{"id":"https://openalex.org/W7170350809","doi":"https://doi.org/10.1186/s12859-026-06538-5","title":"Residual-stream geometry of single-cell foundation models carries incremental gene-regulatory signal across tissues","display_name":"Residual-stream geometry of single-cell foundation models carries incremental gene-regulatory signal across tissues","publication_year":2026,"publication_date":"2026-07-24","ids":{"openalex":"https://openalex.org/W7170350809","doi":"https://doi.org/10.1186/s12859-026-06538-5","pmid":"https://pubmed.ncbi.nlm.nih.gov/42527907"},"language":"en","primary_location":{"id":"doi:10.1186/s12859-026-06538-5","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s12859-026-06538-5","pdf_url":null,"source":{"id":"https://openalex.org/S19032547","display_name":"BMC Bioinformatics","issn_l":"1471-2105","issn":["1471-2105"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320256","host_organization_name":"BioMed Central","host_organization_lineage":["https://openalex.org/P4310320256","https://openalex.org/P4310319965"],"host_organization_lineage_names":["BioMed Central","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BMC Bioinformatics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1186/s12859-026-06538-5","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5143574433","display_name":"Ihor Kendiukhov","orcid":null},"institutions":[{"id":"https://openalex.org/I8087733","display_name":"University of T\u00fcbingen","ror":"https://ror.org/03a1kwz48","country_code":"DE","type":"education","lineage":["https://openalex.org/I8087733"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Ihor Kendiukhov","raw_affiliation_strings":["Institute of Medical Genetics and Applied Genomics, University of T\u00fcbingen, T\u00fcbingen, Germany. ihor.kendiukhov@student.uni-tuebingen.de"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Medical Genetics and Applied Genomics, University of T\u00fcbingen, T\u00fcbingen, Germany. ihor.kendiukhov@student.uni-tuebingen.de","institution_ids":["https://openalex.org/I8087733"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5143574433"],"corresponding_institution_ids":["https://openalex.org/I8087733"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.71976161,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11289","display_name":"Single-cell and spatial transcriptomics","score":0.8852999806404114,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T11289","display_name":"Single-cell and spatial transcriptomics","score":0.8852999806404114,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10505","display_name":"Pluripotent Stem Cells Research","score":0.05380000174045563,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.02370000071823597,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.42250001430511475},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.39500001072883606},{"id":"https://openalex.org/keywords/encode","display_name":"ENCODE","score":0.3711000084877014},{"id":"https://openalex.org/keywords/expression","display_name":"Expression (computer science)","score":0.36910000443458557},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.3626999855041504},{"id":"https://openalex.org/keywords/dna-microarray","display_name":"DNA microarray","score":0.3495999872684479},{"id":"https://openalex.org/keywords/gene-expression","display_name":"Gene expression","score":0.3456000089645386},{"id":"https://openalex.org/keywords/transcription","display_name":"Transcription (linguistics)","score":0.3452000021934509},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.3353999853134155}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49729999899864197},{"id":"https://openalex.org/C70721500","wikidata":"https://www.wikidata.org/wiki/Q177005","display_name":"Computational biology","level":1,"score":0.46650001406669617},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.45249998569488525},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.44339999556541443},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.427700012922287},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.42250001430511475},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.39500001072883606},{"id":"https://openalex.org/C66746571","wikidata":"https://www.wikidata.org/wiki/Q1134833","display_name":"ENCODE","level":3,"score":0.3711000084877014},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.36910000443458557},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.3626999855041504},{"id":"https://openalex.org/C95371953","wikidata":"https://www.wikidata.org/wiki/Q591745","display_name":"DNA microarray","level":4,"score":0.3495999872684479},{"id":"https://openalex.org/C150194340","wikidata":"https://www.wikidata.org/wiki/Q26972","display_name":"Gene expression","level":3,"score":0.3456000089645386},{"id":"https://openalex.org/C179926584","wikidata":"https://www.wikidata.org/wiki/Q207714","display_name":"Transcription (linguistics)","level":2,"score":0.3452000021934509},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.3353999853134155},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.3319999873638153},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.3125999867916107},{"id":"https://openalex.org/C165864922","wikidata":"https://www.wikidata.org/wiki/Q411391","display_name":"Regulation of gene expression","level":3,"score":0.3000999987125397},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.29910001158714294},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.29739999771118164},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.2964000105857849},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.2953999936580658},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.29260000586509705},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2831999957561493},{"id":"https://openalex.org/C16345878","wikidata":"https://www.wikidata.org/wiki/Q107472979","display_name":"Orientation (vector space)","level":2,"score":0.2777000069618225},{"id":"https://openalex.org/C95623464","wikidata":"https://www.wikidata.org/wiki/Q1096149","display_name":"Classifier (UML)","level":2,"score":0.2648000121116638},{"id":"https://openalex.org/C67339327","wikidata":"https://www.wikidata.org/wiki/Q1502576","display_name":"Gene regulatory network","level":4,"score":0.26100000739097595},{"id":"https://openalex.org/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.26010000705718994},{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.25769999623298645},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.2574000060558319}],"mesh":[{"descriptor_ui":"D005786","descriptor_name":"Gene Expression Regulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D005786","descriptor_name":"Gene Expression Regulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D005786","descriptor_name":"Gene Expression Regulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D014157","descriptor_name":"Transcription Factors","qualifier_ui":"Q000378","qualifier_name":"metabolism","is_major_topic":false},{"descriptor_ui":"D014157","descriptor_name":"Transcription Factors","qualifier_ui":"Q000378","qualifier_name":"metabolism","is_major_topic":false},{"descriptor_ui":"D014157","descriptor_name":"Transcription Factors","qualifier_ui":"Q000378","qualifier_name":"metabolism","is_major_topic":false},{"descriptor_ui":"D019295","descriptor_name":"Computational Biology","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":true},{"descriptor_ui":"D019295","descriptor_name":"Computational Biology","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":true},{"descriptor_ui":"D019295","descriptor_name":"Computational Biology","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":true},{"descriptor_ui":"D053263","descriptor_name":"Gene Regulatory Networks","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D053263","descriptor_name":"Gene Regulatory Networks","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D053263","descriptor_name":"Gene Regulatory Networks","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D059010","descriptor_name":"Single-Cell Analysis","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":true},{"descriptor_ui":"D059010","descriptor_name":"Single-Cell Analysis","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":true},{"descriptor_ui":"D059010","descriptor_name":"Single-Cell Analysis","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":true}],"locations_count":4,"locations":[{"id":"doi:10.1186/s12859-026-06538-5","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s12859-026-06538-5","pdf_url":null,"source":{"id":"https://openalex.org/S19032547","display_name":"BMC Bioinformatics","issn_l":"1471-2105","issn":["1471-2105"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320256","host_organization_name":"BioMed Central","host_organization_lineage":["https://openalex.org/P4310320256","https://openalex.org/P4310319965"],"host_organization_lineage_names":["BioMed Central","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BMC Bioinformatics","raw_type":"journal-article"},{"id":"pmid:42527907","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/42527907","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BMC bioinformatics","raw_type":"Journal Article"},{"id":"pmh:oai:doaj.org/article:309243cfa4964a19b47a7c38878a88ab","is_oa":false,"landing_page_url":"https://doaj.org/article/309243cfa4964a19b47a7c38878a88ab","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"BMC Bioinformatics, Vol 27, Iss 1 (2026)","raw_type":"article"},{"id":"pmh:oai:pubmedcentral.nih.gov:13418759","is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13418759/","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"BMC Bioinformatics","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1186/s12859-026-06538-5","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s12859-026-06538-5","pdf_url":null,"source":{"id":"https://openalex.org/S19032547","display_name":"BMC Bioinformatics","issn_l":"1471-2105","issn":["1471-2105"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320256","host_organization_name":"BioMed Central","host_organization_lineage":["https://openalex.org/P4310320256","https://openalex.org/P4310319965"],"host_organization_lineage_names":["BioMed Central","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BMC Bioinformatics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320333403","display_name":"Universit\u00e4tsklinikum T\u00fcbingen","ror":"https://ror.org/00pjgxh97"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W2043793366","https://openalex.org/W2061425021","https://openalex.org/W2062029454","https://openalex.org/W2076513103","https://openalex.org/W2157523980","https://openalex.org/W2616922646","https://openalex.org/W2782454362","https://openalex.org/W2946417913","https://openalex.org/W2997831639","https://openalex.org/W3007309629","https://openalex.org/W3082292479","https://openalex.org/W3133458480","https://openalex.org/W4297243391","https://openalex.org/W4378838672","https://openalex.org/W4392168151"],"related_works":[],"abstract_inverted_index":{"BACKGROUND:":[0],"Single-cell":[1],"foundation":[2],"models":[3,33],"such":[4],"as":[5,325],"scGPT":[6,65],"and":[7,66,109,115,123,132,164,167,171,183,197,257,290,315,333],"Geneformer":[8,67,223],"learn":[9],"rich":[10],"representations":[11,19],"of":[12,48,208,233,266],"gene":[13,21,82,268],"expression":[14,95],"programs,":[15],"but":[16,175],"whether":[17,49,78],"these":[18,32],"encode":[20],"regulatory":[22,56,252,269,309],"relationships":[23],"beyond":[24,94],"expression-level":[25],"confounds":[26],"remains":[27],"unclear.":[28],"Attention":[29],"patterns":[30],"in":[31,64,107,129,201,231,336],"have":[34],"been":[35],"shown":[36],"to":[37,162,168,190,218],"capture":[38],"co-expression":[39],"rather":[40,242,305],"than":[41,243,306],"direct":[42],"regulation,":[43],"leaving":[44],"open":[45],"the":[46,52,73,133,177,206,221,258],"question":[47],"deeper":[50],"representations-particularly":[51],"residual":[53,228,278],"stream-contain":[54],"genuine":[55],"information.":[57],"RESULTS:":[58],"We":[59],"systematically":[60],"investigated":[61],"residual-stream":[62,215],"geometry":[63],"across":[68,288],"four":[69,234],"tissue":[70],"contexts":[71],"from":[72],"Tabula":[74],"Sapiens":[75],"atlas,":[76],"evaluating":[77],"geometric":[79,101,249,259,283],"proximity":[80],"between":[81,187],"vectors":[83],"provides":[84],"incremental":[85,105,262],"predictive":[86],"value":[87,263],"for":[88,296,330],"curated":[89],"TRRUST":[90],"transcription":[91,181],"factor-target":[92],"edges":[93],"confounds.":[96],"Under":[97],"repeated":[98],"stratified":[99],"cross-validation,":[100],"features":[102,250],"provided":[103],"significant":[104,200],"signal":[106,128,260,284,301],"kidney":[108,202],"immune":[110,144],"settings,":[111],"validated":[112],"by":[113],"label-permutation":[114],"geometry-shuffle":[116],"null":[117],"controls;":[118],"centered-cosine":[119],"similarity,":[120],"PCA":[121],"projection":[122],"multi-layer":[124,134],"bundling":[125],"recovered":[126],"comparable":[127,213],"lung":[130,147,151],"tissues,":[131],"bundle":[135],"improved":[136],"every":[137],"domain":[138],"(kidney":[139],"\u0394AUROC":[140],"=":[141],"+":[142,145,148,152,195],"0.122,":[143],"0.042,":[146],"0.028,":[149],"external":[150],"0.027;":[153],"geometry-augmented":[154],"AUROC":[155],"0.60-0.69).":[156],"The":[157,300],"effect":[158],"was":[159],"fully":[160],"robust":[161],"leave-TF-out":[163],"leave-target-out":[165],"cross-validation":[166],"harder":[169],"degree-":[170],"expression-matched":[172],"negative":[173],"edges,":[174],"under":[176],"stricter":[178],"leave-both-out":[179],"split-no":[180],"factor":[182],"no":[184],"target":[185],"shared":[186],"folds-it":[188],"collapsed":[189],"near-zero":[191],"(\u0394AUROC":[192],"at":[193],"most":[194],"0.003,":[196],"not":[198],"statistically":[199],"or":[203],"immune),":[204],"marking":[205],"ceiling":[207],"out-of-entity":[209,316],"generalization.":[210],"With":[211],"a":[212,244,307],"per-layer":[214],"extraction":[216],"applied":[217],"both":[219],"models,":[220],"apparent":[222],"advantage":[224],"mostly":[225],"disappeared":[226],"(small":[227],"gaps":[229],"remained":[230],"three":[232],"domains),":[235],"indicating":[236],"it":[237],"largely":[238],"reflected":[239],"representation-construction":[240],"choices":[241],"substantial":[245],"architectural":[246],"difference.":[247],"Asymmetric":[248],"predicted":[251],"edge":[253,298,331],"orientation":[254],"(AUROC":[255],"0.80-0.90),":[256],"added":[261],"on":[264],"top":[265],"expression-based":[267,293],"network":[270],"(GRN)":[271],"inference":[272,295],"(GENIE3,":[273],"co-expression).":[274],"CONCLUSION:":[275],"Foundation":[276],"model":[277],"streams":[279],"carry":[280],"incremental,":[281],"regulatory-relevant":[282],"that":[285,291],"is":[286,302,313,318,324],"distributed":[287],"layers":[289],"complements":[292],"GRN":[294],"retrospective":[297],"prioritization.":[299],"statistical":[303],"enrichment":[304],"stand-alone":[308],"classifier:":[310],"absolute":[311],"performance":[312],"modest":[314],"generalization":[317],"limited,":[319],"so":[320],"its":[321],"practical":[322],"role":[323],"an":[326],"orthogonal":[327],"evidence":[328],"channel":[329],"re-ranking":[332],"hypothesis":[334],"prioritization":[335],"multi-evidence":[337],"frameworks.":[338]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2026-07-25T00:00:00"}
