{"id":"https://openalex.org/W7217204992","doi":null,"title":"Statistical Physics Methods for Non-Convex Neural Network Models","display_name":"Statistical Physics Methods for Non-Convex Neural Network Models","publication_year":null,"publication_date":null,"ids":{"openalex":"https://openalex.org/W7217204992"},"language":"en","primary_location":{"id":"pmh:oai:iris.unibocconi.it:11565/4074062","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/11565/4074062","pdf_url":"https://iris.unibocconi.it/bitstream/11565/4074062/2/ANNESI%20Thesis.pdf","source":{"id":"https://openalex.org/S7407055170","display_name":"Archivio istituzionale della Ricerca - Bocconi","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/doctoralThesis"},"volume":null,"type":"dissertation","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://iris.unibocconi.it/bitstream/11565/4074062/2/ANNESI%20Thesis.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091292887","display_name":"Brandon Livio Annesi","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"ANNESI, BRANDON LIVIO","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5091292887"],"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/T10320","display_name":"Neural Networks and Applications","score":0.8633000254631042,"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/T10320","display_name":"Neural Networks and Applications","score":0.8633000254631042,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.04490000009536743,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.03550000116229057,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/loss-landscape","display_name":"loss landscape","score":0.6499999761581421},{"id":"https://openalex.org/keywords/replica-method","display_name":"replica method","score":0.7369999885559082},{"id":"https://openalex.org/keywords/critical-capacity","display_name":"critical capacity","score":0.9610000252723694},{"id":"https://openalex.org/keywords/teacher-student-models","display_name":"teacher-student models","score":0.8650000095367432},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"gradient descent","score":0.49900001287460327}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6302000284194946},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.5126000046730042},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.507099986076355},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5044999718666077},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4577000141143799},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.45320001244544983},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.43560001254081726},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4320000112056732},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.42890000343322754},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4187000095844269},{"id":"https://openalex.org/C2775937380","wikidata":"https://www.wikidata.org/wiki/Q1232589","display_name":"Replica","level":2,"score":0.4090000092983246},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.3723999857902527},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3709999918937683},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.36800000071525574},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.3630000054836273},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.33469998836517334},{"id":"https://openalex.org/C99874945","wikidata":"https://www.wikidata.org/wiki/Q188715","display_name":"Statistical mechanics","level":2,"score":0.3312999904155731},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.3292999863624573},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.31150001287460327},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.3084000051021576},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.299699991941452},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.28360000252723694},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.27549999952316284},{"id":"https://openalex.org/C2781390188","wikidata":"https://www.wikidata.org/wiki/Q25203449","display_name":"Spike (software development)","level":2,"score":0.27309998869895935},{"id":"https://openalex.org/C21080849","wikidata":"https://www.wikidata.org/wiki/Q13611879","display_name":"Data point","level":2,"score":0.26989999413490295},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.26499998569488525}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:iris.unibocconi.it:11565/4074062","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/11565/4074062","pdf_url":"https://iris.unibocconi.it/bitstream/11565/4074062/2/ANNESI%20Thesis.pdf","source":{"id":"https://openalex.org/S7407055170","display_name":"Archivio istituzionale della Ricerca - Bocconi","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/doctoralThesis"}],"best_oa_location":{"id":"pmh:oai:iris.unibocconi.it:11565/4074062","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/11565/4074062","pdf_url":"https://iris.unibocconi.it/bitstream/11565/4074062/2/ANNESI%20Thesis.pdf","source":{"id":"https://openalex.org/S7407055170","display_name":"Archivio istituzionale della Ricerca - Bocconi","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/doctoralThesis"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7217204992.pdf","grobid_xml":"https://content.openalex.org/works/W7217204992.grobid-xml"},"referenced_works_count":57,"referenced_works":["https://openalex.org/W1922159006","https://openalex.org/W1964281249","https://openalex.org/W1974572752","https://openalex.org/W1991904924","https://openalex.org/W2001570872","https://openalex.org/W2030225915","https://openalex.org/W2030450972","https://openalex.org/W2033606703","https://openalex.org/W2042942879","https://openalex.org/W2056517685","https://openalex.org/W2060913109","https://openalex.org/W2062313687","https://openalex.org/W2064124064","https://openalex.org/W2066424095","https://openalex.org/W2070784404","https://openalex.org/W2095058792","https://openalex.org/W2101936356","https://openalex.org/W2523060838","https://openalex.org/W2556883406","https://openalex.org/W2566079294","https://openalex.org/W2612837156","https://openalex.org/W2752366553","https://openalex.org/W2805003733","https://openalex.org/W2893759728","https://openalex.org/W2906886359","https://openalex.org/W2963518130","https://openalex.org/W2973471489","https://openalex.org/W2973737673","https://openalex.org/W2990397143","https://openalex.org/W2992043355","https://openalex.org/W2994081359","https://openalex.org/W2997163556","https://openalex.org/W2998438489","https://openalex.org/W3044599724","https://openalex.org/W3091401866","https://openalex.org/W3096771845","https://openalex.org/W3100072991","https://openalex.org/W3130264527","https://openalex.org/W3160443277","https://openalex.org/W3168867926","https://openalex.org/W3172995164","https://openalex.org/W3200668485","https://openalex.org/W3202733572","https://openalex.org/W4289334798","https://openalex.org/W4386091112","https://openalex.org/W4386875438","https://openalex.org/W4387994502","https://openalex.org/W4389130403","https://openalex.org/W4391091872","https://openalex.org/W4391673403","https://openalex.org/W4391709850","https://openalex.org/W4391901266","https://openalex.org/W4392822139","https://openalex.org/W4394709680","https://openalex.org/W4409110105","https://openalex.org/W4409974857","https://openalex.org/W7201835367"],"related_works":["https://openalex.org/W4386875438","https://openalex.org/W4409110105","https://openalex.org/W2002772250","https://openalex.org/W6929218051","https://openalex.org/W4386091112","https://openalex.org/W3013106689","https://openalex.org/W2153069405","https://openalex.org/W4226060898","https://openalex.org/W7217355795","https://openalex.org/W2066925641"],"abstract_inverted_index":{"In":[0,85],"this":[1],"doctoral":[2],"thesis":[3],"I":[4,21,59,94,124,145,185,196,226],"employ":[5],"the":[6,25,30,39,44,52,62,86,91,96,100,111,133,143,178,182,187,192,199,215,223,240,249],"lens":[7],"of":[8,15,18,33,46,54,57,64,114,132,181,235,248],"Statistical":[9],"Physics":[10],"to":[11,28,50,119,177,190,214,242,254],"study":[12,95,203],"a":[13,34,105,148,153,163,204,210,228,232],"number":[14],"non-convex":[16],"models":[17],"Neural":[19],"Networks.":[20],"start":[22],"by":[23,83,142],"using":[24],"replica":[26],"method":[27],"investigate":[29],"loss":[31],"landscape":[32],"prototypical":[35],"neural":[36],"network":[37],"model,":[38,88],"Negative":[40,183],"Perceptron,":[41,184],"and":[42,72,89,103,170,202,251],"use":[43,186],"tool":[45],"Linear":[47],"Mode":[48],"Connectivity":[49],"describe":[51],"connection":[53],"different":[55],"types":[56],"solutions.":[58],"show":[60],"that":[61,75,151,247],"geometry":[63],"such":[65,76,115,167],"solutions":[66,81,136],"can":[67,219],"be":[68,220],"described":[69],"as":[70],"star-shaped,":[71],"numerically":[73],"verify":[74],"connectivity":[77,179],"properties":[78,180],"hold":[79],"for":[80,90,129,239],"found":[82,141],"algorithms.":[84],"same":[87],"Tree-Committee":[92],"Machine,":[93],"critical":[97],"capacity":[98],"under":[99],"full-RSB":[101],"ansatz,":[102],"settle":[104],"long":[106],"standing":[107],"open":[108],"problem":[109],"about":[110],"numerical":[112,255],"value":[113],"threshold.":[116],"Comparing":[117],"it":[118,253],"simulations":[120,256],"with":[121,246,257],"Gradient":[122],"Descent,":[123],"observe":[125,227],"an":[126,159],"algorithmic":[127,173],"gap:":[128],"some":[130],"values":[131],"constraint":[134],"density":[135],"exists":[137],"but":[138],"are":[139],"not":[140],"algorithm.":[144],"also":[146],"introduce":[147],"transition":[149],"line":[150],"separates":[152],"phase":[154,164],"where":[155,165,209,231],"typical":[156],"states":[157],"exhibit":[158],"Overlap":[160],"Gap":[161],"from":[162],"no":[166],"gap":[168],"exists,":[169],"discuss":[171],"potential":[172],"implications.":[174],"Going":[175],"back":[176],"fRSB":[188],"framework":[189],"characterize":[191],"disconnection":[193],"transition.":[194],"Finally":[195],"go":[197],"beyond":[198],"storage":[200],"setting":[201],"Spiked":[205],"Random":[206],"Feature":[207],"Model,":[208],"low":[211],"rank":[212],"correction":[213],"random":[216],"feature":[217],"matrix":[218],"learned,":[221],"in":[222],"teacher-student":[224],"scenario.":[225],"detection":[229],"phenomenon":[230],"minimum":[233],"amount":[234],"data":[236],"is":[237],"needed":[238],"student":[241],"align":[243],"its":[244],"spike":[245],"teacher,":[250],"compare":[252],"real":[258],"datasets.":[259]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-03T00:00:00"}