{"id":"https://openalex.org/W4408185500","doi":"https://doi.org/10.1007/s10994-025-06747-8","title":"Gradient descent fails to learn high-frequency functions and modular arithmetic","display_name":"Gradient descent fails to learn high-frequency functions and modular arithmetic","publication_year":2025,"publication_date":"2025-03-06","ids":{"openalex":"https://openalex.org/W4408185500","doi":"https://doi.org/10.1007/s10994-025-06747-8"},"language":"en","primary_location":{"id":"doi:10.1007/s10994-025-06747-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10994-025-06747-8","pdf_url":null,"source":{"id":"https://openalex.org/S62148650","display_name":"Machine Learning","issn_l":"0885-6125","issn":["0885-6125","1573-0565"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029285634","display_name":"Rustem Takhanov","orcid":"https://orcid.org/0000-0001-7405-8254"},"institutions":[{"id":"https://openalex.org/I60559429","display_name":"Nazarbayev University","ror":"https://ror.org/052bx8q98","country_code":"KZ","type":"education","lineage":["https://openalex.org/I60559429"]}],"countries":["KZ"],"is_corresponding":true,"raw_author_name":"Rustem Takhanov","raw_affiliation_strings":["Nazarbayev University, Kabanbay Batyr Ave., Astana, 010000, Kazakhstan"],"affiliations":[{"raw_affiliation_string":"Nazarbayev University, Kabanbay Batyr Ave., Astana, 010000, Kazakhstan","institution_ids":["https://openalex.org/I60559429"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007740827","display_name":"Maxat Tezekbayev","orcid":"https://orcid.org/0000-0001-8100-2697"},"institutions":[{"id":"https://openalex.org/I60559429","display_name":"Nazarbayev University","ror":"https://ror.org/052bx8q98","country_code":"KZ","type":"education","lineage":["https://openalex.org/I60559429"]}],"countries":["KZ"],"is_corresponding":false,"raw_author_name":"Maxat Tezekbayev","raw_affiliation_strings":["Nazarbayev University, Kabanbay Batyr Ave., Astana, 010000, Kazakhstan"],"affiliations":[{"raw_affiliation_string":"Nazarbayev University, Kabanbay Batyr Ave., Astana, 010000, Kazakhstan","institution_ids":["https://openalex.org/I60559429"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111047963","display_name":"Artur Pak","orcid":null},"institutions":[{"id":"https://openalex.org/I60559429","display_name":"Nazarbayev University","ror":"https://ror.org/052bx8q98","country_code":"KZ","type":"education","lineage":["https://openalex.org/I60559429"]}],"countries":["KZ"],"is_corresponding":false,"raw_author_name":"Artur Pak","raw_affiliation_strings":["Nazarbayev University, Kabanbay Batyr Ave., Astana, 010000, Kazakhstan"],"affiliations":[{"raw_affiliation_string":"Nazarbayev University, Kabanbay Batyr Ave., Astana, 010000, Kazakhstan","institution_ids":["https://openalex.org/I60559429"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048918037","display_name":"Arman Bolatov","orcid":null},"institutions":[{"id":"https://openalex.org/I60559429","display_name":"Nazarbayev University","ror":"https://ror.org/052bx8q98","country_code":"KZ","type":"education","lineage":["https://openalex.org/I60559429"]}],"countries":["KZ"],"is_corresponding":false,"raw_author_name":"Arman Bolatov","raw_affiliation_strings":["Nazarbayev University, Kabanbay Batyr Ave., Astana, 010000, Kazakhstan"],"affiliations":[{"raw_affiliation_string":"Nazarbayev University, Kabanbay Batyr Ave., Astana, 010000, Kazakhstan","institution_ids":["https://openalex.org/I60559429"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053731169","display_name":"Zhenisbek Assylbekov","orcid":"https://orcid.org/0000-0003-0095-9409"},"institutions":[{"id":"https://openalex.org/I162817326","display_name":"Indiana University \u2013 Purdue University Fort Wayne","ror":"https://ror.org/01jxzq227","country_code":"US","type":"education","lineage":["https://openalex.org/I162817326"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhenisbek Assylbekov","raw_affiliation_strings":["Department of Mathematical Sciences, Purdue University Fort Wayne, Fort Wayne, Indiana, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Purdue University Fort Wayne, Fort Wayne, Indiana, USA","institution_ids":["https://openalex.org/I162817326"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5029285634"],"corresponding_institution_ids":["https://openalex.org/I60559429"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":2.6995,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.89175547,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"114","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9998999834060669,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9998999834060669,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.998199999332428,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9973000288009644,"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/gradient-descent","display_name":"Gradient descent","score":0.6077359318733215},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5269903540611267},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.514265239238739},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5117780566215515},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36892998218536377},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33110517263412476},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.22833305597305298},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16849350929260254},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.12200340628623962},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.06340241432189941}],"concepts":[{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6077359318733215},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5269903540611267},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.514265239238739},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5117780566215515},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36892998218536377},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33110517263412476},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.22833305597305298},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16849350929260254},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.12200340628623962},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.06340241432189941}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10994-025-06747-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10994-025-06747-8","pdf_url":null,"source":{"id":"https://openalex.org/S62148650","display_name":"Machine Learning","issn_l":"0885-6125","issn":["0885-6125","1573-0565"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G65465790","display_name":null,"funder_award_id":"20122022FD4131","funder_id":"https://openalex.org/F4320327695","funder_display_name":"Nazarbayev University"}],"funders":[{"id":"https://openalex.org/F4320327695","display_name":"Nazarbayev University","ror":"https://ror.org/052bx8q98"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W122981503","https://openalex.org/W1533675320","https://openalex.org/W2064675550","https://openalex.org/W2064680241","https://openalex.org/W2072631813","https://openalex.org/W2080624030","https://openalex.org/W2119877753","https://openalex.org/W2140283251","https://openalex.org/W2143859313","https://openalex.org/W2171690926","https://openalex.org/W2194775991","https://openalex.org/W2325330392","https://openalex.org/W2509435534","https://openalex.org/W2551387064","https://openalex.org/W2794444783","https://openalex.org/W2963855143","https://openalex.org/W3104396616","https://openalex.org/W3195630663","https://openalex.org/W4226434736","https://openalex.org/W4285077908","https://openalex.org/W4308991248","https://openalex.org/W4382051892","https://openalex.org/W4387355727","https://openalex.org/W4396243922","https://openalex.org/W6636295999","https://openalex.org/W6731278065","https://openalex.org/W6739028767","https://openalex.org/W6845711896","https://openalex.org/W6849213839"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-01-22T23:29:09.771500","created_date":"2025-10-10T00:00:00"}