],"that":[200],"one-sided":[201],"height,":[203],"even":[204],"eventual":[206],"reserve,":[207],"does":[208],"determine":[210],"scale,":[214],"realize":[216],"separation":[218],"by":[219],"smooth":[220],"exact-score":[221],"drifts.":[222],"For":[223],"fixed":[224],"drifts,":[226],"we":[227],"provide":[228],"conservative":[229],"deterministic":[230],"PAC":[232],"compact":[233],"post-hoc":[234],"certification":[235],"templates.":[236]},"counts_by_year":[],"updated_date":"2026-05-02T06:04:40.494371","created_date":"2026-03-24T00:00:00"}
