{"id":"https://openalex.org/W4399115131","doi":"https://doi.org/10.48550/arxiv.2405.17420","title":"Survival of the Fittest Representation: A Case Study with Modular Addition","display_name":"Survival of the Fittest Representation: A Case Study with Modular Addition","publication_year":2024,"publication_date":"2024-05-27","ids":{"openalex":"https://openalex.org/W4399115131","doi":"https://doi.org/10.48550/arxiv.2405.17420"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2405.17420","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2405.17420","pdf_url":"https://arxiv.org/pdf/2405.17420","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2405.17420","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111214500","display_name":"Xiaoman Delores Ding","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ding, Xiaoman Delores","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089640822","display_name":"Zifan Carl Guo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guo, Zifan Carl","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071048251","display_name":"Eric J. Michaud","orcid":"https://orcid.org/0000-0001-7912-1953"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michaud, Eric J.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076825933","display_name":"Ziming Liu","orcid":"https://orcid.org/0000-0002-8867-2682"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Ziming","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5091601455","display_name":"Max Tegmark","orcid":"https://orcid.org/0000-0001-7670-7190"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tegmark, Max","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/T13370","display_name":"Diverse Scientific and Economic Studies","score":0.052299998700618744,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T13370","display_name":"Diverse Scientific and Economic Studies","score":0.052299998700618744,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T14094","display_name":"Italy: Economic History and Contemporary Issues","score":0.04569999873638153,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/survival-of-the-fittest","display_name":"Survival of the fittest","score":0.867892324924469},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.7085935473442078},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5985560417175293},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41062334179878235},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.1333315372467041},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.12651658058166504},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.10686460137367249},{"id":"https://openalex.org/keywords/evolutionary-biology","display_name":"Evolutionary biology","score":0.08352857828140259}],"concepts":[{"id":"https://openalex.org/C22614528","wikidata":"https://www.wikidata.org/wiki/Q721322","display_name":"Survival of the fittest","level":2,"score":0.867892324924469},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.7085935473442078},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5985560417175293},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41062334179878235},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.1333315372467041},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.12651658058166504},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.10686460137367249},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.08352857828140259},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2405.17420","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2405.17420","pdf_url":"https://arxiv.org/pdf/2405.17420","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.2405.17420","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2405.17420","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":"pmh:oai:arXiv.org:2405.17420","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2405.17420","pdf_url":"https://arxiv.org/pdf/2405.17420","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2748952813","https://openalex.org/W2904013997","https://openalex.org/W2020951870","https://openalex.org/W1990781494","https://openalex.org/W2318143347","https://openalex.org/W2990954983","https://openalex.org/W2276754557","https://openalex.org/W657687809","https://openalex.org/W2235413562"],"abstract_inverted_index":{"When":[0],"a":[1,11,50,86,113,172],"neural":[2,51,90],"network":[3,52],"can":[4,167],"learn":[5],"multiple":[6,31,100],"distinct":[7],"algorithms":[8],"to":[9,136,188,200],"solve":[10],"task,":[12],"how":[13],"does":[14],"it":[15,185],"\"choose\"":[16],"between":[17,157],"them":[18],"during":[19],"training?":[20],"To":[21,76],"approach":[22],"this":[23,78],"question,":[24],"we":[25,47,84,143,159],"take":[26],"inspiration":[27],"from":[28,68],"ecology:":[29],"when":[30],"species":[32],"coexist,":[33],"they":[34],"eventually":[35],"reach":[36],"an":[37],"equilibrium":[38],"where":[39],"some":[40],"survive":[41],"while":[42],"others":[43],"die":[44],"out.":[45],"Analogously,":[46],"suggest":[48],"that":[49,97,122,161,184],"at":[53,103,117],"initialization":[54],"contains":[55],"many":[56],"solutions":[57],"(representations":[58],"and":[59,95,129],"algorithms),":[60],"which":[61],"compete":[62],"with":[63,71,111,125,180,196],"each":[64],"other":[65],"under":[66],"pressure":[67],"resource":[69],"constraints,":[70],"the":[72,81,118,123,131,140,151,155,162,165,204],"\"fittest\"":[73],"ultimately":[74],"prevailing.":[75],"investigate":[77],"Survival":[79],"of":[80,164,174,207],"Fittest":[82],"hypothesis,":[83],"conduct":[85],"case":[87],"study":[88],"on":[89,203],"networks":[91],"performing":[92],"modular":[93,181],"addition,":[94],"find":[96,121,160],"these":[98],"networks'":[99],"circular":[101],"representations":[102,191],"different":[104],"Fourier":[105],"frequencies":[106,124],"undergo":[107],"such":[108],"competitive":[109],"dynamics,":[110],"only":[112],"few":[114],"circles":[115,166],"surviving":[116,147],"end.":[119],"We":[120],"high":[126],"initial":[127],"signals":[128],"gradients,":[130],"\"fittest,\"":[132],"are":[133],"more":[134,146],"likely":[135],"survive.":[137],"By":[138],"increasing":[139],"embedding":[141],"dimension,":[142],"also":[144],"observe":[145],"frequencies.":[148],"Inspired":[149],"by":[150,171],"Lotka-Volterra":[152],"equations":[153],"describing":[154],"dynamics":[156,163,206],"species,":[158],"be":[168],"nicely":[169],"characterized":[170],"set":[173],"linear":[175],"differential":[176],"equations.":[177],"Our":[178],"results":[179],"addition":[182],"show":[183],"is":[186],"possible":[187],"decompose":[189],"complicated":[190],"into":[192],"simpler":[193],"components,":[194],"along":[195],"their":[197],"basic":[198],"interactions,":[199],"offer":[201],"insight":[202],"training":[205],"representations.":[208]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}