{"id":"https://openalex.org/W7160951764","doi":"https://doi.org/10.48550/arxiv.2605.09609","title":"Minimal Filling Architectures of Polynomial Neural Networks: Counterexamples, Frontier Search, and Defects","display_name":"Minimal Filling Architectures of Polynomial Neural Networks: Counterexamples, Frontier Search, and Defects","publication_year":2026,"publication_date":"2026-05-10","ids":{"openalex":"https://openalex.org/W7160951764","doi":"https://doi.org/10.48550/arxiv.2605.09609"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.09609","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.09609","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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.2605.09609","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5118698655","display_name":"Kevin Dao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dao, Kevin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5039894662","display_name":"Jose Israel Rodriguez","orcid":"https://orcid.org/0000-0003-3140-9944"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rodriguez, Jose Israel","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/T10320","display_name":"Neural Networks and Applications","score":0.17010000348091125,"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/T10320","display_name":"Neural Networks and Applications","score":0.17010000348091125,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.1624000072479248,"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/T12808","display_name":"Ferroelectric and Negative Capacitance Devices","score":0.11980000138282776,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/counterexample","display_name":"Counterexample","score":0.9546999931335449},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7638999819755554},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6984999775886536},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5751000046730042},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5558000206947327},{"id":"https://openalex.org/keywords/vc-dimension","display_name":"VC dimension","score":0.4203000068664551},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.41359999775886536}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.9546999931335449},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7638999819755554},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6984999775886536},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6215999722480774},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5751000046730042},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5558000206947327},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49480000138282776},{"id":"https://openalex.org/C119322782","wikidata":"https://www.wikidata.org/wiki/Q2662236","display_name":"VC dimension","level":2,"score":0.4203000068664551},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.41359999775886536},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38119998574256897},{"id":"https://openalex.org/C7720571","wikidata":"https://www.wikidata.org/wiki/Q1136880","display_name":"Power of two","level":2,"score":0.3693000078201294},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34689998626708984},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3102000057697296},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.26420000195503235},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.2637999951839447},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.2621000111103058},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26170000433921814},{"id":"https://openalex.org/C2778571376","wikidata":"https://www.wikidata.org/wiki/Q1355821","display_name":"Frontier","level":2,"score":0.260699987411499},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.259799987077713},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.25540000200271606}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.09609","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.09609","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.09609","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.09609","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,40],"provide":[1],"counterexamples":[2,42],"to":[3],"the":[4,20,25,37,68],"unimodal":[5,34],"minimal":[6,30],"filling":[7,31],"architecture":[8,32],"conjecture":[9,26],"for":[10,36],"polynomial":[11],"neural":[12],"networks":[13],"(PNNs)":[14],"with":[15,67],"power":[16],"activation":[17],"functions.":[18],"Fixing":[19],"input":[21],"and":[22,52],"output":[23],"widths,":[24],"states":[27],"that":[28],"any":[29],"has":[33],"widths":[35],"hidden":[38],"layers.":[39],"found":[41],"via":[43],"a":[44],"frontier":[45],"search,":[46],"recursive":[47],"dimension":[48],"bounds":[49],"on":[50],"neurovarieties,":[51],"symbolic":[53],"computation.":[54],"Notably,":[55],"several":[56],"subarchitectures":[57],"of":[58],"our":[59],"main":[60],"example":[61],"exhibit":[62],"large":[63],"defect,":[64],"in":[65,73],"contrast":[66],"predominantly":[69],"small-defect":[70],"behavior":[71],"observed":[72],"prior":[74],"literature.":[75]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-13T00:00:00"}