Izibalo zomshini omusha? Amaphethini amahle kanye nokungabi namandla

Ngokusho kwabanye ochwepheshe, imishini ingasungula noma, uma uthanda, uthole izibalo ezintsha ngokuphelele thina bantu esingakaze sizibone noma sizicabange. Abanye baphikisa ngokuthi imishini ayizisunguli lutho ngokwayo, ingamela kuphela amafomula esiwaziyo ngendlela ehlukile, futhi ayikwazi ukubhekana nezinkinga ezithile zezibalo nhlobo.

Muva nje, iqembu lososayensi abavela ku-Technion Institute kwa-Israel kanye ne-Google bethule isistimu ezenzakalelayo yokukhiqiza ama-theoremuabawubiza ngomshini weRamanujan ngesazi sezibalo Srinivasi Ramanujanaowasungula izinkulungwane zamafomula aphusile kuthiyori yezinombolo enemfundo encane noma engenakho nhlobo. Uhlelo olwakhiwe abacwaningi luguqule inani lamafomula asekuqaleni nabalulekile awenza ama-universal constants avela kuzibalo. Iphepha eliphathelene nalesi sihloko lishicilelwe kumagazini i-Nature.

Enye yamafomula akhiqizwe umshini ingasetshenziswa ukubala inani lokungaguquki kwendawo yonke okubizwa Inombolo yesiCatalan, esebenza kahle kakhulu kunokusebenzisa amafomula aziwa ngaphambilini atholwe umuntu. Nokho, ososayensi bathi Imoto kaRamanujan ayihloselwe ukususa izibalo kubantu, kodwa kunalokho ukunikeza usizo kochwepheshe bezibalo. Nokho, lokhu akusho ukuthi uhlelo lwabo alunayo isifiso sokuvelela. Njengoba bebhala, uMshini "uzama ukulingisa intuition yezibalo yochwepheshe bezibalo abakhulu futhi unikeze namacebiso kwezinye izimfuno zezibalo."

Uhlelo lwenza ukuqagela mayelana namanani ama-universal constants (njengokuthi) abhalwe njengamafomula amahle abizwa ngokuthi amafrakshini aqhubekayo noma izingxenyana eziqhubekayo (1). Leli igama lendlela yokuveza inombolo yangempela njengengxenyana efomini elikhethekile noma umkhawulo wamafrakshini anjalo. Ingxenye eqhubekayo ingaba nomkhawulo noma ibe nama-quotient amaningi ngokungapheli._i/b_i; ingxenye A_k/B_k etholwe ngokulahla izingxenye eziyingxenye engxenyeni eqhubekayo, kusukela ku-(k + 1)th, ibizwa ngokuthi i-kth reduct futhi ingabalwa ngamafomula:_-1= 1, A₀=b₀Ngaphakathi_-1=0,V₀= 1, A_k=b_kA_k-1+a_kA_k-2Ngaphakathi_k=b_kB_k-1+a_kB_k-2; uma ukulandelana kokunciphisa kuhlangana kumkhawulo olinganiselwe, khona-ke ingxenyenamba eqhubekayo ibizwa ngokuthi i-convergent, ngaphandle kwalokho ibizwa ngokuthi i-divergent; ingxenye eqhubekayo ibizwa ngokuthi i-arithmetic uma_i= 1, p₀ kuqediwe, b_i (i>0) - ngokwemvelo; ingxenye eqhubekayo ye-arithmetic iyahlangana; inombolo ngayinye yangempela inweba ibe ingxenyenamba yezibalo eqhubekayo, enomkhawulo ezinambeni ezinengqondo kuphela.

1. Isibonelo sokubhala u-Pi njengengxenye eqhubekayo

Ramanujan umshini algorithm ikhetha noma yimaphi ama-universal constants ohlangothini lwesobunxele nanoma yiziphi izingxenyana eziqhubekayo zohlangothi lwesokudla, bese ibala uhlangothi ngalunye ngokuhlukene ngokunemba okuthile. Uma izinhlangothi zombili zibonakala zigqagqana, amanani abalwa ngokunemba okwengeziwe ukuze kuqinisekiswe ukuthi okufanayo akufani noma ukunemba. Okubalulekile, akhona kakade amafomula akuvumela ukuthi ubale inani lama-universal constants, isibonelo, nganoma yikuphi ukunemba, ngakho okuwukuphela kwesithiyo ekuhloleni ukuhambisana kwekhasi yisikhathi sokubala.

Ngaphambi kokusebenzisa ama-algorithms anjalo, izazi zezibalo kwakudingeka zisebenzise ekhona kakade. ulwazi lwezibalo i amathiyoriyenza umcabango onjalo. Ngenxa yokuqagela okuzenzakalelayo okukhiqizwa ama-algorithms, izazi zezibalo zingazisebenzisa ukuze zidale kabusha amathiyori afihliwe noma imiphumela "enhle" ngaphezulu.

Ukutholwa okuphawuleka kakhulu kwabacwaningi akulona ulwazi olusha kangako njengokucatshangwa okusha kokubaluleka okumangazayo. Lokhu kuvumela ukubalwa kwe-Catalan njalo, i-universal constant okubaluleka kwayo kuyadingeka ezinkingeni eziningi zezibalo. Ukuyiveza njengengxenye eqhubekayo emcabangweni osanda kutholwa kuvumela izibalo ezishesha kakhulu kuze kube manje, okuhlula amafomula angaphambilini athatha isikhathi eside ukucutshungulwa kukhompuyutha. Lokhu kubonakala kuphawula iphuzu elisha lenqubekelaphambili yesayensi yekhompiyutha kusukela lapho amakhompyutha eqala ukushaya abadlali be-chess.

Yini i-AI engakwazi ukuyiphatha

Ama-algorithms womshini Njengoba ubona, benza ezinye izinto ngendlela entsha nephumelelayo. Njengoba bebhekene nezinye izinkinga, abanakuzisiza. Iqembu labacwaningi eNyuvesi yaseWaterloo eCanada bathola ikilasi lezinkinga lisebenzisa ukufunda ngomshini. Ukutholwa kuxhumene nendida echazwe maphakathi nekhulu leminyaka elidlule isazi sezibalo sase-Austria uKurt Gödel.

Isazi sezibalo u-Shai Ben-David nethimba lakhe bethule imodeli yokufunda yomshini ebizwa ngokuthi i-maximum prediction (EMX) ekushicilelweni kujenali i-Nature. Kubukeka sengathi umsebenzi olula wabonakala ungenakwenzeka kubuhlakani bokwenziwa. Inkinga idalwe yiqembu Shay Ben-David kufika phansi ekubikezeleni umkhankaso wokukhangisa onenzuzo enkulu, ogxile kubafundi abavakashela isayithi njalo. Inani lamathuba likhulu kangangokuthi inethiwekhi ye-neural ayikwazi ukuthola umsebenzi ozobikezela kahle ukuziphatha kwabasebenzisi bewebhusayithi, ibe nesampula encane kuphela yedatha etholakalayo.

Kuvele ukuthi ezinye zezinkinga ezidalwa amanethiwekhi e-neural zilingana ne-continuum hypothesis eyenziwe nguGeorg Cantor. Isazi sezibalo saseJalimane safakazela ukuthi i-cardinal yesethi yezinombolo zemvelo ingaphansi kwe-cardinal yesethi yezinombolo zangempela. Wabe esebuza umbuzo angakwazi ukuwuphendula. Okungukuthi, wazibuza ukuthi ngabe kukhona yini isethi engapheli ogama lakhe lingaphansi kwekhadinali isethi yezinombolo zangempelakodwa amandla engeziwe isethi yezinombolo zemvelo.

Isazi sezibalo sase-Austrian sekhulu lesi-XNUMX. Kurt Gödel kwafakazela ukuthi i-continuum hypothesis ayinakunqunywa ohlelweni lwamanje lwezibalo. Manje kuvele ukuthi izazi zezibalo eziklama amanethiwekhi e-neural ziye zabhekana nenkinga efanayo.

Ngakho, nakuba ingabonakali kithi, njengoba sibona, ayinakuzisiza lapho ibhekene nokulinganiselwa okuyisisekelo. Ososayensi bayazibuza ukuthi uma kunezinkinga zalesi sigaba, njengamasethi angapheli, isibonelo.