{"id":"https://openalex.org/W6948279140","doi":"https://doi.org/10.5075/epfl-thesis-10519","title":"Fundamental Limits in Statistical Learning Problems: Block Models and Neural Networks","display_name":"Fundamental Limits in Statistical Learning Problems: Block Models and Neural Networks","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W6948279140","doi":"https://doi.org/10.5075/epfl-thesis-10519"},"language":"en","primary_location":{"id":"pmh:oai:infoscience.epfl.ch:303460","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/198831","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"doctoral thesis"},"type":"dissertation","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://infoscience.epfl.ch/handle/20.500.14299/198831","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Cornacchia, Elisabetta","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Cornacchia, Elisabetta","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"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":true,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.3151000142097473,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.3151000142097473,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.24879999458789825,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.07109999656677246,"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/conjecture","display_name":"Conjecture","score":0.5400999784469604},{"id":"https://openalex.org/keywords/spins","display_name":"Spins","score":0.4973999857902527},{"id":"https://openalex.org/keywords/binary-erasure-channel","display_name":"Binary erasure channel","score":0.4569000005722046},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.4555000066757202},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.44830000400543213},{"id":"https://openalex.org/keywords/fraction","display_name":"Fraction (chemistry)","score":0.44290000200271606},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.41269999742507935},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.3546999990940094},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.3411000072956085}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6215000152587891},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5400999784469604},{"id":"https://openalex.org/C2778870898","wikidata":"https://www.wikidata.org/wiki/Q7577658","display_name":"Spins","level":2,"score":0.4973999857902527},{"id":"https://openalex.org/C149862233","wikidata":"https://www.wikidata.org/wiki/Q864142","display_name":"Binary erasure channel","level":4,"score":0.4569000005722046},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.4555000066757202},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.44830000400543213},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.44290000200271606},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.41269999742507935},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.367900013923645},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36480000615119934},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35740000009536743},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.3546999990940094},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3538999855518341},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.3411000072956085},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3368000090122223},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.32690000534057617},{"id":"https://openalex.org/C166785042","wikidata":"https://www.wikidata.org/wiki/Q190391","display_name":"Central limit theorem","level":2,"score":0.29760000109672546},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.28450000286102295},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.2802000045776367},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.27730000019073486},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.2750999927520752},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.2741999924182892},{"id":"https://openalex.org/C2778790127","wikidata":"https://www.wikidata.org/wiki/Q484885","display_name":"Erasure","level":2,"score":0.26829999685287476},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.25949999690055847},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.2475000023841858},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.243599995970726},{"id":"https://openalex.org/C2777472644","wikidata":"https://www.wikidata.org/wiki/Q16968992","display_name":"Approximate inference","level":3,"score":0.24240000545978546},{"id":"https://openalex.org/C2779982251","wikidata":"https://www.wikidata.org/wiki/Q25053762","display_name":"Stochastic block model","level":3,"score":0.23399999737739563},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.2305999994277954},{"id":"https://openalex.org/C101721835","wikidata":"https://www.wikidata.org/wiki/Q813908","display_name":"Conditional entropy","level":3,"score":0.22939999401569366},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.2214999943971634},{"id":"https://openalex.org/C137002209","wikidata":"https://www.wikidata.org/wiki/Q898521","display_name":"Hidden variable theory","level":3,"score":0.20749999582767487},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.1988999992609024},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.19840000569820404},{"id":"https://openalex.org/C155846161","wikidata":"https://www.wikidata.org/wiki/Q1143367","display_name":"Graphical model","level":2,"score":0.19539999961853027},{"id":"https://openalex.org/C2780704645","wikidata":"https://www.wikidata.org/wiki/Q9251458","display_name":"Observer (physics)","level":2,"score":0.19189999997615814},{"id":"https://openalex.org/C134444547","wikidata":"https://www.wikidata.org/wiki/Q585230","display_name":"Boolean network","level":3,"score":0.19099999964237213},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.18809999525547028},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.18490000069141388}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:infoscience.epfl.ch:303460","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/198831","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"doctoral thesis"},{"id":"doi:10.5075/epfl-thesis-10519","is_oa":true,"landing_page_url":"https://doi.org/10.5075/epfl-thesis-10519","pdf_url":null,"source":{"id":"https://openalex.org/S4306400488","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"thesis"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:303460","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/198831","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"doctoral thesis"},"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":{"This":[0,399],"thesis":[1],"focuses":[2],"on":[3,11,18,48,61,68,74,120,165,169,254,295,402,408,454],"two":[4,218,471],"selected":[5],"learning":[6,246,429,451],"problems:":[7],"1)":[8],"statistical":[9],"inference":[10],"graphs":[12],"models,":[13],"and,":[14],"2)":[15],"gradient":[16,251,293],"descent":[17,252,294],"neural":[19,257,269,490],"networks,":[20],"with":[21,86,217,250,300,319,486,493],"the":[22,29,33,37,41,62,75,78,91,104,110,131,141,145,156,181,190,195,207,211,225,235,239,243,261,306,320,323,339,348,351,368,373,382,392,421,506],"common":[23],"objective":[24],"of":[25,40,52,56,64,71,77,93,97,106,176,210,238,245,263,347,350,391,457,467,502,516],"defining":[26],"and":[27,101,144,168,273,277,283,405,414,427],"analysing":[28],"measures":[30],"that":[31,119,224,279,313,334,366,423,463,498],"characterize":[32],"fundamental":[34],"limits.":[35],"In":[36,80,234,416],"first":[38],"part":[39,237],"thesis,":[42,240],"we":[43,82,222,241,332,443],"consider":[44,83,242,444],"spin":[45],"synchronization":[46,84],"problems":[47],"graphs,":[49],"which":[50],"consist":[51],"reconstructing":[53],"a":[54,65,94,268,274,281,288,296,336,355,379,386,445,458,464,487,513],"vector":[55],"n":[57],"independent":[58,129,139],"spins":[59,92,113,123],"living":[60],"vertices":[63],"graph,":[66],"based":[67],"noisy":[69,292],"observations":[70,143],"their":[72],"interactions":[73],"edges":[76],"graph.":[79,154],"particular,":[81,417],"models":[85,404,410],"erasure":[87],"(BEC)":[88],"side-information,":[89],"where":[90],"small":[95,174],"fraction":[96,175],"nodes":[98],"are":[99,127,136,179,519],"revealed,":[100,180],"investigate":[102],"how":[103,200],"addition":[105],"such":[107,411,425],"side-information":[108],"influences":[109],"correlations":[111],"between":[112,267],"at":[114,124,183,271],"distant":[115,125],"sites.":[116],"We":[117,147,198,259,311,363,461,495],"show":[118,223,312,365,462,497],"trees,":[121,171],"whenever":[122,172],"sites":[126],"nearly":[128,138],"given":[130,140],"edge":[132,142],"observations,":[133],"then":[134,291,364],"they":[135],"still":[137],"side-information.":[146],"conjecture":[148,227,356],"this":[149,201,418],"to":[150,377,434,477],"hold":[151,230],"for":[152,188,205,231,314,395,424,428,450,499],"any":[153,173],"On":[155],"other":[157,409],"hand,":[158],"(Kanade":[159],"et":[160,360],"al.,":[161,361],"2014)":[162],"conjectured":[163],"that,":[164],"regular":[166],"trees":[167],"Galton-Watson":[170],"node":[177],"labels":[178],"boundary":[182],"infinite":[184],"depth":[185,316],"becomes":[186],"ineffective":[187],"detecting":[189],"root":[191],"bit,":[192],"even":[193],"in":[194,308,335,345,358,367,389,481],"reconstruction":[196],"regime.":[197],"explain":[199],"can":[202,325,342],"be":[203,326,343],"used":[204],"computing":[206],"limiting":[208],"entropy":[209],"sparse":[212],"Stochastic":[213],"Block":[214],"Model":[215],"(SBM)":[216],"symmetric":[219],"communities.":[220],"Finally,":[221,442],"latter":[226],"does":[228],"not":[229,286,520],"every":[232],"tree.":[233],"second":[236],"problem":[244],"Boolean":[247,329,393],"target":[248,275,284,307,352],"functions":[249,503],"(GD)":[253],"fully":[255,297,488],"connected":[256,298,489],"networks.":[258],"introduce":[260],"notion":[262],"\"Initial":[264],"Alignment\"":[265],"(INAL)":[266],"network":[270,282,299,491],"initialization":[272,303],"function":[276],"prove":[278,333],"if":[280],"do":[285],"have":[287,435],"noticeable":[289],"INAL,":[290],"i.i.d.":[301],"Gaussian":[302],"cannot":[304],"learn":[305,478],"polynomial":[309],"time.":[310],"finite":[315],"networks":[317],"trained":[318,492],"correlation":[321],"loss,":[322],"result":[324],"extended":[327],"beyond":[328],"inputs.":[330],"Moreover,":[331],"similar":[337],"setting,":[338,371],"generalization":[340],"error":[341,384],"lower-bounded":[344],"terms":[346,390],"noise-stability":[349],"function,":[353],"supporting":[354],"made":[357],"(Zhang":[359],"2021).":[362],"distribution":[369],"shift":[370],"when":[372],"data":[374],"withholding":[375],"corresponds":[376],"freezing":[378],"single":[380],"feature,":[381],"generalisation":[383],"admits":[385],"tight":[387],"characterisation":[388],"influence":[394],"several":[396],"relevant":[397],"architectures.":[398],"is":[400],"shown":[401],"linear":[403],"supported":[406],"experimentally":[407],"as":[412],"MLPs":[413],"Transformers.":[415],"puts":[419],"forward":[420],"hypothesis":[422],"architectures":[426],"logical":[430],"functions,":[431],"GD":[432],"tends":[433],"an":[436],"implicit":[437],"bias":[438],"towards":[439],"low-degree":[440],"representations.":[441],"'curriculum":[446],"learning'":[447],"(CL)":[448],"strategy":[449],"k":[452,479],"-parities":[453,480],"d":[455,482],"bits":[456],"binary":[459],"string.":[460],"wise":[465],"choice":[466],"training":[468],"examples,":[469],"involving":[470,512],"or":[472],"more":[473],"product":[474,517],"distributions,":[475],"allows":[476],"O":[483],"(1)":[484],"time":[485],"GD.":[494],"further":[496],"another":[500],"class":[501],"-":[504,509],"namely":[505],"'Hamming":[507],"mixtures'":[508],"CL":[510],"strategies":[511],"bounded":[514],"number":[515],"distributions":[518],"beneficial.":[521]},"counts_by_year":[],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}