{"id":"https://openalex.org/W7165946310","doi":"https://doi.org/10.48550/arxiv.2606.25194","title":"Hodge Spectral Surrogates for Topology-Constrained Optimization","display_name":"Hodge Spectral Surrogates for Topology-Constrained Optimization","publication_year":2026,"publication_date":"2026-06-23","ids":{"openalex":"https://openalex.org/W7165946310","doi":"https://doi.org/10.48550/arxiv.2606.25194"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.25194","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.25194","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,"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.2606.25194","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5139328221","display_name":"Satoshi Kanno","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kanno, Satoshi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5139329868","display_name":"Yoshi-aki Shimada","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shimada, Yoshi-aki","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9980000257492065,"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":0.9980000257492065,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.00039999998989515007,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.0003000000142492354,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.6610999703407288},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.6211000084877014},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5947999954223633},{"id":"https://openalex.org/keywords/quantum-graph","display_name":"Quantum graph","score":0.5371999740600586},{"id":"https://openalex.org/keywords/betti-number","display_name":"Betti number","score":0.5354999899864197},{"id":"https://openalex.org/keywords/spectral-graph-theory","display_name":"Spectral graph theory","score":0.5162000060081482},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4323999881744385},{"id":"https://openalex.org/keywords/clique-problem","display_name":"Clique problem","score":0.4244999885559082},{"id":"https://openalex.org/keywords/heat-kernel","display_name":"Heat kernel","score":0.39579999446868896}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7936000227928162},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.6610999703407288},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.6211000084877014},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5947999954223633},{"id":"https://openalex.org/C164886730","wikidata":"https://www.wikidata.org/wiki/Q7269054","display_name":"Quantum graph","level":3,"score":0.5371999740600586},{"id":"https://openalex.org/C129621563","wikidata":"https://www.wikidata.org/wiki/Q429593","display_name":"Betti number","level":2,"score":0.5354999899864197},{"id":"https://openalex.org/C74003402","wikidata":"https://www.wikidata.org/wiki/Q3180727","display_name":"Spectral graph theory","level":5,"score":0.5162000060081482},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4323999881744385},{"id":"https://openalex.org/C150997102","wikidata":"https://www.wikidata.org/wiki/Q1196873","display_name":"Clique problem","level":5,"score":0.4244999885559082},{"id":"https://openalex.org/C183212220","wikidata":"https://www.wikidata.org/wiki/Q3345669","display_name":"Heat kernel","level":2,"score":0.39579999446868896},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3905999958515167},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3652999997138977},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.36480000615119934},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3546999990940094},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.3375999927520752},{"id":"https://openalex.org/C2874115","wikidata":"https://www.wikidata.org/wiki/Q17099562","display_name":"Persistent homology","level":2,"score":0.328000009059906},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.3269999921321869},{"id":"https://openalex.org/C196267783","wikidata":"https://www.wikidata.org/wiki/Q4392490","display_name":"Resolvent","level":2,"score":0.32429999113082886},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.31279999017715454},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.30230000615119934},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.2831999957561493},{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.2662999927997589},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.2653999924659729},{"id":"https://openalex.org/C174265945","wikidata":"https://www.wikidata.org/wiki/Q1142889","display_name":"Isolated point","level":4,"score":0.2639999985694885},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2630999982357025},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.2619999945163727},{"id":"https://openalex.org/C140936041","wikidata":"https://www.wikidata.org/wiki/Q1801244","display_name":"Zero-dimensional space","level":4,"score":0.25209999084472656}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.25194","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.25194","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,"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.2606.25194","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.25194","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,"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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Topology-constrained":[0],"optimization":[1,91],"arises":[2],"in":[3,62,93,156,169],"applications":[4],"such":[5],"as":[6,90],"medical":[7],"image":[8],"segmentation,":[9],"geometric":[10],"design,":[11],"and":[12,23,28,101,111,123,130,152,174],"network":[13],"generation,":[14],"where":[15],"global":[16],"structural":[17],"correctness":[18],"matters.":[19],"Yet":[20],"Betti":[21,117,172],"numbers":[22,118],"persistent":[24],"homology":[25],"are":[26,60,87,106],"discrete":[27,46],"combinatorial,":[29],"making":[30],"them":[31],"difficult":[32],"to":[33,119,187],"control":[34],"directly":[35],"by":[36,72],"gradient-based":[37],"optimization.":[38,190],"We":[39,108],"propose":[40],"a":[41,50,63,76,183],"differentiable":[42,125],"framework":[43,181],"that":[44],"replaces":[45],"topological":[47],"counting":[48],"with":[49,176],"soft":[51,85,120],"spectral":[52,78,112],"relaxation":[53],"of":[54],"the":[55,94,97,157],"Hodge":[56,99],"Laplacian.":[57],"Candidate":[58],"simplices":[59],"embedded":[61],"fixed":[64],"ambient":[65],"complex,":[66],"while":[67],"simplex":[68],"inclusion":[69],"is":[70],"represented":[71],"continuous":[73],"activations,":[74],"producing":[75],"smooth":[77],"path":[79],"between":[80],"different":[81],"hard":[82,95,116,171],"complexes.":[83],"The":[84,180],"states":[86],"used":[88],"only":[89],"surrogates;":[92],"limit,":[96],"ordinary":[98],"Laplacian":[100],"its":[102],"homological":[103],"zero":[104],"modes":[105],"recovered.":[107],"establish":[109],"operator-norm":[110],"perturbation":[113],"bounds":[114],"connecting":[115],"near-zero":[121],"modes,":[122],"derive":[124],"objectives":[126],"using":[127],"heat,":[128],"resolvent,":[129],"polynomial":[131],"low-pass":[132],"filters.":[133],"Controlled":[134],"experiments":[135],"on":[136,161],"Vietoris--Rips":[137],"point":[138],"clouds":[139],"show":[140,166],"more":[141],"spatially":[142],"distributed":[143],"gradients,":[144],"reduced":[145],"scale-normalized":[146],"derivative":[147],"variation":[148],"near":[149],"persistence-pairing":[150],"changes,":[151],"geometry-aware":[153],"update":[154],"directions":[155],"tested":[158],"settings.":[159],"Experiments":[160],"graph":[162,178],"clique":[163],"complexes":[164],"further":[165],"controllable":[167],"shifts":[168],"sampled":[170],"regimes":[173],"compatibility":[175],"standard":[177],"objectives.":[179],"provides":[182],"complementary":[184],"Hodge-spectral":[185],"approach":[186],"persistent-homology-based":[188],"topology":[189]},"counts_by_year":[],"updated_date":"2026-08-27T14:10:00.468798","created_date":"2026-06-26T00:00:00"}