{"id":"https://openalex.org/W7017148222","doi":null,"title":"Algorithms and Algorithmic Barriers in High-Dimensional Statistics and Random Combinatorial Structures","display_name":"Algorithms and Algorithmic Barriers in High-Dimensional Statistics and Random Combinatorial Structures","publication_year":2022,"publication_date":"2022-05-01","ids":{"openalex":"https://openalex.org/W7017148222"},"language":"en","primary_location":{"id":"pmh:oai:dspace.mit.edu:1721.1/144485","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/1721.1/144485","pdf_url":"https://dspace.mit.edu/bitstreams/dcd24aa8-eb66-4973-8bc3-f3d9027de52b/download","source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"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":"Thesis"},"volume":null,"type":"dissertation","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://dspace.mit.edu/bitstreams/dcd24aa8-eb66-4973-8bc3-f3d9027de52b/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029207194","display_name":"Eren C. K\u0131z\u0131lda\u011f","orcid":"https://orcid.org/0000-0003-0411-7161","observed_orcids":["https://orcid.org/0000-0003-0411-7161"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kizildag, Eren C.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5029207194"],"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":true,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.3208000063896179,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.3208000063896179,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.25099998712539673,"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":0.17960000038146973,"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/overlap-gap-property","display_name":"overlap gap property","score":0.8849999904632568},{"id":"https://openalex.org/keywords/stable-algorithms","display_name":"stable algorithms","score":0.6790000200271606},{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.7789999842643738},{"id":"https://openalex.org/keywords/ramsey-theory","display_name":"Ramsey theory","score":0.8119999766349792},{"id":"https://openalex.org/keywords/sherrington-kirkpatrick-model","display_name":"Sherrington-Kirkpatrick model","score":0.8690000176429749},{"id":"https://openalex.org/keywords/p-hardness","display_name":"#P-hardness","score":0.7870000004768372},{"id":"https://openalex.org/keywords/average-case-hardness","display_name":"average-case hardness","score":0.6589999794960022},{"id":"https://openalex.org/keywords/two-layer-neural-networks","display_name":"two-layer neural networks","score":0.8220000267028809},{"id":"https://openalex.org/keywords/high-dimensional-statistics","display_name":"high-dimensional statistics","score":0.4650000035762787},{"id":"https://openalex.org/keywords/random-combinatorial-structures","display_name":"random combinatorial structures","score":0.7559999823570251}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5389000177383423},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.5299000144004822},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.5008999705314636},{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.4602999985218048},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.45899999141693115},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4397999942302704},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40290001034736633},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.39969998598098755},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3912000060081482},{"id":"https://openalex.org/C150775274","wikidata":"https://www.wikidata.org/wiki/Q1490646","display_name":"Spin glass","level":2,"score":0.3813999891281128},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3749000132083893},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35929998755455017},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3564000129699707},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.3528999984264374},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.3488999903202057},{"id":"https://openalex.org/C60908668","wikidata":"https://www.wikidata.org/wiki/Q690207","display_name":"Perceptron","level":3,"score":0.34869998693466187},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.34299999475479126},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.33469998836517334},{"id":"https://openalex.org/C1769372","wikidata":"https://www.wikidata.org/wiki/Q3850844","display_name":"Combinatorial principles","level":3,"score":0.32280001044273376},{"id":"https://openalex.org/C13929819","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Random function","level":3,"score":0.3070000112056732},{"id":"https://openalex.org/C2777472644","wikidata":"https://www.wikidata.org/wiki/Q16968992","display_name":"Approximate inference","level":3,"score":0.3059000074863434},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.3025999963283539},{"id":"https://openalex.org/C52386014","wikidata":"https://www.wikidata.org/wiki/Q166211","display_name":"Random element","level":3,"score":0.2973000109195709},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.2906000018119812},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.2728999853134155},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.27070000767707825},{"id":"https://openalex.org/C112291201","wikidata":"https://www.wikidata.org/wiki/Q1336170","display_name":"Ramsey theory","level":2,"score":0.2515000104904175}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:dspace.mit.edu:1721.1/144485","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/1721.1/144485","pdf_url":"https://dspace.mit.edu/bitstreams/dcd24aa8-eb66-4973-8bc3-f3d9027de52b/download","source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"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":"Thesis"}],"best_oa_location":{"id":"pmh:oai:dspace.mit.edu:1721.1/144485","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/1721.1/144485","pdf_url":"https://dspace.mit.edu/bitstreams/dcd24aa8-eb66-4973-8bc3-f3d9027de52b/download","source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"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":"Thesis"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7017148222.pdf","grobid_xml":"https://content.openalex.org/works/W7017148222.grobid-xml"},"referenced_works_count":65,"referenced_works":["https://openalex.org/W813605148","https://openalex.org/W1506591887","https://openalex.org/W1949284707","https://openalex.org/W2126464735","https://openalex.org/W2131172946","https://openalex.org/W2281746805","https://openalex.org/W2399994860","https://openalex.org/W2410678056","https://openalex.org/W2556883406","https://openalex.org/W2558384550","https://openalex.org/W2561193401","https://openalex.org/W2565538933","https://openalex.org/W2604117713","https://openalex.org/W2619069683","https://openalex.org/W2731468224","https://openalex.org/W2741952635","https://openalex.org/W2749772809","https://openalex.org/W2765428107","https://openalex.org/W2765861987","https://openalex.org/W2766371994","https://openalex.org/W2767382501","https://openalex.org/W2768041186","https://openalex.org/W2774044172","https://openalex.org/W2777138330","https://openalex.org/W2785749378","https://openalex.org/W2789756211","https://openalex.org/W2794772933","https://openalex.org/W2808110885","https://openalex.org/W2883468257","https://openalex.org/W2894604724","https://openalex.org/W2898804862","https://openalex.org/W2899790086","https://openalex.org/W2906886359","https://openalex.org/W2911867426","https://openalex.org/W2916136694","https://openalex.org/W2950220847","https://openalex.org/W2963055984","https://openalex.org/W2963383839","https://openalex.org/W2963569411","https://openalex.org/W2964738308","https://openalex.org/W2970176397","https://openalex.org/W2973737673","https://openalex.org/W2974929660","https://openalex.org/W3006049408","https://openalex.org/W3013992185","https://openalex.org/W3093101468","https://openalex.org/W3093317808","https://openalex.org/W3096771845","https://openalex.org/W3130264527","https://openalex.org/W3133768073","https://openalex.org/W3154192357","https://openalex.org/W3155540517","https://openalex.org/W3171822569","https://openalex.org/W3172297973","https://openalex.org/W3196437393","https://openalex.org/W3203355666","https://openalex.org/W3204144240","https://openalex.org/W3209278616","https://openalex.org/W3214183449","https://openalex.org/W4286717651","https://openalex.org/W4297781214","https://openalex.org/W4313203262","https://openalex.org/W4388866379","https://openalex.org/W4391954608","https://openalex.org/W4401974955"],"related_works":["https://openalex.org/W2897326606","https://openalex.org/W4289655175","https://openalex.org/W3133768073","https://openalex.org/W4313203262","https://openalex.org/W7008791483","https://openalex.org/W3202733572","https://openalex.org/W4417493410","https://openalex.org/W198849214","https://openalex.org/W2906886359","https://openalex.org/W2922392056"],"abstract_inverted_index":{"We":[0,92,120,148,259,484,541,608],"focus":[1,36,243,339,454],"on":[2,23,38,211,245,332,341,398,418,456,593],"several":[3,188],"algorithmic":[4,40,82,233,263],"problems":[5,41],"arising":[6,42,346],"from":[7,43,214,347,565],"the":[8,44,50,57,76,79,94,100,109,126,151,162,168,185,192,197,206,218,225,246,262,268,272,279,303,309,316,399,426,431,447,457,468,471,487,504,526,536,544,550,553,578,594,602],"study":[9,45],"of":[10,15,46,64,96,111,146,159,164,187,220,228,265,271,360,459,503,546,601],"random":[11,47,51,238,257,327,566],"combinatorial":[12,48],"structures":[13],"and":[14,56,78,102,114,167,196,294,307,351,380,445,589],"neural":[16,342],"network":[17,343,404,480,579],"models,":[18],"with":[19,84,237,326,370,463,481],"a":[20,68,72,140,178,252,322,406,414,477,509,561,572,586],"particular":[21,116],"emphasis":[22],"computational":[24,86,311],"aspects.":[25],"Our":[26,34,202,241,313,337,357,422,452],"main":[27],"contributions":[28],"are":[29,209,474,515,556],"summarized":[30],"as":[31,89],"follows.":[32],"1.":[33],"first":[35,226,317,358,485],"is":[37,136,177,224,244,275,288,295,315,330,340,455,507,580],"two":[39],"structures:":[49],"number":[52],"partitioning":[53],"problem":[54,264,458],"(NPP)":[55],"symmetric":[58],"binary":[59,372],"perceptron":[60],"model":[61,254,274,306,325],"(SBP).":[62],"Both":[63],"these":[65],"models":[66,124,236,345],"exhibit":[67,125],"so-called":[69,478],"statistical-to-computational":[70],"gap:":[71],"striking":[73],"gap":[74,98],"between":[75],"existential":[77],"best":[80,219],"known":[81,137],"guarantees":[83],"bounded":[85,407],"power":[87],"(such":[88],"polynomial-time":[90],"algorithms).":[91],"investigate":[93,486,543],"nature":[95],"this":[97,223,363,616],"for":[99,143,205,235,255,302,308,321,367,434],"NPP":[101],"SBP":[103],"by":[104,476],"studying":[105],"their":[106],"landscape":[107],"through":[108],"lens":[110],"statistical":[112,323,353,449],"physics":[113,324],"in":[115,384,443,539],"spin":[117,249],"glass":[118,250],"theory.":[119],"establish":[121,260,391],"that":[122,135,183,261,281,287,329,392,411,470,491,525,552,571,577,611],"both":[123,301],"Overlap":[127],"Gap":[128],"Property":[129],"(OGP),":[130],"an":[131,385,494],"intricate":[132],"geometrical":[133],"property":[134],"to":[138,153,231,298,362],"be":[139,299],"rigorous":[141],"barrier":[142,496],"large":[144],"classes":[145,158],"algorithms.":[147,174],"then":[149,542],"leverage":[150],"OGP":[152],"rule":[154],"out":[155],"certain":[156,562],"important":[157,189],"algorithms,":[160],"including":[161,191],"class":[163,182],"stable":[165,207],"algorithms":[166,190,208],"Monte":[169],"Carlo":[170],"Markov":[171],"Chain":[172],"type":[173],"The":[175],"former":[176],"rather":[179],"powerful":[180],"abstract":[181],"captures":[184],"implementation":[186],"approximate":[193],"message":[194],"passing":[195],"low-degree":[198],"polynomial":[199],"based":[200,210,331],"methods.":[201],"hardness":[203,234,319],"results":[204,361,423],"Ramsey":[212,229],"Theory":[213,230],"extremal":[215],"combinatorics.":[216],"To":[217],"our":[221],"knowledge,":[222],"usage":[227],"show":[232,524,570,610],"parameters.":[239],"2.":[240],"second":[242],"Sherrington-Kirkpatrick":[247],"(SK)":[248],"model,":[251],"mean-field":[253],"disordered":[256],"media.":[258],"exactly":[266],"computing":[267],"partition":[269],"function":[270],"SK":[273],"average-case":[276],"hard":[277],"under":[278,393,467,549,597,620],"assumption":[280,286,469,551],"\ud835\udc43":[282,291],"\u0338=":[283,292],"#\ud835\udc43":[284],"(an":[285],"milder":[289],"than":[290],"\ud835\udc41\ud835\udc43":[293],"widely":[296],"believed":[297],"true)":[300],"finite-precision":[304],"arithmetic":[305],"real-valued":[310],"model.":[312],"result":[314,320],"provable":[318],"parameters":[328],"standard":[333],"complexity-theoretical":[334],"assumptions.":[335,624],"3.":[336],"last":[338],"(NN)":[344],"modern":[348],"machine":[349],"learning":[350,460],"high-dimensional":[352],"inference":[354],"tasks.":[355],"\u2022":[356,451],"set":[359],"direction":[364],"establishes":[365],"self-regularity":[366],"two-layer":[368,461],"NNs":[369,444,462],"sigmoid,":[371],"step,":[373],"rectified":[374],"linear":[375],"unit":[376],"(ReLU)":[377],"activation":[378,465],"functions":[379,466],"non-negative":[381],"output":[382,408],"weights":[383,538,555],"algorithm-independent":[386],"manner.":[387],"That":[388,512],"is,":[389,513],"we":[390,523,569,584],"very":[394,621],"mild":[395,622],"distributional":[396,623],"assumptions":[397],"training":[400,416,472,488,595],"data,":[401],"any":[402,500,599],"such":[403,435],"has":[405,439,605],"norm":[409],"provided":[410,576],"it":[412],"attains":[413],"small":[415],"error":[417],"polynomially":[419],"many":[420],"data.":[421],"explain":[424],"why":[425],"overparameterization":[427],"does":[428],"not":[429],"hurt":[430],"generalization":[432],"ability":[433],"architectures.":[436],"This":[437],"conundrum":[438],"been":[440],"observed":[441],"empirically":[442],"defies":[446],"classical":[448],"wisdom.":[450],"final":[453],"quadratic":[464],"data":[473,596,614],"generated":[475,557,613],"teacher":[479],"planted":[482,537,554],"weights.":[483],"aspect,":[489],"establishing":[490],"there":[492,514],"exists":[493],"energy":[495],"\ud835\udc380":[497],"below":[498,520,532],"which":[499,598],"stationary":[501,518],"point":[502],"empirical":[505,603],"risk":[506,604],"necessarily":[508],"global":[510],"optimum.":[511],"no":[516],"spurious":[517],"points":[519],"\ud835\udc380.":[521],"Consequently,":[522],"gradient":[527],"descent":[528],"algorithm,":[529],"when":[530],"initialized":[531],"\ud835\udc380,":[533],"nearly":[534],"recovers":[535],"polynomial-time.":[540],"question":[545],"proper":[547],"initialization":[548,574],"randomly.":[558],"By":[559],"leveraging":[560],"semicircle":[563],"law":[564],"matrix":[567],"theory,":[568],"deterministic":[573],"suffices,":[575],"sufficiently":[581],"overparameterized.":[582],"Finally,":[583],"identify":[585],"simple":[587],"necessary":[588],"sufficient":[590],"geometric":[591],"condition":[592,617],"minimizer":[600],"good":[606],"generalization.":[607],"lastly":[609],"randomly":[612],"satisfy":[615],"almost":[618],"surely":[619]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2025-10-10T00:00:00"}