{"id":"https://openalex.org/W7160322360","doi":"https://doi.org/10.48550/arxiv.2605.02350","title":"A Near-optimal SQ Lower Bound for Smoothed Agnostic Learning of Boolean Halfspaces","display_name":"A Near-optimal SQ Lower Bound for Smoothed Agnostic Learning of Boolean Halfspaces","publication_year":2026,"publication_date":"2026-05-04","ids":{"openalex":"https://openalex.org/W7160322360","doi":"https://doi.org/10.48550/arxiv.2605.02350"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.02350","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02350","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":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.02350","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093682130","display_name":"Tim Sinen","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Sinen, Tim","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5093682130"],"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/T12072","display_name":"Machine Learning and Algorithms","score":0.6600000262260437,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.6600000262260437,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.28780001401901245,"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"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.005400000140070915,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6973999738693237},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.5763999819755554},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.5167999863624573},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5102999806404114},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4377000033855438},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4142000079154968},{"id":"https://openalex.org/keywords/probably-approximately-correct-learning","display_name":"Probably approximately correct learning","score":0.3984000086784363},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.3982999920845032}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6973999738693237},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6855000257492065},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5763999819755554},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.5167999863624573},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5102999806404114},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49309998750686646},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4632999897003174},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4377000033855438},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4142000079154968},{"id":"https://openalex.org/C176248197","wikidata":"https://www.wikidata.org/wiki/Q458526","display_name":"Probably approximately correct learning","level":4,"score":0.3984000086784363},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.3982999920845032},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.3937000036239624},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.3831999897956848},{"id":"https://openalex.org/C136726353","wikidata":"https://www.wikidata.org/wiki/Q903789","display_name":"Disjunctive normal form","level":2,"score":0.37529999017715454},{"id":"https://openalex.org/C2982736386","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Statistical learning","level":2,"score":0.36649999022483826},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35569998621940613},{"id":"https://openalex.org/C50292564","wikidata":"https://www.wikidata.org/wiki/Q2462783","display_name":"Computational learning theory","level":3,"score":0.3188000023365021},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.2913999855518341},{"id":"https://openalex.org/C120068334","wikidata":"https://www.wikidata.org/wiki/Q45343","display_name":"Polynomial regression","level":3,"score":0.2897000014781952},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2549999952316284},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.2547000050544739},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.25209999084472656}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.02350","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02350","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":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.02350","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02350","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":"article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.5952469706535339}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,32],"study":[1],"the":[2,17,58,67],"complexity":[3,42,51],"of":[4,8,54],"smoothed":[5],"agnostic":[6],"learning":[7],"halfspaces":[9],"on":[10],"$\\{\\pm":[11],"1\\}^n$":[12],"under":[13,70],"uniform":[14],"marginals":[15],"in":[16,66],"model":[18],"of~\\cite{KM25},":[19],"where":[20],"each":[21],"input":[22],"coordinate":[23],"is":[24],"independently":[25],"flipped":[26],"with":[27],"probability":[28],"$\u03c3\\in":[29],"(0,":[30],"{1}/{2})$.":[31],"show":[33],"that":[34],"$L^1$":[35],"polynomial":[36],"regression":[37],"achieves":[38],"runtime":[39],"and":[40,44],"sample":[41],"$\\tilde{O}(n^{O(\\log(1/\\varepsilon)/\u03c3)})$,":[43],"prove":[45],"a":[46],"nearly":[47],"matching":[48],"Statistical":[49],"Query":[50],"lower":[52],"bound":[53],"$n^{\u03a9(\\log(1+\u03c3/\\varepsilon^2)/\u03c3)}$.":[55],"This":[56],"complements":[57],"recent":[59],"work":[60],"of~\\cite{DK26},":[61],"which":[62],"established":[63],"analogous":[64],"bounds":[65],"continuous":[68],"setting":[69],"Gaussian":[71],"marginals.":[72]},"counts_by_year":[],"updated_date":"2026-05-15T06:05:50.897203","created_date":"2026-05-06T00:00:00"}
