{"id":"https://openalex.org/W7128089651","doi":"https://doi.org/10.48550/arxiv.2602.04386","title":"Improved Sparse Recovery for Approximate Matrix Multiplication","display_name":"Improved Sparse Recovery for Approximate Matrix Multiplication","publication_year":2026,"publication_date":"2026-02-04","ids":{"openalex":"https://openalex.org/W7128089651","doi":"https://doi.org/10.48550/arxiv.2602.04386"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2602.04386","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.04386","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":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2602.04386","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5125141419","display_name":"Yahel Uffenheimer","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Uffenheimer, Yahel","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5125103749","display_name":"Omri Weinstein","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Weinstein, Omri","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5125141419"],"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":0.9297999739646912,"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":0.9297999739646912,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.029200000688433647,"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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.019700000062584877,"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/matrix-norm","display_name":"Matrix norm","score":0.6653000116348267},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5016999840736389},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4846000075340271},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.482699990272522},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.48159998655319214},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.4772000014781952},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.40529999136924744},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.3937999904155731},{"id":"https://openalex.org/keywords/freivalds-algorithm","display_name":"Freivalds' algorithm","score":0.3901999890804291}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7117000222206116},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.6653000116348267},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.647599995136261},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5016999840736389},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4846000075340271},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.482699990272522},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.48159998655319214},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.4772000014781952},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.40529999136924744},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.3937999904155731},{"id":"https://openalex.org/C38506071","wikidata":"https://www.wikidata.org/wiki/Q6522941","display_name":"Freivalds' algorithm","level":5,"score":0.3901999890804291},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.3817000091075897},{"id":"https://openalex.org/C60761296","wikidata":"https://www.wikidata.org/wiki/Q651480","display_name":"Main diagonal","level":3,"score":0.33559998869895935},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.3346000015735626},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.3330000042915344},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3294999897480011},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.31279999017715454},{"id":"https://openalex.org/C61005703","wikidata":"https://www.wikidata.org/wiki/Q2145211","display_name":"Round-off error","level":2,"score":0.3066999912261963},{"id":"https://openalex.org/C56275529","wikidata":"https://www.wikidata.org/wiki/Q5348937","display_name":"Eight-point algorithm","level":5,"score":0.2971000075340271},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.2962000072002411},{"id":"https://openalex.org/C97542219","wikidata":"https://www.wikidata.org/wiki/Q497863","display_name":"SIMPLE algorithm","level":2,"score":0.29420000314712524},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.2921999990940094},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.29019999504089355},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.2671000063419342},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.265500009059906},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2639999985694885},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.260699987411499},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.25870001316070557}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2602.04386","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.04386","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":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2602.04386","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.04386","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":"article"},"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],"present":[1],"a":[2,26,38,82,92],"simple":[3],"randomized":[4],"algorithm":[5,32,55,76,80,90],"for":[6],"approximate":[7],"matrix":[8,39],"multiplication":[9],"(AMM)":[10],"whose":[11],"error":[12,44,65,71],"scales":[13],"with":[14,41,61,106],"the":[15,31,54,68,89,99,112,116],"*output*":[16,117],"norm":[17,114],"$\\|AB\\|_F$.":[18],"Given":[19],"any":[20],"$n\\times":[21],"n$":[22],"matrices":[23,101],"$A,B$":[24],"and":[25,50],"runtime":[27],"parameter":[28],"$r\\leq":[29],"n$,":[30],"produces":[33],"in":[34,88],"$O(n^2(r+\\log":[35],"n))$":[36],"time,":[37],"$C$":[40],"total":[42,63],"squared":[43,64],"$\\mathbb{E}[\\|C-AB\\|_F^2]\\le":[45],"(1-\\frac{r}{n})\\|AB\\|_F^2$,":[46],"per-entry":[47],"variance":[48],"$\\|AB\\|_F^2/n^2$":[49],"bias":[51],"$\\mathbb{E}[C]=\\frac{r}{n}AB$.":[52],"Alternatively,":[53],"can":[56],"compute":[57],"an":[58],"*unbiased*":[59],"estimation":[60],"expected":[62],"$\\frac{n}{r}\\|{AB}\\|_{F}^2$,":[66],"recovering":[67],"state-of-art":[69],"AMM":[70],"obtained":[72],"by":[73],"Pagh's":[74],"TensorSketch":[75],"(Pagh,":[77],"2013).":[78],"Our":[79],"is":[81,91],"log-factor":[83],"faster.":[84],"The":[85],"key":[86],"insight":[87],"new":[93],"variation":[94],"of":[95,98,115],"pseudo-random":[96],"rotation":[97],"input":[100],"(a":[102],"Fast":[103],"Hadamard":[104],"Transform":[105],"asymmetric":[107],"diagonal":[108],"scaling),":[109],"which":[110],"redistributes":[111],"Frobenius":[113],"$AB$":[118],"uniformly":[119],"across":[120],"its":[121],"entries.":[122]},"counts_by_year":[],"updated_date":"2026-02-07T06:15:42.627816","created_date":"2026-02-07T00:00:00"}
