{"id":"https://openalex.org/W4379177005","doi":"https://doi.org/10.1007/978-3-031-33170-1_4","title":"Formalizing Piecewise Affine Activation Functions of\u00a0Neural Networks in\u00a0Coq","display_name":"Formalizing Piecewise Affine Activation Functions of\u00a0Neural Networks in\u00a0Coq","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4379177005","doi":"https://doi.org/10.1007/978-3-031-33170-1_4"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-33170-1_4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-031-33170-1_4","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/A5014622810","display_name":"A. F. Aleksandrov","orcid":"https://orcid.org/0000-0002-4717-4206"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Andrei Aleksandrov","raw_affiliation_strings":["Technische Universit\u00e4t Berlin, Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0002-4717-4206","affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066537166","display_name":"Kim V\u00f6llinger","orcid":"https://orcid.org/0000-0002-8988-0053"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Kim V\u00f6llinger","raw_affiliation_strings":["Technische Universit\u00e4t Berlin, Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0002-8988-0053","affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5014622810"],"corresponding_institution_ids":["https://openalex.org/I4577782"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":5.7226,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.96606744,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"62","last_page":"78"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9965000152587891,"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":0.9965000152587891,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9767000079154968,"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/T10142","display_name":"Formal Methods in Verification","score":0.9226999878883362,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6998781561851501},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.6925172805786133},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5996845364570618},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5680374503135681},{"id":"https://openalex.org/keywords/gas-meter-prover","display_name":"Gas meter prover","score":0.5529285073280334},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5229792594909668},{"id":"https://openalex.org/keywords/proof-assistant","display_name":"Proof assistant","score":0.5211687088012695},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.46030193567276},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.4449397027492523},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4436865746974945},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4379662275314331},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.4365988075733185},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.42915108799934387},{"id":"https://openalex.org/keywords/automated-reasoning","display_name":"Automated reasoning","score":0.4200300872325897},{"id":"https://openalex.org/keywords/computable-function","display_name":"Computable function","score":0.41392406821250916},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3667146563529968},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.28977447748184204},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.20140060782432556},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1430097222328186},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.09814402461051941}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6998781561851501},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.6925172805786133},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5996845364570618},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5680374503135681},{"id":"https://openalex.org/C159718280","wikidata":"https://www.wikidata.org/wiki/Q5526353","display_name":"Gas meter prover","level":3,"score":0.5529285073280334},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5229792594909668},{"id":"https://openalex.org/C203265346","wikidata":"https://www.wikidata.org/wiki/Q11387554","display_name":"Proof assistant","level":3,"score":0.5211687088012695},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46030193567276},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.4449397027492523},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4436865746974945},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4379662275314331},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.4365988075733185},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.42915108799934387},{"id":"https://openalex.org/C195344581","wikidata":"https://www.wikidata.org/wiki/Q2555318","display_name":"Automated reasoning","level":2,"score":0.4200300872325897},{"id":"https://openalex.org/C54271186","wikidata":"https://www.wikidata.org/wiki/Q1148456","display_name":"Computable function","level":2,"score":0.41392406821250916},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3667146563529968},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.28977447748184204},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.20140060782432556},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1430097222328186},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.09814402461051941},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-031-33170-1_4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-031-33170-1_4","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":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.7699999809265137}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1516308076","https://openalex.org/W1975906542","https://openalex.org/W1988115241","https://openalex.org/W2103496339","https://openalex.org/W2137351629","https://openalex.org/W2225411641","https://openalex.org/W2623933443","https://openalex.org/W2743909828","https://openalex.org/W2747942685","https://openalex.org/W2903710663","https://openalex.org/W2963054787","https://openalex.org/W2980264580","https://openalex.org/W2988480584","https://openalex.org/W2998574230","https://openalex.org/W3006335338","https://openalex.org/W3046662910","https://openalex.org/W3099132019","https://openalex.org/W3205832376","https://openalex.org/W4205950066","https://openalex.org/W4205995027","https://openalex.org/W4206151407","https://openalex.org/W4206570602","https://openalex.org/W4212766343","https://openalex.org/W4242074711","https://openalex.org/W4250663533","https://openalex.org/W4255863451","https://openalex.org/W4323026396","https://openalex.org/W6893957906"],"related_works":["https://openalex.org/W76860425","https://openalex.org/W2160478595","https://openalex.org/W3100311625","https://openalex.org/W2885010049","https://openalex.org/W4246350535","https://openalex.org/W2522499048","https://openalex.org/W2074713291","https://openalex.org/W4214826241","https://openalex.org/W2809689211","https://openalex.org/W1909465604"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}