{"id":"https://openalex.org/W7160430833","doi":"https://doi.org/10.48550/arxiv.2605.03598","title":"Unifying Dynamical Systems and Graph Theory to Mechanistically Understand Computation in Neural Networks","display_name":"Unifying Dynamical Systems and Graph Theory to Mechanistically Understand Computation in Neural Networks","publication_year":2026,"publication_date":"2026-05-05","ids":{"openalex":"https://openalex.org/W7160430833","doi":"https://doi.org/10.48550/arxiv.2605.03598"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.03598","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.03598","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":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.03598","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135509036","display_name":"Jatin Sharma","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sharma, Jatin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065237354","display_name":"Danyal Akarca","orcid":"https://orcid.org/0000-0002-5931-0295"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Goodman, Dan F. M","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5135498086","display_name":"Dan F. M Goodman","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Akarca, Danyal","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.31369999051094055,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.31369999051094055,"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/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.17249999940395355,"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/T10502","display_name":"Advanced Memory and Neural Computing","score":0.15489999949932098,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6129000186920166},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.5645999908447266},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5393000245094299},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4749999940395355},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4699999988079071},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4456000030040741},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.3781999945640564},{"id":"https://openalex.org/keywords/deep-neural-networks","display_name":"Deep neural networks","score":0.3515999913215637}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6947000026702881},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6129000186920166},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.5645999908447266},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5393000245094299},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5134000182151794},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4749999940395355},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4699999988079071},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4456000030040741},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4156000018119812},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.3781999945640564},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.3515999913215637},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.3481999933719635},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.34529998898506165},{"id":"https://openalex.org/C28225019","wikidata":"https://www.wikidata.org/wiki/Q4915005","display_name":"Biological network","level":2,"score":0.34040001034736633},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3231000006198883},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.3151000142097473},{"id":"https://openalex.org/C2986949344","wikidata":"https://www.wikidata.org/wiki/Q9404","display_name":"Neural system","level":2,"score":0.31200000643730164},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.30709999799728394},{"id":"https://openalex.org/C3832189","wikidata":"https://www.wikidata.org/wiki/Q8588916","display_name":"Models of neural computation","level":3,"score":0.2689000070095062},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.2614000141620636}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.03598","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.03598","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":"doi:10.48550/arxiv.2605.03598","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.03598","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":"article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.4136231243610382}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Understanding":[0],"how":[1,87],"biological":[2],"and":[3,17,24,45,68,75,140,207],"artificial":[4],"neural":[5,21,50],"networks":[6,51],"implement":[7],"computation":[8],"from":[9],"connectivity":[10,26],"is":[11,99,174],"a":[12,66,197],"central":[13],"problem":[14],"in":[15,183,204],"neuroscience":[16],"machine":[18],"learning.":[19],"In":[20,78],"systems,":[22],"structural":[23],"functional":[25,215],"are":[27],"known":[28],"to":[29,202],"diverge,":[30],"motivating":[31],"approaches":[32],"that":[33,42,125,146,164,209],"move":[34],"beyond":[35,145],"direct":[36],"connections":[37],"alone.":[38],"Here,":[39],"we":[40,132],"show":[41],"the":[43,63,70,88,122,166,171],"spatial":[44],"temporal":[46,143,162],"function":[47,98,203],"of":[48],"recurrent":[49,205],"(RNNs)":[52],"trained":[53],"on":[54,114],"hierarchically":[55],"modular":[56],"tasks":[57],"can":[58],"be":[59,212],"recovered":[60],"by":[61,83,129,148,160],"modelling":[62],"network":[64,89],"as":[65,108,196],"graph":[67],"analysing":[69],"multi-hop":[71,102,123,138,194],"pathways":[72,82,124,139,216],"between":[73],"input":[74],"output":[76],"units.":[77],"particular,":[79],"decomposing":[80],"these":[81],"hop":[84],"length":[85],"reveals":[86],"temporally":[90],"routes":[91],"information.":[92],"This":[93],"perspective":[94],"reframes":[95],"regularisation:":[96],"if":[97],"implemented":[100],"through":[101],"communication,":[103],"then":[104],"standard":[105,149],"penalties":[106],"such":[107],"L1":[109,150,154],"regularisation,":[110,155],"which":[111,136],"act":[112],"only":[113],"individual":[115,219],"weights,":[116],"constrain":[117,137],"single-hop":[118],"structure":[119,201],"rather":[120,217],"than":[121,218],"support":[126],"computation.":[127],"Motivated":[128],"this":[130],"view,":[131],"introduce":[133],"resolvent-RNNs":[134],"(R-RNNs),":[135],"thereby":[141],"induce":[142],"sparsity":[144,163,210],"achieved":[147],"regularisation.":[151,189],"Compared":[152],"with":[153],"R-RNNs":[156,177],"achieve":[157],"improved":[158],"performance":[159],"inducing":[161],"matches":[165],"task":[167,172],"structure,":[168],"even":[169],"when":[170],"signal":[173],"sparse.":[175],"Moreover,":[176],"exhibit":[178],"stronger":[179],"sparsity-function":[180],"alignment,":[181],"reflected":[182],"their":[184],"increased":[185],"robustness":[186],"under":[187],"strong":[188],"Together,":[190],"our":[191],"results":[192],"identify":[193],"communication":[195],"key":[198],"principle":[199],"linking":[200],"networks,":[206],"suggest":[208],"should":[211],"defined":[213],"over":[214],"parameters.":[220]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-05-07T00:00:00"}