{"id":"https://openalex.org/W7220679972","doi":"https://doi.org/10.48550/arxiv.2610.03735","title":"Nonequivalence of expected free energy and revised system integrated information in noisy permutation networks","display_name":"Nonequivalence of expected free energy and revised system integrated information in noisy permutation networks","publication_year":2026,"publication_date":"2026-09-15","ids":{"openalex":"https://openalex.org/W7220679972","doi":"https://doi.org/10.48550/arxiv.2610.03735"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.03735","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03735","pdf_url":"https://arxiv.org/pdf/2610.03735","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.03735","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084711593","display_name":"Katsuaki Tanabe","orcid":"https://orcid.org/0000-0002-0179-4872","observed_orcids":["https://orcid.org/0000-0002-0179-4872"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tanabe, Katsuaki","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5084711593"],"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/T11883","display_name":"Embodied and Extended Cognition","score":0.48190000653266907,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T11883","display_name":"Embodied and Extended Cognition","score":0.48190000653266907,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10258","display_name":"Philosophy and Theoretical Science","score":0.1469999998807907,"subfield":{"id":"https://openalex.org/subfields/1211","display_name":"Philosophy"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.044599998742341995,"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/integrated-information-theory","display_name":"integrated information theory","score":0.8970000147819519},{"id":"https://openalex.org/keywords/free-energy-principle","display_name":"free energy principle","score":0.9810000061988831},{"id":"https://openalex.org/keywords/active-inference","display_name":"active inference","score":0.9929999709129333},{"id":"https://openalex.org/keywords/expected-free-energy","display_name":"expected free energy","score":0.8659999966621399},{"id":"https://openalex.org/keywords/causal-topology","display_name":"causal topology","score":0.6710000038146973},{"id":"https://openalex.org/keywords/information-content","display_name":"information content","score":0.671999990940094},{"id":"https://openalex.org/keywords/variational-free-energy","display_name":"variational free energy","score":0.7730000019073486},{"id":"https://openalex.org/keywords/specifications","display_name":"specifications","score":0.5799999833106995}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6444000005722046},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.534500002861023},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.5056999921798706},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.4909999966621399},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.447299987077713},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4025999903678894},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4011000096797943},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.3817000091075897},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.37369999289512634},{"id":"https://openalex.org/C70120467","wikidata":"https://www.wikidata.org/wiki/Q515893","display_name":"Free probability","level":2,"score":0.36250001192092896},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.36169999837875366},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.3587000072002411},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3560999929904938},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.3384999930858612},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.320499986410141},{"id":"https://openalex.org/C33724603","wikidata":"https://www.wikidata.org/wiki/Q812540","display_name":"Bayesian network","level":2,"score":0.3174000084400177},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.30790001153945923},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.305400013923645},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.2955999970436096},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.2856000065803528},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.28119999170303345},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27869999408721924},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.2651999890804291},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.2606000006198883},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2605000138282776},{"id":"https://openalex.org/C150921843","wikidata":"https://www.wikidata.org/wiki/Q1170431","display_name":"Resampling","level":2,"score":0.25999999046325684},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.2572000026702881},{"id":"https://openalex.org/C2777472644","wikidata":"https://www.wikidata.org/wiki/Q16968992","display_name":"Approximate inference","level":3,"score":0.2549000084400177},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.2547999918460846},{"id":"https://openalex.org/C917703","wikidata":"https://www.wikidata.org/wiki/Q7239668","display_name":"Predictive inference","level":5,"score":0.25360000133514404}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.03735","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03735","pdf_url":"https://arxiv.org/pdf/2610.03735","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.2610.03735","doi":"https://doi.org/10.48550/arxiv.2610.03735","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.03735","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":"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.03735","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03735","pdf_url":"https://arxiv.org/pdf/2610.03735","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":[{"id":"https://openalex.org/G2919436239","display_name":null,"funder_award_id":"KSAC2025-14","funder_id":"https://openalex.org/F4320334789","funder_display_name":"Japan Science and Technology Agency"}],"funders":[{"id":"https://openalex.org/F4320334789","display_name":"Japan Science and Technology Agency","ror":"https://ror.org/00097mb19"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220679972.pdf","grobid_xml":"https://content.openalex.org/works/W7220679972.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W3039225463","https://openalex.org/W4414971189","https://openalex.org/W7161176875","https://openalex.org/W7203627071"],"related_works":["https://openalex.org/W4414971189","https://openalex.org/W6887754308","https://openalex.org/W7161176875","https://openalex.org/W7165911918","https://openalex.org/W3100708443","https://openalex.org/W2944935347","https://openalex.org/W7212067286","https://openalex.org/W2143844393","https://openalex.org/W7204805360","https://openalex.org/W2811113323"],"abstract_inverted_index":{"The":[0],"free-energy":[1,15,238],"principle":[2],"(FEP)":[3],"and":[4,14,38,56,63,99,107,158,176,190],"active":[5],"inference":[6,229],"describe":[7],"adaptive":[8],"systems":[9],"through":[10,194],"probabilistic":[11],"generative":[12],"models":[13],"functionals,":[16],"whereas":[17,121],"integrated":[18,47,146,221],"information":[19,234],"theory":[20],"(IIT)":[21],"characterizes":[22],"intrinsic":[23],"cause-effect":[24],"organization.":[25],"We":[26,49,70],"separate":[27],"two":[28,155],"questions:":[29],"whether":[30,39],"revised":[31,111,144,218],"IIT":[32,54,112,184,219,226],"quantities":[33],"admit":[34,59],"local":[35,82,203],"free-energy-like":[36],"representations":[37,66],"scalar":[40,237],"expected":[41,101,211],"free":[42,102,212],"energy":[43,103,213],"can":[44],"determine":[45],"system":[46,145,220],"information.":[48,222],"show":[50,159],"that":[51,149,160],"the":[52,94,150,164,169,177,199],"2026":[53],"intrinsic-differentiation":[55],"specification":[57],"terms":[58],"exact":[60,68],"surprisal":[61],"representations,":[62],"hence":[64],"variational-free-energy":[65],"under":[67,104],"inference.":[69],"then":[71],"construct":[72],"noisy":[73,124,135],"binary":[74],"permutation":[75],"networks":[76],"whose":[77],"causal":[78,156,233],"topology":[79],"varies":[80],"while":[81],"transition":[83],"reliability":[84,166],"is":[85],"fixed.":[86],"In":[87],"a":[88,122,140,236],"homogeneous":[89],"state,":[90],"all":[91],"permutations":[92,116],"yield":[93],"same":[95],"one-step":[96],"predictive":[97],"distribution":[98],"state-risk":[100],"common":[105],"preferences":[106],"observation":[108],"models,":[109],"yet":[110],"distinguishes":[113],"them:":[114],"multicycle":[115],"have":[117],"zero":[118],"whole-system":[119],"integration,":[120],"single":[123,136],"cycle":[125],"has":[126],"positive":[127],"integration":[128,179],"at":[129],"intermediate":[130],"reliability.":[131],"For":[132],"an":[133],"n-unit":[134],"cycle,":[137],"we":[138],"derive":[139],"closed-form":[141],"expression":[142],"for":[143,186],"information,":[147],"prove":[148],"minimum-information":[151],"partition":[152,192],"cuts":[153],"exactly":[154],"edges,":[157],"as":[161],"n":[162,187,195],"grows":[163],"optimal":[165],"approaches":[167,173,180],"unity,":[168],"joint":[170],"specified-state":[171],"probability":[172],"one":[174,181],"half,":[175],"maximum":[178],"ibit.":[182],"Numerical":[183],"calculations":[185],"=":[188,196],"2-5":[189],"exhaustive":[191],"enumeration":[193],"8":[197],"reproduce":[198],"analytical":[200],"results.":[201],"Thus,":[202],"surprisal/free-energy":[204],"correspondence":[205],"coexists":[206],"with":[207,227],"global":[208],"non-equivalence:":[209],"equal":[210,217],"does":[214],"not":[215],"imply":[216],"Any":[223],"synthesis":[224],"of":[225],"FEP/active":[228],"must":[230],"retain":[231],"counterfactual":[232],"beyond":[235],"value.":[239]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}