{"id":"https://openalex.org/W7140736305","doi":"https://doi.org/10.48550/arxiv.2603.23831","title":"Unveiling Hidden Convexity in Deep Learning: a Sparse Signal Processing Perspective","display_name":"Unveiling Hidden Convexity in Deep Learning: a Sparse Signal Processing Perspective","publication_year":2026,"publication_date":"2026-03-25","ids":{"openalex":"https://openalex.org/W7140736305","doi":"https://doi.org/10.48550/arxiv.2603.23831"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.23831","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.23831","pdf_url":null,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.23831","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5130656980","display_name":"Emi Zeger","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zeger, Emi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5094581283","display_name":"Mert Pilanci","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pilanci, Mert","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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.7498000264167786,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.7498000264167786,"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/T10036","display_name":"Advanced Neural Network Applications","score":0.045099999755620956,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.02969999983906746,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/perspective","display_name":"Perspective (graphical)","score":0.6772000193595886},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.6561999917030334},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.5648000240325928},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5304999947547913},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.5289000272750854},{"id":"https://openalex.org/keywords/signal","display_name":"SIGNAL (programming language)","score":0.4291999936103821},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.4007999897003174}],"concepts":[{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.6772000193595886},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6759999990463257},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.6561999917030334},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6258999705314636},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.5648000240325928},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5304999947547913},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.5289000272750854},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4778999984264374},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.4291999936103821},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.4007999897003174},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.3594000041484833},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.3499999940395355},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3248000144958496},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.28769999742507935},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.25780001282691956},{"id":"https://openalex.org/C70958404","wikidata":"https://www.wikidata.org/wiki/Q7512728","display_name":"Signal reconstruction","level":4,"score":0.2535000145435333}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.23831","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.23831","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.23831","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.23831","pdf_url":null,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4","score":0.8114867806434631}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Deep":[0],"neural":[1],"networks":[2,94],"(DNNs),":[3],"particularly":[4],"those":[5],"using":[6],"Rectified":[7],"Linear":[8],"Unit":[9],"(ReLU)":[10],"activation":[11],"functions,":[12],"have":[13],"achieved":[14],"remarkable":[15],"success":[16],"across":[17],"diverse":[18],"machine":[19],"learning":[20,120],"tasks,":[21],"including":[22],"image":[23],"recognition,":[24],"audio":[25],"processing,":[26,124],"and":[27,42,59,73,95,108],"language":[28],"modeling.":[29],"Despite":[30],"this":[31,47],"success,":[32],"the":[33,69,84,116],"non-convex":[34],"nature":[35],"of":[36,56,71,87,118],"DNN":[37],"loss":[38,85],"functions":[39],"complicates":[40],"optimization":[41],"limits":[43],"theoretical":[44],"understanding.":[45],"In":[46],"paper,":[48],"we":[49],"highlight":[50],"how":[51],"recently":[52],"developed":[53],"convex":[54],"equivalences":[55],"ReLU":[57,93],"NNs":[58],"their":[60],"connections":[61],"to":[62,104],"sparse":[63],"signal":[64,123,127],"processing":[65,128],"models":[66],"can":[67],"address":[68],"challenges":[70],"training":[72],"understanding":[74],"NNs.":[75],"Recent":[76],"research":[77],"has":[78],"uncovered":[79],"several":[80],"hidden":[81],"convexities":[82],"in":[83,115],"landscapes":[86],"certain":[88],"NN":[89],"architectures,":[90],"notably":[91],"two-layer":[92],"other":[96],"deeper":[97],"or":[98],"varied":[99],"architectures.":[100],"This":[101],"paper":[102],"seeks":[103],"provide":[105],"an":[106],"accessible":[107],"educational":[109],"overview":[110],"that":[111],"bridges":[112],"recent":[113],"advances":[114],"mathematics":[117],"deep":[119],"with":[121],"traditional":[122],"encouraging":[125],"broader":[126],"applications.":[129]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-03-27T00:00:00"}