{"id":"https://openalex.org/W7117733640","doi":"https://doi.org/10.3390/e28010050","title":"Interpreting Performance of Deep Neural Networks with Partial Information Decomposition","display_name":"Interpreting Performance of Deep Neural Networks with Partial Information Decomposition","publication_year":2025,"publication_date":"2025-12-31","ids":{"openalex":"https://openalex.org/W7117733640","doi":"https://doi.org/10.3390/e28010050","pmid":"https://pubmed.ncbi.nlm.nih.gov/41593957"},"language":"en","primary_location":{"id":"doi:10.3390/e28010050","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28010050","pdf_url":"https://www.mdpi.com/1099-4300/28/1/50/pdf?version=1767162982","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/28/1/50/pdf?version=1767162982","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5121667952","display_name":"Tianyue Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210089285","display_name":"Ji Hua Laboratory","ror":"https://ror.org/006aydy55","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210089285"]},{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tianyue Liu","raw_affiliation_strings":["LMIB and SKLCCSE, Beihang University, Beijing 100191, China","School of Artificial Intelligence, Beihang University, Beijing 100191, China","Zhongguancun Laboratory, Beijing 100194, China"],"raw_orcid":"https://orcid.org/0009-0004-3200-1005","affiliations":[{"raw_affiliation_string":"LMIB and SKLCCSE, Beihang University, Beijing 100191, China","institution_ids":["https://openalex.org/I82880672"]},{"raw_affiliation_string":"School of Artificial Intelligence, Beihang University, Beijing 100191, China","institution_ids":["https://openalex.org/I82880672"]},{"raw_affiliation_string":"Zhongguancun Laboratory, Beijing 100194, China","institution_ids":["https://openalex.org/I4210089285"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007759462","display_name":"Binghui Guo","orcid":null},"institutions":[{"id":"https://openalex.org/I4210089285","display_name":"Ji Hua Laboratory","ror":"https://ror.org/006aydy55","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210089285"]},{"id":"https://openalex.org/I4210165198","display_name":"Beijing Advanced Sciences and Innovation Center","ror":"https://ror.org/05qm21180","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165198"]},{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Binghui Guo","raw_affiliation_strings":["Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beijing 100083, China","LMIB and SKLCCSE, Beihang University, Beijing 100191, China","School of Artificial Intelligence, Beihang University, Beijing 100191, China","Zhongguancun Laboratory, Beijing 100194, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beijing 100083, China","institution_ids":["https://openalex.org/I4210165198"]},{"raw_affiliation_string":"LMIB and SKLCCSE, Beihang University, Beijing 100191, China","institution_ids":["https://openalex.org/I82880672"]},{"raw_affiliation_string":"School of Artificial Intelligence, Beihang University, Beijing 100191, China","institution_ids":["https://openalex.org/I82880672"]},{"raw_affiliation_string":"Zhongguancun Laboratory, Beijing 100194, China","institution_ids":["https://openalex.org/I4210089285"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059111171","display_name":"Ziqiao Yin","orcid":"https://orcid.org/0000-0003-4340-5414"},"institutions":[{"id":"https://openalex.org/I4210089285","display_name":"Ji Hua Laboratory","ror":"https://ror.org/006aydy55","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210089285"]},{"id":"https://openalex.org/I4210165198","display_name":"Beijing Advanced Sciences and Innovation Center","ror":"https://ror.org/05qm21180","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165198"]},{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ziqiao Yin","raw_affiliation_strings":["Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beijing 100083, China","Hangzhou Internation Innovation Institute of Beihang University, Hangzhou 311115, China","LMIB and SKLCCSE, Beihang University, Beijing 100191, China","School of Artificial Intelligence, Beihang University, Beijing 100191, China","Zhongguancun Laboratory, Beijing 100194, China"],"raw_orcid":"https://orcid.org/0000-0003-4340-5414","affiliations":[{"raw_affiliation_string":"Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beijing 100083, China","institution_ids":["https://openalex.org/I4210165198"]},{"raw_affiliation_string":"Hangzhou Internation Innovation Institute of Beihang University, Hangzhou 311115, China","institution_ids":["https://openalex.org/I82880672"]},{"raw_affiliation_string":"LMIB and SKLCCSE, Beihang University, Beijing 100191, China","institution_ids":["https://openalex.org/I82880672"]},{"raw_affiliation_string":"School of Artificial Intelligence, Beihang University, Beijing 100191, China","institution_ids":["https://openalex.org/I82880672"]},{"raw_affiliation_string":"Zhongguancun Laboratory, Beijing 100194, China","institution_ids":["https://openalex.org/I4210089285"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025047593","display_name":"Zhilong Mi","orcid":"https://orcid.org/0000-0002-7811-7204"},"institutions":[{"id":"https://openalex.org/I4210165198","display_name":"Beijing Advanced Sciences and Innovation Center","ror":"https://ror.org/05qm21180","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165198"]},{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhilong Mi","raw_affiliation_strings":["Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beijing 100083, China","LMIB and SKLCCSE, Beihang University, Beijing 100191, China","School of Artificial Intelligence, Beihang University, Beijing 100191, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beijing 100083, China","institution_ids":["https://openalex.org/I4210165198"]},{"raw_affiliation_string":"LMIB and SKLCCSE, Beihang University, Beijing 100191, China","institution_ids":["https://openalex.org/I82880672"]},{"raw_affiliation_string":"School of Artificial Intelligence, Beihang University, Beijing 100191, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5121665871","display_name":"Donghui Jin","orcid":null},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Donghui Jin","raw_affiliation_strings":["LMIB and SKLCCSE, Beihang University, Beijing 100191, China","School of Artificial Intelligence, Beihang University, Beijing 100191, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LMIB and SKLCCSE, Beihang University, Beijing 100191, China","institution_ids":["https://openalex.org/I82880672"]},{"raw_affiliation_string":"School of Artificial Intelligence, Beihang University, Beijing 100191, China","institution_ids":["https://openalex.org/I82880672"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5007759462"],"corresponding_institution_ids":["https://openalex.org/I4210089285","https://openalex.org/I4210165198","https://openalex.org/I82880672"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.78213141,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"1","first_page":"50","last_page":"50"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.5852000117301941,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.5852000117301941,"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.08160000294446945,"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/T10036","display_name":"Advanced Neural Network Applications","score":0.061799999326467514,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.8486999869346619},{"id":"https://openalex.org/keywords/encode","display_name":"ENCODE","score":0.6380000114440918},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5641000270843506},{"id":"https://openalex.org/keywords/redundancy","display_name":"Redundancy (engineering)","score":0.5455999970436096},{"id":"https://openalex.org/keywords/deep-neural-networks","display_name":"Deep neural networks","score":0.43619999289512634},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.3479999899864197}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.8486999869346619},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7221999764442444},{"id":"https://openalex.org/C66746571","wikidata":"https://www.wikidata.org/wiki/Q1134833","display_name":"ENCODE","level":3,"score":0.6380000114440918},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5753999948501587},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5641000270843506},{"id":"https://openalex.org/C152124472","wikidata":"https://www.wikidata.org/wiki/Q1204361","display_name":"Redundancy (engineering)","level":2,"score":0.5455999970436096},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.4618000090122223},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.45840001106262207},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.43619999289512634},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.3479999899864197},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.31310001015663147},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.2653000056743622},{"id":"https://openalex.org/C3020402766","wikidata":"https://www.wikidata.org/wiki/Q104376712","display_name":"Prior information","level":2,"score":0.2565000057220459},{"id":"https://openalex.org/C28427503","wikidata":"https://www.wikidata.org/wiki/Q13580300","display_name":"Internal model","level":3,"score":0.25290000438690186},{"id":"https://openalex.org/C2988416141","wikidata":"https://www.wikidata.org/wiki/Q6031139","display_name":"Information loss","level":2,"score":0.25110000371932983}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e28010050","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28010050","pdf_url":"https://www.mdpi.com/1099-4300/28/1/50/pdf?version=1767162982","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:41593957","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41593957","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":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:1b15d9333f8e46cd8908cc778d6f3259","is_oa":true,"landing_page_url":"https://doaj.org/article/1b15d9333f8e46cd8908cc778d6f3259","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 28, Iss 1, p 50 (2025)","raw_type":"article"},{"id":"pmh:oai:pubmedcentral.nih.gov:12839711","is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC12839711/","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":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e28010050","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28010050","pdf_url":"https://www.mdpi.com/1099-4300/28/1/50/pdf?version=1767162982","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.8290109634399414,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G8655508424","display_name":null,"funder_award_id":"2021ZD0201302","funder_id":"https://openalex.org/F4320329860","funder_display_name":"National Science and Technology Major Project"}],"funders":[{"id":"https://openalex.org/F4320329860","display_name":"National Science and Technology Major Project","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7117733640.pdf","grobid_xml":"https://content.openalex.org/works/W7117733640.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1890016494","https://openalex.org/W1899852503","https://openalex.org/W1995875735","https://openalex.org/W2031342017","https://openalex.org/W2152587044","https://openalex.org/W2183341477","https://openalex.org/W2194775991","https://openalex.org/W2622826443","https://openalex.org/W2753338388","https://openalex.org/W2788728386","https://openalex.org/W2803439868","https://openalex.org/W2884001105","https://openalex.org/W2963163009","https://openalex.org/W2963446712","https://openalex.org/W2964184826","https://openalex.org/W2991526369","https://openalex.org/W3116074996","https://openalex.org/W3189482654","https://openalex.org/W4384820866","https://openalex.org/W4386075227","https://openalex.org/W4386076667","https://openalex.org/W4390729136","https://openalex.org/W4399282900"],"related_works":[],"abstract_inverted_index":{"Robustness":[0],"to":[1,38,92,151],"distributional":[2],"shifts":[3],"remains":[4,41],"a":[5,102],"critical":[6],"limitation":[7],"for":[8,51,129],"deploying":[9],"deep":[10],"neural":[11],"networks":[12],"(DNNs)":[13],"in":[14,20],"real-world":[15],"applications.":[16],"While":[17],"DNNs":[18],"excel":[19],"standard":[21],"benchmarks,":[22],"their":[23],"performance":[24,96],"often":[25],"deteriorates":[26],"under":[27,97],"unseen":[28],"or":[29,66],"perturbed":[30],"conditions.":[31],"Understanding":[32],"how":[33,62],"internal":[34,136],"information":[35,57,107,137],"representations":[36],"relate":[37],"such":[39],"robustness":[40,52,145],"underexplored.":[42],"In":[43],"this":[44],"work,":[45],"we":[46],"propose":[47],"an":[48],"interpretable":[49],"framework":[50],"assessment":[53,146],"based":[54],"on":[55,115],"partial":[56],"decomposition":[58],"(PID),":[59],"which":[60,119],"quantifies":[61],"neurons":[63],"redundantly,":[64],"uniquely,":[65],"synergistically":[67],"encode":[68],"task-relevant":[69],"information.":[70],"Analysis":[71],"of":[72,105,143],"PID":[73],"measures":[74],"computed":[75],"from":[76,118],"clean":[77],"inputs":[78],"reveals":[79],"that":[80],"models":[81],"characterized":[82],"by":[83],"higher":[84,103],"redundancy":[85],"rates":[86,90],"and":[87,131,139],"lower":[88],"synergy":[89],"tend":[91],"maintain":[93],"more":[94],"stable":[95],"various":[98],"natural":[99],"corruptions.":[100],"Additionally,":[101],"rate":[104],"unique":[106],"is":[108,122],"positively":[109],"associated":[110],"with":[111],"improved":[112],"classification":[113],"accuracy":[114],"the":[116,120,141],"data":[117],"measure":[121],"computed.":[123],"These":[124],"findings":[125],"provide":[126],"new":[127],"insights":[128],"understanding":[130],"comparing":[132],"model":[133],"behavior":[134],"through":[135],"analysis,":[138],"highlight":[140],"feasibility":[142],"lightweight":[144],"without":[147],"requiring":[148],"extensive":[149],"access":[150],"corrupted":[152],"data.":[153]},"counts_by_year":[],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2025-12-31T00:00:00"}
