Sijongene neengxaki zokwandisa kwiimeko ezininzi zehlabathi lokwenyani apho kufuneka sichonge ubuncinci okanye ubuninzi bomsebenzi.
Qwalasela umsebenzi ukuba ube lumelo lwemathematika lwenkqubo, kwaye ukumisela ubuncinci okanye ubuninzi bayo kunokubaluleka kwiinkqubo ezahlukeneyo ezifana nokufunda ngomatshini, ubunjineli, imali, kunye nezinye.
Qwalasela imbonakalo-mhlaba eneenduli kunye neentlambo, kwaye injongo yethu kukufumana eyona ndawo isezantsi (ubuncinci) ukuya kwindawo yethu ngokukhawuleza.
Sihlala sisebenzisa i-gradient descent algorithms ukusombulula imiceli mngeni yokuphucula. Ezi algorithms ziindlela zokuphinda-phinda zokwandisa zokunciphisa umsebenzi ngokuthatha amanyathelo kwicala lewona mnqantsa wehla (negative gradient).
I-gradient ibonakalisa isalathiso ngokunyuka kakhulu kumsebenzi, kwaye ukuhamba kwelinye icala kusikhokelela kubuncinci.
Yintoni kanye kanye iGradient Descent Algorithm?
Ukwehla kwegradient yindlela edumileyo yokuphinda-phinda yokumisela ubuncinci (okanye ubuninzi) bomsebenzi.
Sisixhobo esibalulekileyo kwiinkalo ezininzi, kuquka yokufunda umatshini, ukufunda nzulu, ubukrelekrele bokwenziwa, ubunjineli, kunye nezezimali.
Umgaqo-siseko we-algorithm usekelwe ekusebenziseni kwayo i-gradient, ebonisa isalathiso sokunyuka okubukhali kwixabiso lomsebenzi.
I-algorithm ngokufanelekileyo ijonga ubume bomsebenzi ukuya kowona buncinci ngokuthatha amanyathelo ngokuphindaphindiweyo kwicala elichaseneyo njengodidi, ngokuphinda-phinda ukucokisa isisombululo kude kuhlangane.
Kutheni Sisebenzisa i-Gradient Descent Algorithms?
Kwabaqalayo, banokusetyenziselwa ukusombulula iingxaki ezahlukeneyo zokuphucula, kubandakanya nezo zineendawo ezinomgangatho ophezulu kunye nemisebenzi enzima.
Okwesibini, banokufumana izisombululo ezifanelekileyo ngokukhawuleza, ngakumbi xa isisombululo sokuhlalutya singafumaneki okanye sibiza kakhulu.
Ubuchwephesha bokwehla kwegradient bunokala kakhulu kwaye bunokuphatha ngempumelelo iiseti zedatha ezinkulu.
Ngenxa yoko, zisetyenziswa kakhulu kwi umatshini wokufunda iialgorithms njengokuqeqesha iinethiwekhi ze-neural ukufunda kwidatha kunye nokuguqula iiparamitha zabo ukunciphisa iimpazamo zokuqikelela.
Umzekelo oneenkcukacha zokuhla kweGradient
Makhe sijonge kumzekelo oneenkcukacha ngakumbi ukuze siqonde ngcono ubuchule bokwehla komgangatho.
Cinga ngomsebenzi we-2D f(x) = x2, eyenza igophe elisisiseko leparabolic elinobuncinane kwi (0,0). I-algorithm yokwehla kwe-gradient iya kusetyenziswa ukumisela le ndawo incinci.
Inyathelo 1: Ukuqaliswa
I-algorithm yokwehla kwegradient iqala ngokuqalisa ixabiso le-variable x, emelwe njengo-x0.
Ixabiso lokuqala linokuba nempembelelo enkulu ekusebenzeni kwe-algorithm.
Ukuqaliswa ngokungenamkhethe okanye ukusebenzisa ulwazi lwangaphambili lwengxaki ziindlela ezimbini eziqhelekileyo. Cinga ukuba x₀ = 3 ekuqaleni kwetyala lethu.
Inyathelo 2: Bala iGradiyenti
Ithareyidi yomsebenzi f(x) kwindawo yangoku x₀. kufuneka emva koko ibalwe.
Ithambeka libonisa ukuthambeka okanye izinga lotshintsho lomsebenzi kuloo ndawo ithile.
Sibala i-derivative malunga no x ukwenzela umsebenzi f(x) = x2, obonelela ngo-f'(x) = 2x. Sifumana i-gradient ku-x0 njengo-2 * 3 = 6 ngokufaka u-x₀ = 3 endaweni yokubala i-gradient.
Inyathelo 3: Hlaziya iiParamitha
Sisebenzisa ulwazi lwegradient, sihlaziya ixabiso lika-x ngolu hlobo lulandelayo: x = x₀ – α * f'(x₀), apho u-α (alpha) ebonisa izinga lokufunda.
Ireyithi yokufunda yi-hyperparameter emisela ubungakanani benyathelo ngalinye kwinkqubo yohlaziyo. Ukuseta ireyithi yokufunda efanelekileyo kubalulekile kuba izinga lokufunda elicothayo linokubangela Algorithm ukuthatha uphindaphindo oluninzi ukufikelela ubuncinane.
Izinga lokufunda eliphezulu, kwelinye icala, linokubangela ukuba i-algorithm igxumeke okanye isilele ukudibana. Masithathe izinga lokufunda lika-α = 0.1 ngenxa yalo mzekelo.
Inyathelo lesi-4: Phinda-phinda
Emva kokuba sinexabiso elihlaziyiweyo lika-x, siphinda iNyathelo 2 kunye ne-3 ngenani elimiselweyo lokuphindaphinda okanye de utshintsho ku-x lube luncinci, lubonisa ukuhlangana.
Indlela ibala i-gradient, ihlaziya ixabiso lika-x, kwaye iqhubeleka nenkqubo kuphindaphindo ngalunye, ivumela ukuba isondele kowona mncinci.
Inyathelo lesi-5: Ukudibana
Ubuchwephesha buyadibana emva kokuphinda-phinda okumbalwa ukuya kwindawo apho uhlaziyo olongezelelweyo aluchaphazeli ngokubonakalayo ixabiso lomsebenzi.
Kwimeko yethu, njengoko uphindaphindo luqhubeka, u-x uya kusondela ku-0, ixabiso elincinci le-f (x) = x^2. Inani lokuphindaphinda okuyimfuneko ekuhlanganeni limiselwa yimiba efana nezinga lokufunda elikhethiweyo kunye nobunzima bomsebenzi owenziwayo.
Ukukhetha inqanaba lokuFunda ()
Ukukhetha izinga lokufunda elamkelekileyo () kubalulekile kwi-algorithm yokwehla komgangatho. Njengoko bekutshiwo ngaphambili, ireyithi yokufunda esezantsi inokubangela ukudibana okucothayo, ngelixa izinga lokufunda eliphezulu linokubangela ukudubuleka kakhulu kunye nokusilela ukuhlangana.
Ukufumana ibhalansi efanelekileyo kubalulekile ekuqinisekiseni ukuba i-algorithm idibanisa kwiyona nto ifunekayo ngokufanelekileyo ngokusemandleni.
Ukuhlengahlengisa izinga lokufunda kudla ngokuba yinkqubo yovavanyo kunye neempazamo xa kusenziwa. Abaphandi kunye noochwephesha bahlala bezama ngamazinga okufunda ahlukeneyo ukuze babone ukuba bakuchaphazela njani ukuhlangana kwe-algorithm kumngeni wabo othile.
Ukuphatha i-Non-Convex Functions
Ngelixa umzekelo owandulelayo unomsebenzi olula we-convex, imiba emininzi yokwenyani yelizwe lokwenyani ibandakanya imisebenzi engeyiyo i-convex kunye neeminima ezininzi zasekhaya.
Xa kusetyenziswa ukwehla komgangatho kwiimeko ezinjalo, indlela inokudibana ifikelele kubuncinci bendawo kunobuncinane behlabathi.
Iindlela ezininzi ezihambele phambili zokwehla kwe-gradient ziye zaphuhliswa ukoyisa lo mba. I-Stochastic Gradient Descent (SGD) yenye indlela enjalo eyenza i-randomness ngokukhetha i-subset engabonakaliyo yamanqaku edatha (eyaziwa ngokuba yi-mini-batch) ukubala i-gradient kwi-iteration nganye.
Le sampulu ingakhethiyo ivumela i-algorithm yokuthintela i-minima yendawo kwaye iphonononge izahlulo ezitsha zommandla womsebenzi, ukonyusa amathuba okufumana ubuncinci obungcono.
UAdam (Uqikelelo lomzuzu olungelelaniswayo) lolunye uguquko olubalaseleyo, oluyindlela yokuphucula inqanaba lokufunda edibanisa izibonelelo zazo zombini i-RMSprop kunye nesantya.
U-Adam ulungisa ireyithi yokufunda kwipharamitha nganye ngokutshintshatshintshayo ngokusekwe kulwazi lwangaphambili lwegradient, olunokubangela ukuhlangana okungcono kwimisebenzi engeyiyo i-convex.
Olu tshintsho luphucukileyo lwe-gradient descent lungqineke lusebenza kakuhle ekuphatheni imisebenzi entsonkothileyo kwaye luye lwaba zizixhobo ezisemgangathweni zokufunda koomatshini kunye nokufunda nzulu, apho imiba yokuphucula i-non-convex ixhaphakile.
Inyathelo lesi-6: Yiba nomfanekiso-ngqondweni Inkqubela Yakho
Makhe sibone inkqubela ye-algorithm yokwehla kwe-gradient ukuze siqonde ngcono inkqubo yayo yokuphindaphinda. Qwalasela igrafu ene-x-axis emele uphinda-phindo kunye ne-axis engu-y emele ixabiso lomsebenzi f(x).
Njengoko i-algorithm iphinda-phinda, ixabiso lika-x lisondela ku-zero kwaye, ngenxa yoko, ixabiso lomsebenzi liyehla ngenyathelo ngalinye. Xa icwangciswe kwigrafu, oku kuya kubonisa intsingiselo ehlayo eyahlukileyo, ebonisa inkqubela ye-algorithm yokufikelela kowona mncinci.
Inyathelo lesi-7: ULungisanise kakuhle iNqanaba lokuFunda
Izinga lokufunda () yinto ebalulekileyo ekusebenzeni kwe-algorithm. Ngokwesiqhelo, ukumisela izinga lokufunda elifanelekileyo kuhlala kufuna uvavanyo kunye neempazamo.
Ezinye iindlela zokuphucula, ezinje ngeeshedyuli zomgangatho wokufunda, zinokutshintsha izinga lokufunda ngokuguqukayo ngexesha loqeqesho, ziqale ngexabiso eliphezulu kwaye zilehlise ngokuthe ngcembe njengoko i-algorithm isondela ekuhlanganeni.
Le ndlela inceda ukulinganisa phakathi kophuhliso olukhawulezayo ekuqaleni kunye nokuzinza kufuphi nokuphela kwenkqubo yokuphucula.
Omnye umzekelo: Ukunciphisa i-Quadratic Function
Makhe sijonge omnye umzekelo ukuze siqonde ngcono ukwehla komgangatho.
Qwalasela i-dimensional quadratic function g(x) = (x – 5)^2. Ku-x = 5, lo msebenzi ngokufanayo unobuncinane. Ukufumana obu buncinane, siya kusebenzisa i-gradient descent.
1. Ukuqaliswa: Masiqale ngo-x0 = 8 njengendawo yethu yokuqala.
2. Bala i-gradient ye-g(x): g'(x) = 2(x – 5). Xa sifaka endaweni ka-x0 = 8, i-gradient ku-x0 ngu-2 * (8 – 5) = 6.
3. Nge = 0.2 njengezinga lethu lokufunda, sihlaziya x ngolu hlobo lulandelayo: x = x₀ – α * g'(x₀) = 8 – 0.2 * 6 = 6.8.
4. Phindaphinda: Siphinda amanyathelo 2 kunye no-3 kangangoko kuyimfuneko de kufikelelwe ekuhlanganeni. Umjikelo ngamnye usondeza u-x kwi-5, ixabiso elincinci le-g (x) = (x - 5)2.
5. Ukudibanisa: Indlela ekugqibeleni iya kudibanisa kwi-x = 5, ixabiso elincinci le-g (x) = (x - 5)2.
Uthelekiso lwemilinganiselo yokuFunda
Masithelekise isantya sokuhlangana sokwehla komgangatho kumazinga okufunda ahlukeneyo, yithi α = 0.1, α = 0.2, kunye no-α = 0.5 kumzekelo wethu omtsha. Siyabona ukuba izinga lokufunda elisezantsi (umz., = 0.1) liya kubangela ukudibanisa ixesha elide kodwa ubuncinane obuchanekileyo.
Izinga lokufunda eliphakamileyo (umz., = 0.5) liya kudibana ngokukhawuleza kodwa linokuthi ligqithise okanye lijikeleze malunga nokona kuncinci, okukhokelela ekuchanekeni okubi.
Umzekelo we-Multimodal wokuPhathwa koMsebenzi we-Non-Convex
Qwalasela h (x) = isono (x) + 0.5x, umsebenzi non-convex.
Kukho iiminima ezininzi zasekuhlaleni kunye nobuninzi balo msebenzi. Ngokuxhomekeke kwindawo yokuqala kunye nezinga lokufunda, sinokudibana kuyo nayiphi na i-minima yasekhaya sisebenzisa ukwehla kwe-gradient eqhelekileyo.
Sinokuyicombulula le nto ngokusebenzisa iindlela eziphucukileyo zokuphucula ezifana ne-Adam okanye i-stochastic gradient descent (SGD). Ezi ndlela zisebenzisa amazinga okufunda okuguquguqukayo okanye isampulu engacwangciswanga ukuphonononga imimandla eyahlukeneyo yembonakalo-mhlaba yomsebenzi, okonyusa amathuba okufumana ubuncinci obungcono.
isiphelo
Ii-algorithms ze-gradient descent zizixhobo ezinamandla zokuphucula ezisetyenziswa ngokubanzi kuluhlu olubanzi lwamashishini. Bafumana elona lisezantsi (okanye ubuninzi) bomsebenzi ngokuhlaziya ngokuphindaphindiweyo iiparamitha ezisekelwe kwicala lothambeka.
Ngenxa yobume be-algorithm yokuphindaphinda, iyakwazi ukuphatha iindawo ezinobungakanani obuphezulu kunye nemisebenzi entsonkothileyo, iyenza ibe yimfuneko ekufundeni koomatshini kunye nokusetyenzwa kwedatha.
Ukwehla kweGradient ngokulula kunokujongana nobunzima behlabathi lokwenyani kwaye kube negalelo elikhulu ekukhuleni kwetekhnoloji kunye nokwenziwa kwezigqibo okuqhutywa yidatha ngokukhetha ngononophelo inqanaba lokufunda kunye nokusebenzisa iiyantlukwano eziphambili ezifana nokwehla kwestochastic gradient kunye noAdam.
Shiya iMpendulo