{"id":"https://openalex.org/W7160998469","doi":"https://doi.org/10.48550/arxiv.2605.11558","title":"A Composite Activation Function for Learning Stable Binary Representations","display_name":"A Composite Activation Function for Learning Stable Binary Representations","publication_year":2026,"publication_date":"2026-05-12","ids":{"openalex":"https://openalex.org/W7160998469","doi":"https://doi.org/10.48550/arxiv.2605.11558"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.11558","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.11558","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.2605.11558","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063311287","display_name":"Seokhun Park","orcid":"https://orcid.org/0009-0009-3246-5367"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Park, Seokhun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136047774","display_name":"Choeun Kim","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kim, Choeun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136055761","display_name":"Kwanho Lee","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lee, Kwanho","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136083575","display_name":"Sehyun Park","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Park, Sehyun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029245952","display_name":"Insung Kong","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kong, Insung","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5011264910","display_name":"Yongdai Kim","orcid":"https://orcid.org/0000-0002-9434-5645"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kim, Yongdai","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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.38089999556541443,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.38089999556541443,"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.25200000405311584,"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":0.12240000069141388,"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/heaviside-step-function","display_name":"Heaviside step function","score":0.9320999979972839},{"id":"https://openalex.org/keywords/activation-function","display_name":"Activation function","score":0.7092000246047974},{"id":"https://openalex.org/keywords/sigmoid-function","display_name":"Sigmoid function","score":0.6912000179290771},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6751000285148621},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6172000169754028},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5726000070571899},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.47620001435279846},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.44290000200271606},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.4198000133037567},{"id":"https://openalex.org/keywords/binary-function","display_name":"Binary function","score":0.40549999475479126}],"concepts":[{"id":"https://openalex.org/C7980502","wikidata":"https://www.wikidata.org/wiki/Q322339","display_name":"Heaviside step function","level":2,"score":0.9320999979972839},{"id":"https://openalex.org/C38365724","wikidata":"https://www.wikidata.org/wiki/Q4677469","display_name":"Activation function","level":3,"score":0.7092000246047974},{"id":"https://openalex.org/C81388566","wikidata":"https://www.wikidata.org/wiki/Q526668","display_name":"Sigmoid function","level":3,"score":0.6912000179290771},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6751000285148621},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6172000169754028},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5726000070571899},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5440999865531921},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5202999711036682},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.47620001435279846},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4699000120162964},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.44290000200271606},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.4198000133037567},{"id":"https://openalex.org/C105462591","wikidata":"https://www.wikidata.org/wiki/Q3737844","display_name":"Binary function","level":3,"score":0.40549999475479126},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.39910000562667847},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.3919999897480011},{"id":"https://openalex.org/C155032097","wikidata":"https://www.wikidata.org/wiki/Q798503","display_name":"Backpropagation","level":3,"score":0.37229999899864197},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.36880001425743103},{"id":"https://openalex.org/C188441871","wikidata":"https://www.wikidata.org/wiki/Q7554146","display_name":"Softmax function","level":3,"score":0.36880001425743103},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3686000108718872},{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.36169999837875366},{"id":"https://openalex.org/C66905080","wikidata":"https://www.wikidata.org/wiki/Q17005494","display_name":"Binary classification","level":3,"score":0.3517000079154968},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.335099995136261},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3246000111103058},{"id":"https://openalex.org/C190502265","wikidata":"https://www.wikidata.org/wiki/Q17069496","display_name":"MNIST database","level":3,"score":0.3246000111103058},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3199999928474426},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.3158999979496002},{"id":"https://openalex.org/C37061001","wikidata":"https://www.wikidata.org/wiki/Q3531721","display_name":"Binary Independence Model","level":3,"score":0.2838999927043915},{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.2815999984741211},{"id":"https://openalex.org/C98458673","wikidata":"https://www.wikidata.org/wiki/Q917657","display_name":"Step function","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.2700999975204468},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2696000039577484},{"id":"https://openalex.org/C193828747","wikidata":"https://www.wikidata.org/wiki/Q864118","display_name":"Binary image","level":4,"score":0.26829999685287476},{"id":"https://openalex.org/C34736171","wikidata":"https://www.wikidata.org/wiki/Q918333","display_name":"Preprocessor","level":2,"score":0.26820001006126404},{"id":"https://openalex.org/C149810388","wikidata":"https://www.wikidata.org/wiki/Q5374873","display_name":"Emulation","level":2,"score":0.2669000029563904},{"id":"https://openalex.org/C160633673","wikidata":"https://www.wikidata.org/wiki/Q355198","display_name":"Pixel","level":2,"score":0.26330000162124634},{"id":"https://openalex.org/C53442348","wikidata":"https://www.wikidata.org/wiki/Q745101","display_name":"Content-addressable memory","level":3,"score":0.2549000084400177},{"id":"https://openalex.org/C52622490","wikidata":"https://www.wikidata.org/wiki/Q1026626","display_name":"Feature extraction","level":2,"score":0.2513999938964844}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.11558","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.11558","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.2605.11558","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.11558","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Activation":[0,58],"functions":[1],"play":[2],"a":[3,61,79,91],"central":[4],"role":[5],"in":[6,26,103],"neural":[7,37,119],"networks":[8,38],"by":[9],"shaping":[10],"internal":[11],"representations.":[12,149],"Recently,":[13],"learning":[14],"binary":[15],"activation":[16],"representations":[17],"has":[18],"attracted":[19],"significant":[20],"attention":[21],"due":[22],"to":[23,64,145,169],"their":[24,45],"advantages":[25],"computational":[27],"and":[28,85,116,155],"memory":[29],"efficiency,":[30],"as":[31,33,44,78],"well":[32],"interpretability.":[34],"However,":[35],"training":[36,71],"with":[39,72,127],"Heaviside":[40,66,118],"activations":[41],"remains":[42],"challenging,":[43],"non-differentiability":[46],"obstructs":[47],"standard":[48,173],"gradient-based":[49,73,128],"optimization.":[50,74,129],"In":[51],"this":[52],"paper,":[53],"we":[54,131],"propose":[55],"Heavy":[56],"Tailed":[57],"Function":[59],"(HTAF),":[60],"smooth":[62],"approximation":[63],"the":[65,104],"function":[67,84],"that":[68,88,109,142,159],"enables":[69,161],"stable":[70,162],"We":[75,107],"construct":[76],"HTAF":[77,126,144],"sigmoid":[80],"hyperbolic":[81],"tangent":[82],"composite":[83],"theoretically":[86],"show":[87,108],"it":[89],"maintains":[90],"large":[92],"gradient":[93,101],"mass":[94],"around":[95],"zero":[96],"inputs":[97],"while":[98,164],"exhibiting":[99],"slower":[100],"decay":[102],"tail":[105],"regions.":[106],"Spiking":[110],"Neural":[111,114],"Networks,":[112],"Binary":[113],"Networks":[115,120],"Deep":[117],"can":[121],"be":[122],"trained":[123],"stably":[124],"using":[125],"Finally,":[130],"introduce":[132],"Implicit":[133],"Concept":[134],"Bottleneck":[135],"Models":[136],"(ICBMs),":[137],"an":[138],"interpretable":[139],"image":[140,156],"model":[141],"leverages":[143],"induce":[146],"discrete":[147],"feature":[148],"Extensive":[150],"experiments":[151],"across":[152],"various":[153],"architectures":[154],"datasets":[157],"demonstrate":[158],"ICBM":[160],"discretization":[163],"achieving":[165],"prediction":[166],"performance":[167],"comparable":[168],"or":[170],"better":[171],"than":[172],"models.":[174]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-14T00:00:00"}