{"id":"https://openalex.org/W3211075221","doi":null,"title":"Logical Activation Functions: Logit-space equivalents of Boolean Operators.","display_name":"Logical Activation Functions: Logit-space equivalents of Boolean Operators.","publication_year":2021,"publication_date":"2021-10-22","ids":{"openalex":"https://openalex.org/W3211075221","mag":"3211075221"},"language":"en","primary_location":{"id":"mag:3211075221","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/pdf/2110.11940.pdf","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://arxiv.org/pdf/2110.11940.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Scott Lowe","orcid":"https://orcid.org/0000-0002-5237-3867","observed_orcids":["https://orcid.org/0000-0002-5237-3867"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Scott Lowe","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-5237-3867","affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Robert L. Earle","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robert L. Earle","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058980104","display_name":"Jason d\u2019Eon","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jason d\u2019Eon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088920905","display_name":"Thomas P. Trappenberg","orcid":"https://orcid.org/0000-0002-6144-8963","observed_orcids":["https://orcid.org/0000-0002-6144-8963"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thomas Trappenberg","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-6144-8963","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5082789942","display_name":"Sageev Oore","orcid":"https://orcid.org/0000-0002-8130-3569","observed_orcids":["https://orcid.org/0000-0002-8130-3569"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sageev Oore","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-8130-3569","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/T10320","display_name":"Neural Networks and Applications","score":0.9702000021934509,"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/T10320","display_name":"Neural Networks and Applications","score":0.9702000021934509,"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":0.01889999955892563,"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"}},{"id":"https://openalex.org/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.0019000000320374966,"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/activation-functions","display_name":"activation functions","score":0.753000020980835},{"id":"https://openalex.org/keywords/boolean-operators","display_name":"Boolean operators","score":0.800000011920929},{"id":"https://openalex.org/keywords/neural-network-activation-functions","display_name":"neural network activation functions","score":0.3869999945163727},{"id":"https://openalex.org/keywords/feature-independence","display_name":"feature independence","score":0.4410000145435333},{"id":"https://openalex.org/keywords/compositional-zero-shot-learning","display_name":"compositional zero-shot learning","score":0.8450000286102295},{"id":"https://openalex.org/keywords/abstract-thinking","display_name":"abstract thinking","score":0.8659999966621399},{"id":"https://openalex.org/keywords/image-classification","display_name":"image classification","score":0.6729999780654907},{"id":"https://openalex.org/keywords/transfer-learning","display_name":"transfer learning","score":0.9900000095367432}],"concepts":[{"id":"https://openalex.org/C140331021","wikidata":"https://www.wikidata.org/wiki/Q1868104","display_name":"Logit","level":2,"score":0.7670548558235168},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5303300619125366},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49085885286331177},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3769426941871643},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35203230381011963},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3286718726158142},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.280710905790329}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:3211075221","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/pdf/2110.11940.pdf","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:3211075221","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/pdf/2110.11940.pdf","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1500903679","https://openalex.org/W1819710477","https://openalex.org/W1948251820","https://openalex.org/W1951216520","https://openalex.org/W2000420612","https://openalex.org/W2015627422","https://openalex.org/W2101295242","https://openalex.org/W2112796928","https://openalex.org/W2115733720","https://openalex.org/W2118730391","https://openalex.org/W2118858186","https://openalex.org/W2138011018","https://openalex.org/W2161850243","https://openalex.org/W2194775991","https://openalex.org/W2302255633","https://openalex.org/W2335728318","https://openalex.org/W2338522602","https://openalex.org/W2533598788","https://openalex.org/W2547207889","https://openalex.org/W2607735137","https://openalex.org/W2624413595","https://openalex.org/W2749581528","https://openalex.org/W2795247881","https://openalex.org/W2949736877","https://openalex.org/W2962834855","https://openalex.org/W2962851953","https://openalex.org/W2963690694","https://openalex.org/W2969937244","https://openalex.org/W2998412226","https://openalex.org/W3010694149","https://openalex.org/W3038964916","https://openalex.org/W3118608800"],"related_works":["https://openalex.org/W7133224912","https://openalex.org/W4391655826","https://openalex.org/W3036091391","https://openalex.org/W4405389419","https://openalex.org/W2912446367","https://openalex.org/W4415783342","https://openalex.org/W3096184750","https://openalex.org/W2885968973","https://openalex.org/W3095034705","https://openalex.org/W2467394243"],"abstract_inverted_index":{"Neuronal":[0],"representations":[1],"within":[2,21,87],"artificial":[3],"neural":[4,88,120],"networks":[5],"are":[6,41],"commonly":[7],"understood":[8],"as":[9,115],"logits,":[10],"representing":[11],"the":[12,22,30,45,52,65,138,142],"log-odds":[13],"score":[14],"of":[15,19,38,64,128,137,166],"presence":[16],"(versus":[17],"absence)":[18],"features":[20,40],"stimulus.":[23],"Under":[24],"this":[25,70],"interpretation,":[26],"we":[27,59,133],"can":[28,112],"derive":[29],"probability":[31,54],"$P(x_0":[32],"\\land":[33],"x_1)$":[34],"that":[35],"a":[36,57,61,126,164],"pair":[37],"independent":[39],"both":[42,153],"present":[43],"in":[44,119,154,157],"stimulus":[46],"from":[47],"their":[48,161],"logits.":[49],"By":[50],"converting":[51],"resulting":[53],"back":[55],"into":[56],"logit,":[58],"obtain":[60],"logit-space":[62,139],"equivalent":[63],"AND":[66,99],"operation.":[67],"However,":[68],"since":[69],"function":[71,118],"involves":[72],"taking":[73],"multiple":[74],"exponents":[75],"and":[76,108,144,156,159,175],"logarithms,":[77],"it":[78],"is":[79,125],"not":[80],"well":[81],"suited":[82],"to":[83,130,141],"be":[84,113],"directly":[85],"used":[86],"networks.":[89,121],"We":[90,147],"thus":[91],"constructed":[92,134],"an":[93,116],"efficient":[94,135],"approximation":[95],"named":[96],"$\\text{AND}_\\text{AIL}$":[97,124],"(the":[98],"operator":[100],"Approximate":[101],"for":[102],"Independent":[103],"Logits)":[104],"utilizing":[105],"only":[106],"comparison":[107],"addition":[109],"operations,":[110],"which":[111],"deployed":[114,148],"activation":[117,151],"Like":[122],"MaxOut,":[123],"generalization":[127],"ReLU":[129],"two-dimensions.":[131],"Additionally,":[132],"approximations":[136],"equivalents":[140],"OR":[143],"XNOR":[145],"operators.":[146],"these":[149],"new":[150],"functions,":[152],"isolation":[155],"conjunction,":[158],"demonstrated":[160],"effectiveness":[162],"on":[163],"variety":[165],"tasks":[167],"including":[168],"image":[169],"classification,":[170],"transfer":[171],"learning,":[172],"abstract":[173],"reasoning,":[174],"compositional":[176],"zero-shot":[177],"learning.":[178]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2021-11-08T00:00:00"}