{"id":"https://openalex.org/W7160875855","doi":"https://doi.org/10.48550/arxiv.2605.07270","title":"bispectrum: Selective G-Bispectra Made Practical","display_name":"bispectrum: Selective G-Bispectra Made Practical","publication_year":2026,"publication_date":"2026-05-08","ids":{"openalex":"https://openalex.org/W7160875855","doi":"https://doi.org/10.48550/arxiv.2605.07270"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2605.07270","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.07270","pdf_url":"https://arxiv.org/pdf/2605.07270","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":"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/2605.07270","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036489530","display_name":"Johan Mathe","orcid":"https://orcid.org/0009-0000-8096-574X","observed_orcids":["https://orcid.org/0009-0000-8096-574X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mathe, Johan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045842784","display_name":"Adele Myers","orcid":"https://orcid.org/0000-0001-6887-1820","observed_orcids":["https://orcid.org/0000-0001-6887-1820"]},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Myers, Adele","raw_affiliation_strings":["UC Santa Barbara Santa Barbara , CA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UC Santa Barbara Santa Barbara , CA","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5094077329","display_name":"Simon Mataigne","orcid":"https://orcid.org/0009-0004-1970-8102","observed_orcids":["https://orcid.org/0009-0004-1970-8102"]},"institutions":[{"id":"https://openalex.org/I95674353","display_name":"UCLouvain","ror":"https://ror.org/02495e989","country_code":"BE","type":"education","lineage":["https://openalex.org/I95674353"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Mataigne, Simon","raw_affiliation_strings":["UCLouvain Louvain-la-Neuve , Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UCLouvain Louvain-la-Neuve , Belgium","institution_ids":["https://openalex.org/I95674353"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083733004","display_name":"Nina Miolane","orcid":"https://orcid.org/0000-0002-1200-9024","observed_orcids":["https://orcid.org/0000-0002-1200-9024"]},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Miolane, Nina","raw_affiliation_strings":["UC Santa Barbara Santa Barbara , CA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UC Santa Barbara Santa Barbara , CA","institution_ids":["https://openalex.org/I154570441"]}]}],"institutions":[],"countries_distinct_count":2,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.31150001287460327,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.31150001287460327,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.21570000052452087,"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/T10036","display_name":"Advanced Neural Network Applications","score":0.07779999822378159,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/group-invariance","display_name":"group invariance","score":0.8939999938011169},{"id":"https://openalex.org/keywords/pooling-layers","display_name":"pooling layers","score":0.6420000195503235},{"id":"https://openalex.org/keywords/pytorch","display_name":"PyTorch","score":0.828000009059906},{"id":"https://openalex.org/keywords/computational-cost-reduction","display_name":"computational complexity reduction","score":0.5189999938011169},{"id":"https://openalex.org/keywords/image-classification","display_name":"image classification","score":0.3869999945163727}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7045999765396118},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6722000241279602},{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.6370000243186951},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.6266999840736389},{"id":"https://openalex.org/C70437156","wikidata":"https://www.wikidata.org/wiki/Q7228652","display_name":"Pooling","level":2,"score":0.5946999788284302},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5206000208854675},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.4846000075340271},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4779999852180481},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.45730000734329224},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.3781000077724457},{"id":"https://openalex.org/C75294576","wikidata":"https://www.wikidata.org/wiki/Q5165192","display_name":"Contextual image classification","level":3,"score":0.35760000348091125},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.34880000352859497},{"id":"https://openalex.org/C43521106","wikidata":"https://www.wikidata.org/wiki/Q2165493","display_name":"Pipeline (software)","level":2,"score":0.34529998898506165},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.33180001378059387},{"id":"https://openalex.org/C34413123","wikidata":"https://www.wikidata.org/wiki/Q170978","display_name":"Robotics","level":3,"score":0.3158000111579895},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.3091000020503998},{"id":"https://openalex.org/C113775141","wikidata":"https://www.wikidata.org/wiki/Q428691","display_name":"Computer engineering","level":1,"score":0.3061000108718872},{"id":"https://openalex.org/C63000827","wikidata":"https://www.wikidata.org/wiki/Q3080428","display_name":"Software portability","level":2,"score":0.29510000348091125},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.2930000126361847},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.2865000069141388},{"id":"https://openalex.org/C79581498","wikidata":"https://www.wikidata.org/wiki/Q1367530","display_name":"Suite","level":2,"score":0.28519999980926514},{"id":"https://openalex.org/C65909025","wikidata":"https://www.wikidata.org/wiki/Q1945033","display_name":"Monocular","level":2,"score":0.28360000252723694},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.2671999931335449},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26669999957084656},{"id":"https://openalex.org/C175309249","wikidata":"https://www.wikidata.org/wiki/Q725864","display_name":"Pipeline transport","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2605.07270","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.07270","pdf_url":"https://arxiv.org/pdf/2605.07270","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2605.07270","doi":"https://doi.org/10.48550/arxiv.2605.07270","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.07270","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:2605.07270","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.07270","pdf_url":"https://arxiv.org/pdf/2605.07270","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":"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/W7160875855.pdf","grobid_xml":"https://content.openalex.org/works/W7160875855.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1635256758","https://openalex.org/W1970595491","https://openalex.org/W1994906459","https://openalex.org/W2093835340","https://openalex.org/W2772723798","https://openalex.org/W4286588524","https://openalex.org/W4387211733","https://openalex.org/W4401925479","https://openalex.org/W4402012187","https://openalex.org/W4403281596","https://openalex.org/W4413371874","https://openalex.org/W4417097988","https://openalex.org/W6967298549","https://openalex.org/W7133185931","https://openalex.org/W7133205831"],"related_works":["https://openalex.org/W4415795812","https://openalex.org/W4295106997","https://openalex.org/W1970595491","https://openalex.org/W1635256758","https://openalex.org/W4417097988","https://openalex.org/W1994401216","https://openalex.org/W3168407340","https://openalex.org/W4414788692","https://openalex.org/W2083978879","https://openalex.org/W4387500824"],"abstract_inverted_index":{"Many":[0],"machine":[1],"learning":[2],"tasks":[3],"are":[4],"invariant":[5,18,107,199],"under":[6],"transformations":[7],"such":[8],"as":[9,124],"translations":[10],"and":[11,33,85,112,129,146,180,203],"rotations.":[12],"The":[13,104],"$G$-bispectrum":[14],"is":[15,31,106],"a":[16,21,25,38,173,187],"complete":[17],"that":[19],"determines":[20],"signal":[22],"up":[23,108],"to":[24,67,74,88,109],"group":[26,57],"action,":[27],"but":[28],"its":[29],"computation":[30],"costly":[32],"existing":[34],"implementations":[35],"each":[36],"cover":[37],"single":[39],"group.":[40],"We":[41,121],"present":[42],"bispectrum,":[43],"an":[44,163],"open-source,":[45],"fully":[46],"unit-tested":[47],"PyTorch":[48],"library":[49,105],"providing":[50],"efficient,":[51],"differentiable":[52],"selective":[53,97,114],"$G$-bispectra":[54,115,195],"for":[55,69,76,90,201],"seven":[56],"actions.":[58],"Selectivity":[59],"reduces":[60],"the":[61,80],"number":[62],"of":[63,186],"coefficients":[64],"from":[65,72,86],"$O(|G|^2)$":[66],"$O(|G|)$":[68],"finite":[70,202],"groups,":[71],"$O(m^{5/2})$":[73],"$O(m)$":[75],"planar":[77],"rotations":[78,93],"on":[79,119,127,144,148,155,168],"disk":[81],"with":[82,162],"$m$":[83],"harmonics,":[84],"$\u0398(L^3)$":[87],"$\u0398(L^2)$":[89],"spherical":[91,98,174],"3D":[92],"using":[94],"our":[95,160],"augmented":[96],"bispectrum":[99],"at":[100,176,190],"band":[101],"limit":[102],"$L$.":[103],"floating-point":[110],"error":[111],"computes":[113],"in":[116],"sub-millisecond":[117],"time":[118],"GPU.":[120],"evaluate":[122],"them":[123],"pooling":[125,138,150],"layers":[126,200],"PatchCamelyon":[128],"OrganMNIST3D":[130],"against":[131],"five":[132],"baselines.":[133],"Across":[134],"46":[135],"comparisons,":[136],"bispectral":[137],"remains":[139],"competitive,":[140],"matching":[141,172],"all":[142],"baselines":[143],"PCam":[145],"improving":[147],"max":[149],"by":[151],"5.0":[152],"percentage":[153,184],"points":[154,185],"OrganMNIST3D.":[156],"On":[157],"Spherical":[158],"MNIST,":[159],"method":[161],"MLP":[164],"head":[165],"reaches":[166],"95.8%":[167],"rotated":[169],"test":[170],"digits,":[171],"CNN":[175],"$4\\times$":[177],"lower":[178,192],"latency":[179],"coming":[181],"within":[182],"0.3":[183],"tensor-product":[188],"network":[189],"$364\\times$":[191],"latency.":[193],"Selective":[194],"provide":[196],"fast,":[197],"competitive":[198],"continuous":[204],"groups.":[205]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-05-12T00:00:00"}
