{"id":"https://openalex.org/W7220688549","doi":"https://doi.org/10.48550/arxiv.2610.04264","title":"Adaptive Bregman Alternating Projections for Feasible Gromov-Wasserstein Learning","display_name":"Adaptive Bregman Alternating Projections for Feasible Gromov-Wasserstein Learning","publication_year":2026,"publication_date":"2026-10-03","ids":{"openalex":"https://openalex.org/W7220688549","doi":"https://doi.org/10.48550/arxiv.2610.04264"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.04264","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04264","pdf_url":"https://arxiv.org/pdf/2610.04264","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/2610.04264","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074303353","display_name":"Aoran Zhang","orcid":"https://orcid.org/0009-0000-4439-1320","observed_orcids":["https://orcid.org/0009-0000-4439-1320","https://orcid.org/0009-0008-2753-8472","https://orcid.org/0000-0002-5002-0347"]},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhang, Aoran","raw_affiliation_strings":["Department of Electrical and Computer Engineering , Rice University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering , Rice University","institution_ids":["https://openalex.org/I74775410"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047076392","display_name":"C\u00e9sar A. Uribe","orcid":"https://orcid.org/0000-0002-7080-9724","observed_orcids":["https://orcid.org/0000-0002-7080-9724"]},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Uribe, C\u00e9sar A.","raw_affiliation_strings":["Department of Electrical and Computer Engineering , Rice University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering , Rice University","institution_ids":["https://openalex.org/I74775410"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I74775410"],"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.7768999934196472,"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":0.7768999934196472,"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":0.053300000727176666,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.026000000536441803,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/adaptive-penalty","display_name":"adaptive penalty","score":0.47099998593330383},{"id":"https://openalex.org/keywords/kullback-leibler-divergence","display_name":"Kullback-Leibler divergence","score":0.6840000152587891},{"id":"https://openalex.org/keywords/backtracking","display_name":"backtracking","score":0.5049999952316284},{"id":"https://openalex.org/keywords/stationarity","display_name":"stationarity","score":0.4950000047683716},{"id":"https://openalex.org/keywords/convergence-analysis","display_name":"convergence analysis","score":0.6060000061988831},{"id":"https://openalex.org/keywords/graph-alignment","display_name":"graph alignment","score":0.8700000047683716},{"id":"https://openalex.org/keywords/domain-adaptation","display_name":"domain adaptation","score":0.8069999814033508},{"id":"https://openalex.org/keywords/nonconvex-optimization","display_name":"non-convex optimization","score":0.6990000009536743}],"concepts":[{"id":"https://openalex.org/C156884757","wikidata":"https://www.wikidata.org/wiki/Q798554","display_name":"Backtracking","level":2,"score":0.6110000014305115},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6107000112533569},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5907999873161316},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5751000046730042},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.46959999203681946},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46939998865127563},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46389999985694885},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4496999979019165},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3889999985694885},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.385699987411499},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.38440001010894775},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3804999887943268},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3337000012397766},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3328000009059906},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3260999917984009},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3197999894618988},{"id":"https://openalex.org/C109839438","wikidata":"https://www.wikidata.org/wiki/Q1762039","display_name":"Cutting-plane method","level":3,"score":0.2957000136375427},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.2939999997615814},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2912999987602234},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.2881999909877777},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.28700000047683716},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.2770000100135803},{"id":"https://openalex.org/C22367795","wikidata":"https://www.wikidata.org/wiki/Q7625208","display_name":"Structured prediction","level":2,"score":0.27619999647140503},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.2644999921321869},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.26249998807907104},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.25450000166893005},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.251800000667572}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.04264","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04264","pdf_url":"https://arxiv.org/pdf/2610.04264","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.2610.04264","doi":"https://doi.org/10.48550/arxiv.2610.04264","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.04264","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:2610.04264","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04264","pdf_url":"https://arxiv.org/pdf/2610.04264","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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220688549.pdf","grobid_xml":"https://content.openalex.org/works/W7220688549.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4324321290","https://openalex.org/W4280603580","https://openalex.org/W7160504642","https://openalex.org/W4379251962","https://openalex.org/W7128397538","https://openalex.org/W7215133739","https://openalex.org/W7133232288","https://openalex.org/W2890430524","https://openalex.org/W4280619635","https://openalex.org/W4384918436"],"abstract_inverted_index":{"The":[0],"Gromov-Wasserstein":[1],"(GW)":[2],"problem":[3],"compares":[4],"structured":[5],"distributions":[6],"without":[7],"requiring":[8],"a":[9,44,55,60,76,80,107,120,127,156,213],"shared":[10],"feature":[11],"space":[12],"or":[13],"known":[14],"correspondences,":[15],"but":[16],"its":[17,40],"nonconvex":[18],"objective":[19,161,188,222],"and":[20,36,74,96,164,172,177,187,201,221,228],"coupled":[21],"marginal":[22,196],"constraints":[23],"make":[24],"computation":[25],"challenging.":[26],"Bregman":[27],"alternating":[28,34,72],"projected":[29,203],"gradient":[30],"(BAPG)":[31],"uses":[32],"inexpensive":[33],"row":[35],"column":[37],"updates,":[38],"yet":[39],"fixed-penalty":[41,57,140,191,231],"relaxation":[42],"leaves":[43],"persistent":[45],"feasibility":[46,100,197,227],"gap.":[47],"We":[48,86,104],"propose":[49],"Adaptive":[50],"KL-BAPG":[51,192],"(A-KL-BAPG),":[52],"which":[53],"combines":[54],"finite":[56,88],"burn-in":[58],"with":[59],"guarded":[61],"increasing-penalty":[62],"phase.":[63],"At":[64],"each":[65,94],"tail":[66],"iteration,":[67],"the":[68,91,99,113,124,132,148,185,195,202],"method":[69],"reuses":[70],"BAPG's":[71],"updates":[73],"backtracks":[75],"delayed-power":[77],"step":[78],"until":[79],"Sinkhorn-inspired":[81],"projective-diameter":[82],"safeguard":[83],"is":[84],"satisfied.":[85],"prove":[87],"termination":[89],"of":[90,126,159,190],"backtracking":[92],"at":[93],"iteration":[95],"show":[97,152,212],"that":[98,153],"gap":[101,198],"vanishes":[102],"asymptotically.":[103],"further":[105],"establish":[106],"best-iterate":[108],"$O(1/\\log":[109],"N)$":[110],"bound":[111],"for":[112,131,147],"weighted":[114],"squared":[115],"corrected":[116],"residual":[117,205],"and,":[118],"under":[119],"support":[121],"regularity":[122],"condition,":[123],"existence":[125],"stationary":[128],"accumulation":[129],"point":[130],"original":[133],"GW":[134],"problem.":[135,150],"This":[136],"distinguishes":[137],"A-KL-BAPG":[138,154,216],"from":[139],"BAPG,":[141],"whose":[142],"stationarity":[143,165,204,229],"guarantees":[144],"are":[145],"given":[146],"relaxed":[149],"Experiments":[151],"achieves":[155],"favorable":[157],"balance":[158],"accuracy,":[160],"value,":[162],"feasibility,":[163],"relative":[166],"to":[167],"BAPG":[168],"variants,":[169],"projection-based":[170],"methods,":[171],"task-specific":[173],"baselines.":[174],"For":[175],"synthetic":[176],"real":[178],"graph":[179],"alignment":[180],"problems,":[181],"it":[182],"closely":[183],"matches":[184],"accuracy":[186,220],"value":[189],"while":[193,224],"reducing":[194],"by":[199,206],"62-99%":[200],"28-98%.":[207],"Heterogeneous":[208],"domain":[209],"adaptation":[210],"experiments":[211],"similar":[214],"pattern:":[215],"maintains":[217],"comparable":[218],"target":[219],"values":[223],"achieving":[225],"better":[226],"than":[230],"KL-BAPG.":[232]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-07T00:00:00"}