{"id":"https://openalex.org/W7225322953","doi":"https://doi.org/10.6084/m9.figshare.34922955","title":"Hardware-Accelerated Hypercomplex Learning via OPMT for high arbitrary dimension","display_name":"Hardware-Accelerated Hypercomplex Learning via OPMT for high arbitrary dimension","publication_year":2026,"publication_date":"2026-11-05","ids":{"openalex":"https://openalex.org/W7225322953","doi":"https://doi.org/10.6084/m9.figshare.34922955"},"language":"en","primary_location":{"id":"doi:10.6084/m9.figshare.34922955","doi":"https://doi.org/10.6084/m9.figshare.34922955","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.34922955","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.6084/m9.figshare.34922955","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049133609","display_name":"maher ben abdessalem","orcid":"https://orcid.org/0000-0001-5948-9718","observed_orcids":["https://orcid.org/0000-0001-5948-9718"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"maher ben abdessalem","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-5948-9718","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5049133609"],"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.7426999807357788,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.7426999807357788,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.14329999685287476,"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.05900000035762787,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/cayley-dickson-algebras","display_name":"Cayley-Dickson algebras","score":0.9959999918937683},{"id":"https://openalex.org/keywords/parameter-compression","display_name":"parameter compression","score":0.8069999814033508},{"id":"https://openalex.org/keywords/gpu-kernel-optimization","display_name":"GPU kernel optimization","score":0.7289999723434448},{"id":"https://openalex.org/keywords/cuda","display_name":"CUDA","score":0.5950000286102295},{"id":"https://openalex.org/keywords/structural-regularization","display_name":"structural regularization","score":0.527999997138977},{"id":"https://openalex.org/keywords/noise-robustness","display_name":"noise robustness","score":0.7419999837875366},{"id":"https://openalex.org/keywords/mnist","display_name":"MNIST","score":0.7020000219345093}],"concepts":[{"id":"https://openalex.org/C203249530","wikidata":"https://www.wikidata.org/wiki/Q837414","display_name":"Hypercomplex number","level":3,"score":0.9733999967575073},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6082000136375427},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5982000231742859},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.47839999198913574},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4512999951839447},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.4426000118255615},{"id":"https://openalex.org/C190502265","wikidata":"https://www.wikidata.org/wiki/Q17069496","display_name":"MNIST database","level":3,"score":0.42410001158714294},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.4075999855995178},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.39010000228881836},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.3564999997615814},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.3490999937057495},{"id":"https://openalex.org/C2781137444","wikidata":"https://www.wikidata.org/wiki/Q237105","display_name":"Sharpening","level":2,"score":0.34790000319480896},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3456000089645386},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34380000829696655},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3370000123977661},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.31709998846054077},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.31540000438690186},{"id":"https://openalex.org/C2778119891","wikidata":"https://www.wikidata.org/wiki/Q477690","display_name":"CUDA","level":2,"score":0.30230000615119934},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.3009999990463257},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2946000099182129},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2919999957084656},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2913999855518341},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C53051483","wikidata":"https://www.wikidata.org/wiki/Q861555","display_name":"Cube (algebra)","level":2,"score":0.27709999680519104},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.2750000059604645},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.26989999413490295},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.26260000467300415},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.25189998745918274},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.2500999867916107}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.6084/m9.figshare.34922955","doi":"https://doi.org/10.6084/m9.figshare.34922955","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.34922955","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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"},{"id":"doi:10.6084/m9.figshare.34922955.v1","doi":"https://doi.org/10.6084/m9.figshare.34922955.v1","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.34922955.v1","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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"},{"id":"doi:10.6084/m9.figshare.34922955.v2","doi":"https://doi.org/10.6084/m9.figshare.34922955.v2","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.34922955.v2","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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"},{"id":"doi:10.6084/m9.figshare.34922955.v3","doi":"https://doi.org/10.6084/m9.figshare.34922955.v3","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.34922955.v3","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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"}],"best_oa_location":{"id":"doi:10.6084/m9.figshare.34922955","doi":"https://doi.org/10.6084/m9.figshare.34922955","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.34922955","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7225302545","https://openalex.org/W7171409440","https://openalex.org/W4385991984","https://openalex.org/W4410361499","https://openalex.org/W4312984359","https://openalex.org/W4414517985","https://openalex.org/W3120074043","https://openalex.org/W4387870893","https://openalex.org/W3126659343","https://openalex.org/W3196137477"],"abstract_inverted_index":{"High-dimensional":[0],"hypercomplex":[1,40],"neural":[2],"networks":[3],"utilizing":[4],"Cayley-Dickson":[5],"algebras":[6],"have":[7],"historically":[8],"been":[9],"throttled":[10],"by":[11,133],"computational":[12],"bottlenecks,":[13],"scaling":[14],"quadratically":[15],"$O(N^2)$":[16],"due":[17],"to":[18,96],"recursive":[19],"sign":[20,64],"lookups":[21],"or":[22],"dense":[23,98],"tensor":[24],"storage":[25],"overhead.":[26],"We":[27,66],"use":[28],"Theorem":[29],"(OPMT)":[30],"and":[31,61],"which":[32],"collapses":[33],"the":[34,115,119,148],"spatial":[35],"coordinate":[36],"geometry":[37,117],"of":[38,52,92,118,136],"arbitrary-dimension":[39],"multiplication":[41],"into":[42],"native,":[43],"hardware-level":[44],"bitwise":[45],"operations.":[46],"By":[47],"preserving":[48],"index":[49],"order":[50,135],"instead":[51],"executing":[53],"component":[54],"transposition,":[55],"we":[56],"achieve":[57],"exact":[58],"$\\mathcal{O}(1)$":[59],"constant-time":[60],"$\\mathcal{O}(n)$":[62],"logarithmic-time":[63],"navigation.":[65],"implement":[67],"this":[68],"architecture":[69],"in":[70,138],"an":[71,123,134],"optimized":[72],"GPU":[73],"kernel":[74],"using":[75],"parallelized":[76],"CUDA":[77],"streams.":[78],"Benchmarks":[79],"on":[80],"MNIST":[81],"demonstrate":[82],"that":[83],"our":[84],"Hypercomplex":[85],"(HC)":[86],"engine":[87],"achieves":[88],"a":[89],"parameter":[90],"compression":[91],"over":[93],"86$\\times$":[94],"relative":[95],"standard":[97,128],"fully-connected":[99],"layers":[100],"($12,298$":[101],"parameters":[102],"vs.":[103],"$1,059,850$":[104],"parameters)":[105],"while":[106],"retaining":[107],"$97.05\\%$":[108],"accuracy.":[109],"Furthermore,":[110],"under":[111,147],"extreme":[112],"noise":[113],"conditions,":[114],"architectural":[116],"OPMT":[120],"acts":[121],"as":[122],"intrinsic":[124],"structural":[125],"regularizer,":[126],"outperforming":[127],"Ordinary":[129],"Least":[130],"Squares":[131],"(OLS)":[132],"magnitude":[137],"mean":[139],"squared":[140],"error.":[141],"Our":[142],"software":[143],"framework":[144],"is":[145],"open-sourced":[146],"AGPLv3":[149],"license.":[150]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-11-06T00:00:00"}