{"id":"https://openalex.org/W7128478600","doi":"https://doi.org/10.48550/arxiv.2602.07930","title":"Patches of Nonlinearity: Instruction Vectors in Large Language Models","display_name":"Patches of Nonlinearity: Instruction Vectors in Large Language Models","publication_year":2026,"publication_date":"2026-02-08","ids":{"openalex":"https://openalex.org/W7128478600","doi":"https://doi.org/10.48550/arxiv.2602.07930"},"language":"en","primary_location":{"id":"pmh:oai:tubiblio.ulb.tu-darmstadt.de:159557","is_oa":false,"landing_page_url":"http://tubiblio.ulb.tu-darmstadt.de/view/person/Bigoulaeva=3AIrina=3A=3A.html>","pdf_url":null,"source":{"id":"https://openalex.org/S4377196390","display_name":"TUbilio (Technical University of Darmstadt)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I31512782","host_organization_name":"Technische Universit\u00e4t Darmstadt","host_organization_lineage":["https://openalex.org/I31512782"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"NonPeerReviewed"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081295642","display_name":"Irina Bigoulaeva","orcid":"https://orcid.org/0000-0002-6955-981X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bigoulaeva, Irina","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125512597","display_name":"Jonas Rohweder","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rohweder, Jonas","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Dutta, Subhabrata","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dutta, Subhabrata","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5125533502","display_name":"Iryna Gurevych","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gurevych, Iryna","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5081295642"],"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/T11714","display_name":"Multimodal Machine Learning Applications","score":0.22830000519752502,"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/T11714","display_name":"Multimodal Machine Learning Applications","score":0.22830000519752502,"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/T10028","display_name":"Topic Modeling","score":0.12219999730587006,"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/T10181","display_name":"Natural Language Processing Techniques","score":0.07680000364780426,"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/representation","display_name":"Representation (politics)","score":0.7103999853134155},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.5569999814033508},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.5461999773979187},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5437999963760376},{"id":"https://openalex.org/keywords/language-model","display_name":"Language model","score":0.49869999289512634},{"id":"https://openalex.org/keywords/scope","display_name":"Scope (computer science)","score":0.41620001196861267},{"id":"https://openalex.org/keywords/causal-model","display_name":"Causal model","score":0.38920000195503235},{"id":"https://openalex.org/keywords/linear-model","display_name":"Linear model","score":0.3630000054836273}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7335000038146973},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.7103999853134155},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5837000012397766},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.5569999814033508},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.5461999773979187},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5437999963760376},{"id":"https://openalex.org/C204321447","wikidata":"https://www.wikidata.org/wiki/Q30642","display_name":"Natural language processing","level":1,"score":0.515999972820282},{"id":"https://openalex.org/C137293760","wikidata":"https://www.wikidata.org/wiki/Q3621696","display_name":"Language model","level":2,"score":0.49869999289512634},{"id":"https://openalex.org/C2778012447","wikidata":"https://www.wikidata.org/wiki/Q1034415","display_name":"Scope (computer science)","level":2,"score":0.41620001196861267},{"id":"https://openalex.org/C11671645","wikidata":"https://www.wikidata.org/wiki/Q5054567","display_name":"Causal model","level":2,"score":0.38920000195503235},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.3630000054836273},{"id":"https://openalex.org/C175154964","wikidata":"https://www.wikidata.org/wiki/Q380077","display_name":"Task analysis","level":3,"score":0.361299991607666},{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.36090001463890076},{"id":"https://openalex.org/C59404180","wikidata":"https://www.wikidata.org/wiki/Q17013334","display_name":"Feature learning","level":2,"score":0.326200008392334},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3253999948501587},{"id":"https://openalex.org/C88871306","wikidata":"https://www.wikidata.org/wiki/Q7208287","display_name":"Point process","level":2,"score":0.302700012922287},{"id":"https://openalex.org/C195324797","wikidata":"https://www.wikidata.org/wiki/Q33742","display_name":"Natural language","level":2,"score":0.30079999566078186},{"id":"https://openalex.org/C64357122","wikidata":"https://www.wikidata.org/wiki/Q1149766","display_name":"Causality (physics)","level":2,"score":0.29420000314712524},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.2921999990940094},{"id":"https://openalex.org/C161301231","wikidata":"https://www.wikidata.org/wiki/Q3478658","display_name":"Knowledge representation and reasoning","level":2,"score":0.2863999903202057},{"id":"https://openalex.org/C96199812","wikidata":"https://www.wikidata.org/wiki/Q2145290","display_name":"Mental representation","level":3,"score":0.2840999960899353},{"id":"https://openalex.org/C2983448237","wikidata":"https://www.wikidata.org/wiki/Q1078276","display_name":"Language understanding","level":2,"score":0.2775999903678894},{"id":"https://openalex.org/C188147891","wikidata":"https://www.wikidata.org/wiki/Q147638","display_name":"Cognitive science","level":1,"score":0.2754000127315521},{"id":"https://openalex.org/C87868495","wikidata":"https://www.wikidata.org/wiki/Q750843","display_name":"Information processing","level":2,"score":0.27309998869895935},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.26499998569488525},{"id":"https://openalex.org/C66024118","wikidata":"https://www.wikidata.org/wiki/Q1122506","display_name":"Computational model","level":2,"score":0.2524999976158142}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:tubiblio.ulb.tu-darmstadt.de:159557","is_oa":false,"landing_page_url":"http://tubiblio.ulb.tu-darmstadt.de/view/person/Bigoulaeva=3AIrina=3A=3A.html>","pdf_url":null,"source":{"id":"https://openalex.org/S4377196390","display_name":"TUbilio (Technical University of Darmstadt)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I31512782","host_organization_name":"Technische Universit\u00e4t Darmstadt","host_organization_lineage":["https://openalex.org/I31512782"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"NonPeerReviewed"},{"id":"pmh:doi:10.48550/arxiv.2602.07930","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.07930","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.07930","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.07930","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[{"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4","score":0.8079448938369751}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Despite":[0],"the":[1,92,95,105,125,137,142,151],"recent":[2],"success":[3],"of":[4,16,33,47,82,94,129],"instruction-tuned":[5],"language":[6,119],"models":[7,18,120],"and":[8,42,52],"their":[9],"ubiquitous":[10],"usage,":[11],"very":[12],"little":[13],"is":[14,65,122],"known":[15],"how":[17,37],"process":[19],"instructions":[20],"internally.":[21],"In":[22],"this":[23,27],"work,":[24],"we":[25,60,73,109],"address":[26],"gap":[28],"from":[29,124],"a":[30,79,111],"mechanistic":[31,101],"point":[32],"view":[34],"by":[35],"investigating":[36],"instruction-specific":[38],"representations":[39,139],"are":[40,148],"constructed":[41],"utilized":[43],"in":[44,68,100,118,141,150],"different":[45,145],"stages":[46],"post-training:":[48],"Supervised":[49],"Fine-Tuning":[50],"(SFT)":[51],"Direct":[53],"Preference":[54],"Optimization":[55],"(DPO).":[56],"Via":[57],"causal":[58,88,107],"mediation,":[59],"identify":[61],"that":[62,121,156],"instruction":[63],"representation":[64,97],"fairly":[66],"localized":[67],"models.":[69],"These":[70],"representations,":[71],"which":[72],"call":[74],"Instruction":[75],"Vectors":[76],"(IVs),":[77],"demonstrate":[78],"curious":[80],"juxtaposition":[81],"linear":[83,96,127],"separability":[84],"along":[85],"with":[86],"non-linear":[87,106],"interaction,":[89,108],"broadly":[90],"questioning":[91],"scope":[93],"hypothesis":[98],"commonplace":[99],"interpretability.":[102],"To":[103],"disentangle":[104],"propose":[110],"novel":[112],"method":[113],"to":[114,154],"localize":[115],"information":[116,146],"processing":[117],"free":[123],"implicit":[126],"assumptions":[128],"patching-based":[130],"techniques.":[131],"We":[132],"find":[133],"that,":[134],"conditioned":[135],"on":[136],"task":[138],"formed":[140],"early":[143],"layers,":[144],"pathways":[147],"selected":[149],"later":[152],"layers":[153],"solve":[155],"task,":[157],"i.e.,":[158],"IVs":[159],"act":[160],"as":[161],"circuit":[162],"selectors.":[163]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2026-02-11T00:00:00"}
