{"id":"https://openalex.org/W7221810185","doi":"https://doi.org/10.48550/arxiv.2610.17269","title":"Measuring Learned Equivariance: An Information Theoretic Approach","display_name":"Measuring Learned Equivariance: An Information Theoretic Approach","publication_year":2026,"publication_date":"2026-10-12","ids":{"openalex":"https://openalex.org/W7221810185","doi":"https://doi.org/10.48550/arxiv.2610.17269"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.17269","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.17269","pdf_url":"https://arxiv.org/pdf/2610.17269","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","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/2610.17269","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102783760","display_name":"Claire Schlesinger","orcid":"https://orcid.org/0009-0000-2533-1242","observed_orcids":["https://orcid.org/0009-0000-2533-1242"]},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Schlesinger, Claire","raw_affiliation_strings":["College of Computer Sciences Northeastern University Boston , MA 02115 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer Sciences Northeastern University Boston , MA 02115 , USA","institution_ids":["https://openalex.org/I12912129"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086781628","display_name":"Wolfgang Gatterbauer","orcid":"https://orcid.org/0000-0002-9614-0504","observed_orcids":["https://orcid.org/0000-0002-9614-0504"]},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gatterbauer, Wolfgang","raw_affiliation_strings":["College of Computer Sciences Northeastern University Boston , MA 02115 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer Sciences Northeastern University Boston , MA 02115 , USA","institution_ids":["https://openalex.org/I12912129"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020217201","display_name":"Robin Walters","orcid":"https://orcid.org/0000-0001-7751-2379","observed_orcids":["https://orcid.org/0000-0001-7751-2379"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Walters, Robin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.30320000648498535,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.30320000648498535,"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/T10320","display_name":"Neural Networks and Applications","score":0.20029999315738678,"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/T10036","display_name":"Advanced Neural Network Applications","score":0.09969999641180038,"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/data-augmentation","display_name":"data augmentation","score":0.9229999780654907},{"id":"https://openalex.org/keywords/normalized-mutual-information","display_name":"normalized mutual information","score":0.8629999756813049},{"id":"https://openalex.org/keywords/centered-kernel-alignment","display_name":"centered kernel alignment","score":0.9509999752044678},{"id":"https://openalex.org/keywords/intermediate-representation","display_name":"intermediate representation","score":0.6069999933242798},{"id":"https://openalex.org/keywords/group-actions","display_name":"group actions","score":0.5809999704360962},{"id":"https://openalex.org/keywords/feature-transformation","display_name":"feature transformation","score":0.4869999885559082}],"concepts":[{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.6514000296592712},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6018999814987183},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.5449000000953674},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.536300003528595},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5241000056266785},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49480000138282776},{"id":"https://openalex.org/C152139883","wikidata":"https://www.wikidata.org/wiki/Q252973","display_name":"Mutual information","level":2,"score":0.4844000041484833},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4722999930381775},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4641999900341034},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4341000020503998},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4212000072002411},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40849998593330383},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.38440001010894775},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.37560001015663147},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.3716999888420105},{"id":"https://openalex.org/C2993626508","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Transformation group","level":2,"score":0.3287999927997589},{"id":"https://openalex.org/C54940322","wikidata":"https://www.wikidata.org/wiki/Q3997740","display_name":"Orthogonal transformation","level":2,"score":0.31139999628067017},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.30379998683929443},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.29829999804496765},{"id":"https://openalex.org/C59404180","wikidata":"https://www.wikidata.org/wiki/Q17013334","display_name":"Feature learning","level":2,"score":0.296999990940094},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.2948000133037567},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.26820001006126404},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.2515999972820282},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.25099998712539673}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.17269","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.17269","pdf_url":"https://arxiv.org/pdf/2610.17269","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.17269","doi":"https://doi.org/10.48550/arxiv.2610.17269","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.17269","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:2610.17269","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.17269","pdf_url":"https://arxiv.org/pdf/2610.17269","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","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/W7221810185.pdf","grobid_xml":"https://content.openalex.org/works/W7221810185.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1995875735","https://openalex.org/W4296580612","https://openalex.org/W4307786362","https://openalex.org/W4365515032","https://openalex.org/W4385805044","https://openalex.org/W4404565424","https://openalex.org/W7128058155"],"related_works":["https://openalex.org/W4385805044","https://openalex.org/W6992305744","https://openalex.org/W4403883858","https://openalex.org/W4414812724","https://openalex.org/W3093554712","https://openalex.org/W4413823739","https://openalex.org/W3122369936","https://openalex.org/W7116984659","https://openalex.org/W2751412330","https://openalex.org/W3156686014"],"abstract_inverted_index":{"Learning":[0],"symmetries":[1],"through":[2],"data":[3],"augmentation":[4,91],"offers":[5],"an":[6,80],"alternative":[7],"to":[8,52],"architectural":[9],"equivariance,":[10],"but":[11],"does":[12],"not":[13,34],"guarantee":[14,82],"that":[15,43,97,112],"a":[16,37,58,76],"network":[17],"respects":[18],"those":[19],"symmetries.":[20],"Measuring":[21],"learned":[22,98],"equivariance":[23,44,99],"is":[24],"especially":[25],"difficult":[26],"for":[27,83],"intermediate":[28],"representations,":[29],"whose":[30],"group":[31],"actions":[32],"are":[33],"specified.":[35],"In":[36],"finite":[38],"discrete":[39],"setting,":[40],"we":[41,69],"show":[42],"requires":[45],"representations":[46,105],"of":[47],"original":[48],"and":[49,89],"transformed":[50],"inputs":[51],"determine":[53],"one":[54],"another":[55],"exactly,":[56],"yielding":[57],"test":[59],"based":[60],"on":[61],"normalized":[62],"mutual":[63],"information":[64],"(NMI).":[65],"For":[66],"high-dimensional":[67],"activations,":[68],"use":[70],"centered":[71],"kernel":[72],"alignment":[73],"(CKA)":[74],"as":[75],"scalable":[77],"test,":[78],"with":[79],"exact":[81],"orthogonal":[84],"feature":[85],"transformations.":[86],"Across":[87],"architectures":[88],"tasks,":[90],"usually":[92],"increases":[93],"transformation":[94,110],"consistency,":[95],"showing":[96],"can":[100],"be":[101],"probed":[102],"directly":[103],"from":[104],"without":[106],"recovering":[107],"the":[108],"hidden":[109],"rules":[111],"relate":[113],"them.":[114]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-15T00:00:00"}
