{"id":"https://openalex.org/W7213349633","doi":"https://doi.org/10.48550/arxiv.2609.15498","title":"Same path, different walk: a mechanistic comparison of looped and stacked transformer encoders on 12-lead ECG","display_name":"Same path, different walk: a mechanistic comparison of looped and stacked transformer encoders on 12-lead ECG","publication_year":2026,"publication_date":"2026-09-14","ids":{"openalex":"https://openalex.org/W7213349633","doi":"https://doi.org/10.48550/arxiv.2609.15498"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.15498","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15498","pdf_url":"https://arxiv.org/pdf/2609.15498","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.15498","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135934466","display_name":"Pawel Olszowiec","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210128738","display_name":"Samsung (Poland)","ror":"https://ror.org/0381acm07","country_code":"PL","type":"company","lineage":["https://openalex.org/I2250650973","https://openalex.org/I4210128738"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Olszowiec, Pawel","raw_affiliation_strings":["Samsung AI Center , Warsaw , Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Samsung AI Center , Warsaw , Poland","institution_ids":["https://openalex.org/I4210128738"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084262755","display_name":"Micha\u0142 Byra","orcid":"https://orcid.org/0000-0002-5759-2516","observed_orcids":["https://orcid.org/0000-0002-5759-2516"]},"institutions":[{"id":"https://openalex.org/I4210128738","display_name":"Samsung (Poland)","ror":"https://ror.org/0381acm07","country_code":"PL","type":"company","lineage":["https://openalex.org/I2250650973","https://openalex.org/I4210128738"]},{"id":"https://openalex.org/I99542240","display_name":"Polish Academy of Sciences","ror":"https://ror.org/01dr6c206","country_code":"PL","type":"government","lineage":["https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Byra, Michal","raw_affiliation_strings":["IFTR , Polish Academy of Sciences , Warsaw , Poland","Samsung AI Center , Warsaw , Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IFTR , Polish Academy of Sciences , Warsaw , Poland","institution_ids":["https://openalex.org/I99542240"]},{"raw_affiliation_string":"Samsung AI Center , Warsaw , Poland","institution_ids":["https://openalex.org/I4210128738"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135975836","display_name":"Grzegorz Gruszczynski","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210128738","display_name":"Samsung (Poland)","ror":"https://ror.org/0381acm07","country_code":"PL","type":"company","lineage":["https://openalex.org/I2250650973","https://openalex.org/I4210128738"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Gruszczynski, Grzegorz","raw_affiliation_strings":["Samsung AI Center , Warsaw , Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Samsung AI Center , Warsaw , Poland","institution_ids":["https://openalex.org/I4210128738"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061412045","display_name":"Grzegorz Stefa\u0144ski","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210128738","display_name":"Samsung (Poland)","ror":"https://ror.org/0381acm07","country_code":"PL","type":"company","lineage":["https://openalex.org/I2250650973","https://openalex.org/I4210128738"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Stefanski, Grzegorz","raw_affiliation_strings":["Samsung AI Center , Warsaw , Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Samsung AI Center , Warsaw , Poland","institution_ids":["https://openalex.org/I4210128738"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085509906","display_name":"Alberto Presta","orcid":"https://orcid.org/0000-0001-6590-3604","observed_orcids":["https://orcid.org/0000-0001-6590-3604"]},"institutions":[{"id":"https://openalex.org/I4210128738","display_name":"Samsung (Poland)","ror":"https://ror.org/0381acm07","country_code":"PL","type":"company","lineage":["https://openalex.org/I2250650973","https://openalex.org/I4210128738"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Presta, Alberto","raw_affiliation_strings":["Samsung AI Center , Warsaw , Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Samsung AI Center , Warsaw , Poland","institution_ids":["https://openalex.org/I4210128738"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T11021","display_name":"ECG Monitoring and Analysis","score":0.9750999808311462,"subfield":{"id":"https://openalex.org/subfields/2705","display_name":"Cardiology and Cardiovascular Medicine"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T11021","display_name":"ECG Monitoring and Analysis","score":0.9750999808311462,"subfield":{"id":"https://openalex.org/subfields/2705","display_name":"Cardiology and Cardiovascular Medicine"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T13702","display_name":"Machine Learning in Healthcare","score":0.007600000128149986,"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":0.002400000113993883,"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/recurrent-transformer","display_name":"recurrent transformer","score":0.6769999861717224},{"id":"https://openalex.org/keywords/vision-transformer","display_name":"vision transformer","score":0.6299999952316284},{"id":"https://openalex.org/keywords/12-lead-electrocardiogram","display_name":"12-lead ECG","score":0.875},{"id":"https://openalex.org/keywords/ecg-classification","display_name":"ECG classification","score":0.8429999947547913},{"id":"https://openalex.org/keywords/ptb-xl","display_name":"PTB-XL","score":0.7950000166893005},{"id":"https://openalex.org/keywords/parameter-efficiency","display_name":"parameter efficiency","score":0.722000002861023},{"id":"https://openalex.org/keywords/latent-representations","display_name":"latent representations","score":0.7689999938011169},{"id":"https://openalex.org/keywords/geometric-similarity","display_name":"geometric similarity","score":0.5419999957084656},{"id":"https://openalex.org/keywords/training-dynamics","display_name":"training dynamics","score":0.6259999871253967},{"id":"https://openalex.org/keywords/out-of-distribution-generalization","display_name":"out-of-distribution generalization","score":0.7279999852180481},{"id":"https://openalex.org/keywords/representation-collapse","display_name":"representation collapse","score":0.7020000219345093}],"concepts":[{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.605400025844574},{"id":"https://openalex.org/C118505674","wikidata":"https://www.wikidata.org/wiki/Q42586063","display_name":"Encoder","level":2,"score":0.5687999725341797},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5557000041007996},{"id":"https://openalex.org/C66322947","wikidata":"https://www.wikidata.org/wiki/Q11658","display_name":"Transformer","level":3,"score":0.5501999855041504},{"id":"https://openalex.org/C33347731","wikidata":"https://www.wikidata.org/wiki/Q285210","display_name":"Stacking","level":2,"score":0.545799970626831},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5066999793052673},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.4025000035762787},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.39879998564720154},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.3799000084400177},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.3693000078201294},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.33730000257492065},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.3280999958515167},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.31299999356269836},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30250000953674316},{"id":"https://openalex.org/C59404180","wikidata":"https://www.wikidata.org/wiki/Q17013334","display_name":"Feature learning","level":2,"score":0.29899999499320984},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2987000048160553},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.2912999987602234},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.28940001130104065},{"id":"https://openalex.org/C206588197","wikidata":"https://www.wikidata.org/wiki/Q846574","display_name":"Reuse","level":2,"score":0.2863999903202057},{"id":"https://openalex.org/C52622490","wikidata":"https://www.wikidata.org/wiki/Q1026626","display_name":"Feature extraction","level":2,"score":0.2824999988079071},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.26660001277923584},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.25119999051094055}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.15498","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15498","pdf_url":"https://arxiv.org/pdf/2609.15498","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.2609.15498","doi":"https://doi.org/10.48550/arxiv.2609.15498","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.15498","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:2609.15498","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15498","pdf_url":"https://arxiv.org/pdf/2609.15498","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":[{"id":"https://openalex.org/F4320332195","display_name":"Samsung","ror":"https://ror.org/04w3jy968"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213349633.pdf","grobid_xml":"https://content.openalex.org/works/W7213349633.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4415798219","https://openalex.org/W7196947222","https://openalex.org/W7155494834","https://openalex.org/W7160448695","https://openalex.org/W7214422038","https://openalex.org/W7154745101","https://openalex.org/W4415332328","https://openalex.org/W7160917974","https://openalex.org/W4207081024","https://openalex.org/W7128775486"],"abstract_inverted_index":{"Recurrent":[0],"Transformers":[1],"reusing":[2],"their":[3,17,105],"weights":[4],"rather":[5],"than":[6],"stacking":[7],"$L$":[8,52],"distinct":[9],"layers":[10],"are":[11],"becoming":[12],"widely":[13],"adopted":[14],"due":[15],"to":[16],"parameter":[18,80],"efficiency":[19],"[1,2,3].":[20],"However,":[21],"the":[22,42,70,123],"exact":[23],"representational":[24],"and":[25,30,59,113,133],"dynamical":[26],"differences":[27],"between":[28],"looped":[29],"stacked":[31],"architectures":[32,94],"remain":[33],"uncharacterized.":[34],"This":[35],"paper":[36],"presents":[37],"a":[38],"controlled":[39],"study":[40],"on":[41,63],"example":[43],"of":[44,131],"bViT":[45,58,82,108],"model":[46],"[1]":[47],"applying":[48],"one":[49],"weight-tied":[50],"block":[51],"times.":[53],"We":[54],"train":[55],"two":[56],"models:":[57],"standard":[60],"ViT":[61,127],"[4]":[62],"12-lead":[64],"electrocardiogram":[65],"(ECG)":[66],"classification":[67],"tasks":[68],"from":[69,122],"PTB-XL":[71],"dataset":[72],"under":[73],"identical":[74],"training":[75],"protocols.":[76],"Despite":[77],"an":[78,100],"$8.9\\times$":[79],"reduction,":[81],"achieves":[83],"accuracy":[84],"parity":[85],"with":[86],"ViT.":[87],"Geometric":[88],"similarity":[89],"metrics":[90],"demonstrate":[91],"that":[92],"both":[93],"construct":[95],"comparable":[96],"latent":[97],"representations":[98,132],"in":[99],"equivalent":[101],"canonical":[102],"order.":[103],"Crucially,":[104],"dynamics":[106],"differ:":[107],"exhibits":[109,128],"smaller":[110],"step":[111],"sizes":[112],"inter-patient":[114],"sensitivity,":[115],"as":[116,118],"well":[117],"near-neutral":[119],"behavior":[120],"away":[121],"data":[124],"manifold,":[125],"whereas":[126],"collapsing":[129],"dimensionality":[130],"out-of-distribution":[134],"feature":[135],"expansion.":[136]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-16T00:00:00"}