{"id":"https://openalex.org/W4367189403","doi":"https://doi.org/10.48550/arxiv.2304.13061","title":"iMixer: hierarchical Hopfield network implies an invertible, implicit and iterative MLP-Mixer","display_name":"iMixer: hierarchical Hopfield network implies an invertible, implicit and iterative MLP-Mixer","publication_year":2023,"publication_date":"2023-04-25","ids":{"openalex":"https://openalex.org/W4367189403","doi":"https://doi.org/10.48550/arxiv.2304.13061"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2304.13061","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2304.13061","pdf_url":"https://arxiv.org/pdf/2304.13061","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2304.13061","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047076115","display_name":"Toshihiro Ota","orcid":"https://orcid.org/0000-0002-7303-5648","observed_orcids":["https://orcid.org/0000-0002-7303-5648"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ota, Toshihiro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5084053028","display_name":"Masato Taki","orcid":"https://orcid.org/0000-0002-5375-7862","observed_orcids":["https://orcid.org/0000-0002-5375-7862"]},"institutions":[{"id":"https://openalex.org/I133557312","display_name":"Rikkyo University","ror":"https://ror.org/00x194q47","country_code":"JP","type":"education","lineage":["https://openalex.org/I133557312"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Taki, Masato","raw_affiliation_strings":["Rikkyo University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rikkyo University","institution_ids":["https://openalex.org/I133557312"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":3,"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":0.8457000255584717,"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":0.8457000255584717,"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/T10320","display_name":"Neural Networks and Applications","score":0.1103999987244606,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.01549999974668026,"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/mlp-mixer","display_name":"MLP-Mixer","score":0.9810000061988831},{"id":"https://openalex.org/keywords/invertible-neural-networks","display_name":"invertible neural networks","score":0.8009999990463257},{"id":"https://openalex.org/keywords/implicit-neural-representations","display_name":"implicit neural representations","score":0.6800000071525574},{"id":"https://openalex.org/keywords/image-classification","display_name":"image classification","score":0.7749999761581421}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6985170841217041},{"id":"https://openalex.org/C66322947","wikidata":"https://www.wikidata.org/wiki/Q11658","display_name":"Transformer","level":3,"score":0.6967161297798157},{"id":"https://openalex.org/C46421273","wikidata":"https://www.wikidata.org/wiki/Q1407668","display_name":"Hopfield network","level":3,"score":0.6897794604301453},{"id":"https://openalex.org/C197352929","wikidata":"https://www.wikidata.org/wiki/Q1074074","display_name":"Inductive bias","level":4,"score":0.6449340581893921},{"id":"https://openalex.org/C38858127","wikidata":"https://www.wikidata.org/wiki/Q5441228","display_name":"Feed forward","level":2,"score":0.5518506169319153},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.5354578495025635},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5142902731895447},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.510994553565979},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4494301676750183},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.43535077571868896},{"id":"https://openalex.org/C53442348","wikidata":"https://www.wikidata.org/wiki/Q745101","display_name":"Content-addressable memory","level":3,"score":0.41747233271598816},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4017545282840729},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.36508941650390625},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3519465923309326},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.19064953923225403},{"id":"https://openalex.org/C28006648","wikidata":"https://www.wikidata.org/wiki/Q6934509","display_name":"Multi-task learning","level":3,"score":0.16408056020736694},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.10560774803161621},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.09319022297859192},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.07258987426757812},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.06526967883110046},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0},{"id":"https://openalex.org/C201995342","wikidata":"https://www.wikidata.org/wiki/Q682496","display_name":"Systems engineering","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2304.13061","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2304.13061","pdf_url":"https://arxiv.org/pdf/2304.13061","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2304.13061","doi":"https://doi.org/10.48550/arxiv.2304.13061","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2304.13061","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,"listed_in":[],"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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2304.13061","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2304.13061","pdf_url":"https://arxiv.org/pdf/2304.13061","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4367189403.pdf","grobid_xml":"https://content.openalex.org/works/W4367189403.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W2746314669","https://openalex.org/W3122855748","https://openalex.org/W3158846111","https://openalex.org/W3182042768","https://openalex.org/W7133218158"],"related_works":["https://openalex.org/W4399836922","https://openalex.org/W3157506437","https://openalex.org/W2136221963","https://openalex.org/W4299731259","https://openalex.org/W7160852149","https://openalex.org/W4221151141","https://openalex.org/W3127151792","https://openalex.org/W4417095160","https://openalex.org/W3196691776","https://openalex.org/W3169210662"],"abstract_inverted_index":{"In":[0,76],"the":[1,5,14,26,51,68,72,81,84,112,116,121,135,165,173,176,180],"last":[2],"few":[3],"years,":[4],"success":[6],"of":[7,16,71,96,126,192],"Transformers":[8,60],"in":[9],"computer":[10],"vision":[11],"has":[12],"stimulated":[13],"discovery":[15],"many":[17],"alternative":[18],"models":[19,34,58,182],"that":[20,108,147,172],"compete":[21],"with":[22,138],"Transformers,":[23],"such":[24],"as":[25,123,184],"MLP-Mixer.":[27,168],"Despite":[28],"their":[29],"weak":[30],"inductive":[31],"bias,":[32],"these":[33],"have":[35],"achieved":[36],"performance":[37,137,159],"comparable":[38,160],"to":[39,83,115,161],"well-studied":[40],"convolutional":[41],"neural":[42,102],"networks.":[43],"Recent":[44],"studies":[45],"on":[46,67,141],"modern":[47],"Hopfield":[48,88,177],"networks":[49,178],"suggest":[50],"correspondence":[52,82,174],"between":[53,175],"certain":[54],"energy-based":[55],"associative":[56],"memory":[57],"and":[59,63,90,129,145,157,179],"or":[61,162],"MLP-Mixer,":[62],"shed":[64],"some":[65],"light":[66],"theoretical":[69],"background":[70],"Transformer-type":[73],"architectures":[74],"design.":[75],"this":[77],"paper,":[78],"we":[79],"generalize":[80],"recently":[85],"introduced":[86],"hierarchical":[87],"network,":[89],"find":[91,146],"iMixer,":[92,148],"a":[93,185,189],"novel":[94],"generalization":[95],"MLP-Mixer":[97],"model.":[98],"Unlike":[99],"ordinary":[100],"feedforward":[101],"networks,":[103],"iMixer":[104],"involves":[105],"MLP":[106],"layers":[107],"propagate":[109],"forward":[110],"from":[111],"output":[113],"side":[114],"input":[117],"side.":[118],"We":[119,133],"characterize":[120],"module":[122],"an":[124],"example":[125],"invertible,":[127],"implicit,":[128],"iterative":[130],"mixing":[131],"module.":[132],"evaluate":[134],"model":[136],"various":[139],"datasets":[140],"image":[142],"classification":[143],"tasks,":[144],"despite":[149],"its":[150],"unique":[151],"architecture,":[152],"exhibits":[153],"stable":[154],"learning":[155],"capabilities":[156],"achieves":[158],"better":[163],"than":[164],"baseline":[166],"vanilla":[167],"The":[169],"results":[170],"imply":[171],"Mixer":[181],"serves":[183],"principle":[186],"for":[187],"understanding":[188],"broader":[190],"class":[191],"Transformer-like":[193],"architecture":[194],"designs.":[195]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2023-04-28T00:00:00"}