{"id":"https://openalex.org/W2345809749","doi":"https://doi.org/10.1109/isit.2016.7541482","title":"Deep convolutional neural networks on cartoon functions","display_name":"Deep convolutional neural networks on cartoon functions","publication_year":2016,"publication_date":"2016-07-01","ids":{"openalex":"https://openalex.org/W2345809749","doi":"https://doi.org/10.1109/isit.2016.7541482","mag":"2345809749"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2016.7541482","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2016.7541482","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1605.00031","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Philipp Grohs","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Philipp Grohs","raw_affiliation_strings":["Dept. Math., ETH Zurich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Dept. Math., ETH Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Thomas Wiatowski","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Thomas Wiatowski","raw_affiliation_strings":["Dept. IT &amp; EE, ETH Zurich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Dept. IT &amp; EE, ETH Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":null,"display_name":"Helmut B\u00f6lcskei","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Helmut B\u00f6lcskei","raw_affiliation_strings":["Dept. IT &amp; EE, ETH Zurich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Dept. IT &amp; EE, ETH Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":null,"apc_paid":null,"fwci":1.3557,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.86655095,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"1163","last_page":"1167"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10036","display_name":"Advanced Neural Network Applications","score":0.996999979019165,"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"}},"topics":[{"id":"https://openalex.org/T10036","display_name":"Advanced Neural Network Applications","score":0.996999979019165,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.996999979019165,"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/T10638","display_name":"Optical measurement and interference techniques","score":0.9969000220298767,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.7240999937057495},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6984999775886536},{"id":"https://openalex.org/keywords/convolutional-neural-network","display_name":"Convolutional neural network","score":0.6771000027656555},{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.6675999760627747},{"id":"https://openalex.org/keywords/deformation","display_name":"Deformation (meteorology)","score":0.657800018787384},{"id":"https://openalex.org/keywords/translation","display_name":"Translation (biology)","score":0.6301000118255615},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.5473999977111816},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.38589999079704285}],"concepts":[{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.7240999937057495},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6984999775886536},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.6771000027656555},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.6675999760627747},{"id":"https://openalex.org/C204366326","wikidata":"https://www.wikidata.org/wiki/Q3027650","display_name":"Deformation (meteorology)","level":2,"score":0.657800018787384},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.6301000118255615},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.54830002784729},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.5473999977111816},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5133000016212463},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.38589999079704285},{"id":"https://openalex.org/C158154518","wikidata":"https://www.wikidata.org/wiki/Q7310970","display_name":"Relevance (law)","level":2,"score":0.3490999937057495},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3479999899864197},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3434000015258789},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.32580000162124634},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3222000002861023},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.3109000027179718},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.2915000021457672},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.28060001134872437},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.27959999442100525},{"id":"https://openalex.org/C2776608160","wikidata":"https://www.wikidata.org/wiki/Q4785462","display_name":"Natural (archaeology)","level":2,"score":0.266400009393692},{"id":"https://openalex.org/C2777042112","wikidata":"https://www.wikidata.org/wiki/Q5281658","display_name":"Discontinuity (linguistics)","level":2,"score":0.25429999828338623}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/isit.2016.7541482","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2016.7541482","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1605.00031","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1605.00031","pdf_url":"https://arxiv.org/pdf/1605.00031","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1605.00031","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1605.00031","pdf_url":"https://arxiv.org/pdf/1605.00031","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1535448269","https://openalex.org/W1605417594","https://openalex.org/W1762506961","https://openalex.org/W1994906459","https://openalex.org/W1997146646","https://openalex.org/W2112796928","https://openalex.org/W2139427956","https://openalex.org/W2163922914","https://openalex.org/W2208541107","https://openalex.org/W2546302380","https://openalex.org/W2919115771","https://openalex.org/W4236421521","https://openalex.org/W4255272544","https://openalex.org/W6634343353","https://openalex.org/W6687483927","https://openalex.org/W6687596921","https://openalex.org/W6787972765"],"related_works":[],"abstract_inverted_index":{"Wiatowski":[0],"and":[1,8,33,65,68],"B\u00f6lcskei,":[2],"2015,":[3],"proved":[4],"that":[5,84],"deformation":[6,45,81,94],"stability":[7,46,82,95],"vertical":[9],"translation":[10,37],"invariance":[11,38],"of":[12,55,76,100],"deep":[13],"convolutional":[14],"neural":[15],"network-based":[16],"feature":[17],"extractors":[18],"are":[19,69],"guaranteed":[20],"by":[21,104],"the":[22,29,36,44,98],"network":[23],"structure":[24],"per":[25],"se":[26],"rather":[27],"than":[28],"specific":[30],"convolution":[31],"kernels":[32],"non-linearities.":[34],"While":[35],"result":[39,83],"applies":[40],"to":[41],"square-integrable":[42],"functions,":[43],"bound":[47],"holds":[48],"for":[49,97],"band-limited":[50],"functions":[51,102],"only.":[52],"Many":[53],"signals":[54],"practical":[56],"relevance":[57],"(such":[58],"as":[59],"natural":[60],"images)":[61],"exhibit,":[62],"however,":[63],"sharp":[64],"curved":[66],"discontinuities":[67],"hence":[70],"not":[71],"band-limited.":[72],"The":[73],"main":[74],"contribution":[75],"this":[77],"paper":[78],"is":[79],"a":[80],"takes":[85],"these":[86],"structural":[87],"properties":[88],"into":[89],"account.":[90],"Specifically,":[91],"we":[92],"establish":[93],"bounds":[96],"class":[99],"cartoon":[101],"introduced":[103],"Donoho,":[105],"2001.":[106]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4}],"updated_date":"2026-03-21T06:30:42.041108","created_date":"2016-06-24T00:00:00"}
