{"id":"https://openalex.org/W3206132569","doi":"https://doi.org/10.1007/978-3-031-06773-0_17","title":"Permutation Invariance of\u00a0Deep Neural Networks with\u00a0ReLUs","display_name":"Permutation Invariance of\u00a0Deep Neural Networks with\u00a0ReLUs","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W3206132569","doi":"https://doi.org/10.1007/978-3-031-06773-0_17","mag":"3206132569"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-06773-0_17","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-031-06773-0_17","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5050767084","display_name":"Diganta Mukhopadhyay","orcid":null},"institutions":[{"id":"https://openalex.org/I19149307","display_name":"Chennai Mathematical Institute","ror":"https://ror.org/04zp24820","country_code":"IN","type":"education","lineage":["https://openalex.org/I19149307"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Diganta Mukhopadhyay","raw_affiliation_strings":["Chennai Mathematical Institute, Chennai, India"],"affiliations":[{"raw_affiliation_string":"Chennai Mathematical Institute, Chennai, India","institution_ids":["https://openalex.org/I19149307"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101709558","display_name":"Kumar Madhukar","orcid":"https://orcid.org/0000-0001-5686-9758"},"institutions":[{"id":"https://openalex.org/I68891433","display_name":"Indian Institute of Technology Delhi","ror":"https://ror.org/049tgcd06","country_code":"IN","type":"education","lineage":["https://openalex.org/I68891433"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Kumar Madhukar","raw_affiliation_strings":["Indian Institute of Technology Delhi, Delhi, India"],"affiliations":[{"raw_affiliation_string":"Indian Institute of Technology Delhi, Delhi, India","institution_ids":["https://openalex.org/I68891433"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039897432","display_name":"Mandayam Srivas","orcid":null},"institutions":[{"id":"https://openalex.org/I19149307","display_name":"Chennai Mathematical Institute","ror":"https://ror.org/04zp24820","country_code":"IN","type":"education","lineage":["https://openalex.org/I19149307"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Mandayam Srivas","raw_affiliation_strings":["Chennai Mathematical Institute, Chennai, India"],"affiliations":[{"raw_affiliation_string":"Chennai Mathematical Institute, Chennai, India","institution_ids":["https://openalex.org/I19149307"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5050767084"],"corresponding_institution_ids":["https://openalex.org/I19149307"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00850288,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"318","last_page":"337"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","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/T11689","display_name":"Adversarial Robustness in Machine Learning","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/T11242","display_name":"Nuclear Materials and Properties","score":0.9473999738693237,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10645","display_name":"Cardiac Arrest and Resuscitation","score":0.9340000152587891,"subfield":{"id":"https://openalex.org/subfields/2711","display_name":"Emergency Medicine"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.7525448799133301},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7235006093978882},{"id":"https://openalex.org/keywords/deep-neural-networks","display_name":"Deep neural networks","score":0.5371540188789368},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5229701995849609},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4870043396949768},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4831504225730896},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4741979241371155},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4699772894382477},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.4608355164527893},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.4447779059410095},{"id":"https://openalex.org/keywords/abstraction","display_name":"Abstraction","score":0.4342295527458191},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.42223310470581055},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2935482859611511},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.24737629294395447},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.20983457565307617}],"concepts":[{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.7525448799133301},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7235006093978882},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.5371540188789368},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5229701995849609},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4870043396949768},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4831504225730896},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4741979241371155},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4699772894382477},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.4608355164527893},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.4447779059410095},{"id":"https://openalex.org/C124304363","wikidata":"https://www.wikidata.org/wiki/Q673661","display_name":"Abstraction","level":2,"score":0.4342295527458191},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.42223310470581055},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2935482859611511},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.24737629294395447},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.20983457565307617},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-031-06773-0_17","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-031-06773-0_17","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1480909796","https://openalex.org/W2165073069","https://openalex.org/W2543296129","https://openalex.org/W2594877703","https://openalex.org/W2791251367","https://openalex.org/W2794609696","https://openalex.org/W2807040120","https://openalex.org/W2869036160","https://openalex.org/W2890472662","https://openalex.org/W2899156512","https://openalex.org/W2900153411","https://openalex.org/W2957311447","https://openalex.org/W2962692913","https://openalex.org/W2963054787","https://openalex.org/W2963208512","https://openalex.org/W2967595108","https://openalex.org/W2970212174","https://openalex.org/W2982540258","https://openalex.org/W2998574230","https://openalex.org/W3091350347","https://openalex.org/W3094683669","https://openalex.org/W3096553286","https://openalex.org/W3102139284","https://openalex.org/W3145532460","https://openalex.org/W3188209232"],"related_works":["https://openalex.org/W12248495","https://openalex.org/W8052147","https://openalex.org/W637774","https://openalex.org/W11753786","https://openalex.org/W9918680","https://openalex.org/W9779297","https://openalex.org/W4919037","https://openalex.org/W12307245","https://openalex.org/W124579","https://openalex.org/W677840"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}