{"id":"https://openalex.org/W7160078252","doi":"https://doi.org/10.48550/arxiv.2605.00082","title":"Hyperspherical Forward-Forward with Prototypical Representations","display_name":"Hyperspherical Forward-Forward with Prototypical Representations","publication_year":2026,"publication_date":"2026-04-30","ids":{"openalex":"https://openalex.org/W7160078252","doi":"https://doi.org/10.48550/arxiv.2605.00082"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.00082","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.00082","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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.2605.00082","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102659002","display_name":"Shalini Sarode","orcid":"https://orcid.org/0009-0007-9968-4068"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sarode, Shalini","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135275370","display_name":"Brian Moser","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Moser, Brian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039686567","display_name":"Joachim Folz","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Folz, Joachim","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029509133","display_name":"Federico Raue","orcid":"https://orcid.org/0000-0002-8604-6207"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Raue, Federico","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5099038777","display_name":"Tobias Nauen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nauen, Tobias","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053202923","display_name":"Stanislav Frolov","orcid":"https://orcid.org/0000-0003-2700-5031"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Frolov, Stanislav","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5135213106","display_name":"Andreas Dengel","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dengel, Andreas","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/T10036","display_name":"Advanced Neural Network Applications","score":0.30880001187324524,"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"}},"topics":[{"id":"https://openalex.org/T10036","display_name":"Advanced Neural Network Applications","score":0.30880001187324524,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.2689000070095062,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.06920000165700912,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.6233000159263611},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5532000064849854},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5385000109672546},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.5181000232696533},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.49380001425743103},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.4864000082015991},{"id":"https://openalex.org/keywords/core","display_name":"Core (optical fiber)","score":0.4284000098705292},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.42640000581741333},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4198000133037567}],"concepts":[{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.6233000159263611},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5885999798774719},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5532000064849854},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5385000109672546},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.5181000232696533},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.49869999289512634},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.49380001425743103},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.4864000082015991},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4713999927043915},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.4284000098705292},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.42640000581741333},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4198000133037567},{"id":"https://openalex.org/C2778775528","wikidata":"https://www.wikidata.org/wiki/Q5135432","display_name":"Closing (real estate)","level":2,"score":0.38499999046325684},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3564000129699707},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.35600000619888306},{"id":"https://openalex.org/C187029079","wikidata":"https://www.wikidata.org/wiki/Q958679","display_name":"Cognitive reframing","level":2,"score":0.3553999960422516},{"id":"https://openalex.org/C2779227376","wikidata":"https://www.wikidata.org/wiki/Q6505497","display_name":"Layer (electronics)","level":2,"score":0.3366999924182892},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3346000015735626},{"id":"https://openalex.org/C2777168461","wikidata":"https://www.wikidata.org/wiki/Q42196253","display_name":"Set operations","level":3,"score":0.31779998540878296},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.3163999915122986},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.31209999322891235},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.31040000915527344},{"id":"https://openalex.org/C52622490","wikidata":"https://www.wikidata.org/wiki/Q1026626","display_name":"Feature extraction","level":2,"score":0.29440000653266907},{"id":"https://openalex.org/C66905080","wikidata":"https://www.wikidata.org/wiki/Q17005494","display_name":"Binary classification","level":3,"score":0.2897000014781952},{"id":"https://openalex.org/C2777472644","wikidata":"https://www.wikidata.org/wiki/Q16968992","display_name":"Approximate inference","level":3,"score":0.28540000319480896},{"id":"https://openalex.org/C75294576","wikidata":"https://www.wikidata.org/wiki/Q5165192","display_name":"Contextual image classification","level":3,"score":0.2809000015258789},{"id":"https://openalex.org/C175154964","wikidata":"https://www.wikidata.org/wiki/Q380077","display_name":"Task analysis","level":3,"score":0.2800000011920929},{"id":"https://openalex.org/C160633673","wikidata":"https://www.wikidata.org/wiki/Q355198","display_name":"Pixel","level":2,"score":0.27230000495910645},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.2653000056743622},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2599000036716461},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.2565999925136566},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.2554999887943268}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.00082","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.00082","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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.2605.00082","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.00082","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":[{"score":0.6507705450057983,"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"Forward-Forward":[1,42],"(FF)":[2],"algorithm":[3],"presents":[4],"a":[5,18,25,44,65,70,76,85,115],"compelling,":[6],"bio-inspired":[7],"alternative":[8],"to":[9,56,69,132,136,164],"backpropagation.":[10,153],"However,":[11],"while":[12,108],"efficient":[13],"in":[14,114],"training,":[15],"it":[16,120],"has":[17],"computationally":[19],"prohibitive":[20],"inference":[21,113],"process":[22],"that":[23,32,47,91],"requires":[24],"separate":[26],"forward":[27,117],"pass":[28],"for":[29],"every":[30],"class":[31],"is":[33,55,130],"evaluated.":[34],"In":[35],"this":[36,49,82],"work,":[37],"we":[38,156],"introduce":[39],"the":[40,58,103,124,150,159],"Hyperspherical":[41],"(HFF),":[43],"novel":[45],"reformulation":[46],"resolves":[48],"critical":[50],"bottleneck.":[51],"Our":[52,128],"core":[53],"innovation":[54,101],"reframe":[57],"local":[59,106],"objective":[60],"of":[61,87,105],"each":[62],"layer":[63],"from":[64],"binary":[66],"goodness-of-fit":[67],"task":[68],"direct":[71],"multi-class":[72],"classification":[73,147],"problem":[74],"within":[75],"hyperspherical":[77],"feature":[78],"space.":[79],"We":[80],"achieve":[81],"by":[83],"learning":[84],"set":[86],"class-specific,":[88],"unit-norm":[89],"prototypes":[90],"act":[92],"as":[93],"geometric":[94],"anchors":[95],"and":[96,112,140,172],"implicit":[97],"negatives.":[98],"This":[99],"architectural":[100],"preserves":[102],"benefits":[104],"training":[107],"enabling":[109],"weight":[110],"update":[111],"single":[116],"pass,":[118],"making":[119],">40x":[121],"faster":[122],"than":[123],"original":[125],"FF":[126],"algorithm.":[127],"method":[129],"simple":[131],"implement,":[133],"scales":[134],"effectively":[135],"modern":[137],"convolutional":[138],"architectures,":[139],"achieves":[141],"superior":[142],"accuracy":[143,169],"on":[144,170],"standard":[145],"image":[146],"benchmarks,":[148],"closing":[149],"gap":[151],"with":[152,174],"Most":[154],"notably,":[155],"are":[157],"among":[158],"first":[160],"greedy":[161],"local-learning":[162],"methods":[163],"report":[165],"over":[166],"25%":[167],"top-1":[168],"ImageNet-1k,":[171],"65.96%":[173],"transfer":[175],"learning.":[176]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-05T00:00:00"}