{"id":"https://openalex.org/W7155494918","doi":"https://doi.org/10.48550/arxiv.2604.21100","title":"Preconditioned DeltaNet: Curvature-aware Sequence Modeling for Linear Recurrences","display_name":"Preconditioned DeltaNet: Curvature-aware Sequence Modeling for Linear Recurrences","publication_year":2026,"publication_date":"2026-04-22","ids":{"openalex":"https://openalex.org/W7155494918","doi":"https://doi.org/10.48550/arxiv.2604.21100"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.21100","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.21100","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":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.2604.21100","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134561694","display_name":"Neehal Tumma","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tumma, Neehal","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039869719","display_name":"Noel Loo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Loo, Noel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5134529644","display_name":"Daniela Rus","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rus, Daniela","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/T10028","display_name":"Topic Modeling","score":0.20730000734329224,"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"}},"topics":[{"id":"https://openalex.org/T10028","display_name":"Topic Modeling","score":0.20730000734329224,"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":0.10509999841451645,"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/T11948","display_name":"Machine Learning in Materials Science","score":0.0843999981880188,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.6176999807357788},{"id":"https://openalex.org/keywords/softmax-function","display_name":"Softmax function","score":0.5188000202178955},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.44839999079704285},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.3621000051498413},{"id":"https://openalex.org/keywords/linear-regression","display_name":"Linear regression","score":0.3555999994277954},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.33009999990463257},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.3269999921321869},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.31459999084472656}],"concepts":[{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.6176999807357788},{"id":"https://openalex.org/C188441871","wikidata":"https://www.wikidata.org/wiki/Q7554146","display_name":"Softmax function","level":3,"score":0.5188000202178955},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5059999823570251},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.491100013256073},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.44839999079704285},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4325999915599823},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4174000024795532},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.3621000051498413},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.3555999994277954},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33160001039505005},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.33009999990463257},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.3269999921321869},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.31459999084472656},{"id":"https://openalex.org/C176370821","wikidata":"https://www.wikidata.org/wiki/Q1826459","display_name":"Linear space","level":2,"score":0.3107999861240387},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.30410000681877136},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.2906999886035919},{"id":"https://openalex.org/C41587187","wikidata":"https://www.wikidata.org/wiki/Q1501882","display_name":"Generalized linear model","level":2,"score":0.28139999508857727},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.27619999647140503},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.2761000096797943},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2750000059604645},{"id":"https://openalex.org/C67186912","wikidata":"https://www.wikidata.org/wiki/Q367664","display_name":"Data modeling","level":2,"score":0.2741999924182892},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2696000039577484},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.2653000056743622},{"id":"https://openalex.org/C81669768","wikidata":"https://www.wikidata.org/wiki/Q2359161","display_name":"Precision and recall","level":2,"score":0.2635999917984009},{"id":"https://openalex.org/C201292218","wikidata":"https://www.wikidata.org/wiki/Q740970","display_name":"Recurrence relation","level":2,"score":0.2565000057220459},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2533999979496002}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.21100","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.21100","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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.21100","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.21100","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":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":{"To":[0],"address":[1,104],"the":[2,34,53,73,92,95,114,127,131,187],"increasing":[3],"long-context":[4],"compute":[5],"limitations":[6],"of":[7,36,42,94,116,154],"softmax":[8],"attention,":[9],"several":[10],"subquadratic":[11],"recurrent":[12],"operators":[13],"have":[14],"been":[15],"developed.":[16],"This":[17],"work":[18,43],"includes":[19],"models":[20],"such":[21],"as":[22,61,83],"Mamba-2,":[23],"DeltaNet,":[24,155],"Gated":[25],"DeltaNet":[26],"(GDN),":[27],"and":[28,126,157,183,189],"Kimi":[29],"Delta":[30],"Attention":[31],"(KDA).":[32],"As":[33],"space":[35],"recurrences":[37,60,79,174],"grows,":[38],"a":[39,69,144],"parallel":[40,162],"line":[41],"has":[44],"arisen":[45],"to":[46,75,86,109,150],"taxonomize":[47],"them.":[48,166],"One":[49],"compelling":[50],"view":[51],"is":[52],"test-time":[54],"regression":[55],"(TTR)":[56],"framework,":[57],"which":[58],"interprets":[59],"performing":[62],"online":[63,117],"least":[64,118],"squares":[65],"updates":[66],"that":[67,170],"learn":[68],"linear":[70,124],"map":[71],"from":[72,113],"keys":[74],"values.":[76],"Existing":[77],"delta-rule":[78,173],"can":[80],"be":[81],"seen":[82],"first-order":[84],"approximations":[85],"this":[87,101,105,138,147],"objective,":[88],"but":[89],"notably":[90],"ignore":[91],"curvature":[93],"least-squares":[96],"loss":[97],"during":[98],"optimization.":[99],"In":[100],"work,":[102],"we":[103,120,136,168],"by":[106,142],"introducing":[107],"preconditioning":[108],"these":[110],"recurrences.":[111],"Starting":[112],"theory":[115,139],"squares,":[119],"derive":[121],"equivalences":[122],"between":[123],"attention":[125],"delta":[128],"rule":[129],"in":[130,140],"exactly":[132],"preconditioned":[133,152,172],"case.":[134],"Next,":[135],"realize":[137],"practice":[141],"proposing":[143],"diagonal":[145],"approximation:":[146],"enables":[148],"us":[149],"introduce":[151],"variants":[153],"GDN,":[156],"KDA":[158],"alongside":[159],"efficient":[160],"chunkwise":[161],"algorithms":[163],"for":[164],"computing":[165],"Empirically,":[167],"find":[169],"our":[171],"yield":[175],"consistent":[176],"performance":[177],"improvements":[178],"across":[179],"synthetic":[180],"recall":[181],"benchmarks":[182],"language":[184],"modeling":[185],"at":[186],"340M":[188],"1B":[190],"scale.":[191]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-25T00:00:00"}