Timakumana ndi zovuta za kukhathamiritsa muzochitika zenizeni zenizeni komwe timafunikira kuzindikira ntchito yochepera kapena yochulukirapo.
Ganizirani ntchito ngati chiwonetsero cha masamu pamakina, ndipo kudziwa kuchuluka kwake kapena kuchuluka kwake kungakhale kofunikira pazinthu zosiyanasiyana monga kuphunzira pamakina, uinjiniya, ndalama, ndi zina.
Ganizirani za malo okhala ndi mapiri ndi zigwa, ndipo cholinga chathu ndikupeza malo otsika kwambiri (ochepera) kuti tifike komwe tikupita mwachangu momwe tingathere.
Nthawi zambiri timagwiritsa ntchito ma algorithms a gradient kuti tithane ndi zovuta zotere. Ma aligorivimuwa ndi njira zopititsira patsogolo zochepetsera ntchito pochita masitepe polowera komwe kumatsika kwambiri (negative gradient).
Ma gradient amawonetsa komwe akulowera ndikuwonjezereka kwambiri kwa ntchitoyo, ndipo kuyenda kwina kumatifikitsa pocheperako.
Kodi Gradient Descent Algorithm ndi chiyani kwenikweni?
Kutsika kwa gradient ndi njira yodziwika bwino yodziwira kuchuluka (kapena kupitilira) kwa ntchito.
Ndi chida chofunikira m'magawo angapo, kuphatikiza makina kuphunzira, kuphunzira mozama, luntha lochita kupanga, uinjiniya, ndi zachuma.
Mfundo yayikulu ya algorithm imachokera pakugwiritsa ntchito gradient, yomwe imawonetsa komwe kukukwera kwambiri kwa mtengo wantchitoyo.
Ma aligorivimu amayendetsa bwino mawonekedwe a ntchitoyo kulowera pang'onopang'ono pochita masitepe mobwerezabwereza mbali ina ngati gradient, ndikukonzanso yankho mpaka kulumikizana.
Chifukwa Chiyani Timagwiritsa Ntchito Ma Algorithms a Gradient Descent?
Poyambira, atha kugwiritsidwa ntchito kuthetsa mavuto osiyanasiyana okhathamiritsa, kuphatikiza omwe ali ndi malo apamwamba komanso ntchito zovuta.
Chachiwiri, atha kupeza mayankho abwino mwachangu, makamaka ngati njira yowunikira ilibe kapena yokwera mtengo kwambiri.
Njira zakutsika kwa gradient ndizovuta kwambiri ndipo zimatha kuthana bwino ndi ma dataset akuluakulu.
Chifukwa chake, amagwiritsidwa ntchito kwambiri makina kuphunzira algorithms monga kuphunzitsa ma neural network kuti aphunzire kuchokera ku data ndikusintha magawo awo kuti achepetse zolakwika zolosera.
Chitsanzo Chatsatanetsatane cha Masitepe Otsika Ma Gradient
Tiyeni tiwone chitsanzo chatsatanetsatane kuti timvetsetse bwino njira yotsika ya gradient.
Ganizirani za 2D ntchito f(x) = x2, yomwe imapanga mapindikidwe ofunikira okhala ndi osachepera pa (0,0). Kutsika kwa gradient algorithm kudzagwiritsidwa ntchito kudziwa malo ochepa awa.
Gawo 1: Kuyambitsa
Kutsika kwa gradient algorithm kumayamba ndikuyambitsa mtengo wamitundu x, yoimiridwa ngati x0.
Mtengo woyambira ukhoza kukhudza kwambiri magwiridwe antchito a algorithm.
Kuyambitsa mwachisawawa kapena kugwiritsa ntchito chidziwitso choyambirira cha vutoli ndi njira ziwiri zodziwika bwino. Tangoganizani kuti x₀ = 3 koyambirira kwa mlandu wathu.
Khwerero 2: Werengani Ma Gradient
Maonekedwe a ntchito f(x) pamalo apano x₀. ziyenera kuwerengedwa.
Kutsetsereka kumawonetsa kutsetsereka kapena kuchuluka kwa kusintha kwa ntchito pamalo omwewo.
Timawerengera zotuluka pa x pa ntchito f(x) = x2, yomwe imapereka f'(x) = 2x. Timapeza gradient pa x0 monga 2 * 3 = 6 mwa kulowetsa x ₀ = 3 mu chiwerengero cha gradient.
Khwerero 3: Sinthani Parameters
Pogwiritsa ntchito chidziwitso cha gradient, timasintha mtengo wa x motere: x = x₀ - α * f'(x₀), pamene α (alpha) amatanthauza mlingo wophunzirira.
Mlingo wophunzirira ndi hyperparameter yomwe imatsimikizira kukula kwa gawo lililonse pakukonzanso. Kukhazikitsa mlingo woyenera wophunzirira ndikofunikira chifukwa kutsika pang'onopang'ono kungayambitse aligorivimu kutenga kubwerezabwereza kochuluka kuti mufikire zochepa.
Kuchuluka kwa maphunziro, kumbali ina, kungapangitse kuti ma algorithm adutse kapena kulephera kuphatikizika. Tiyeni tiganizire kuchuluka kwa maphunziro a α = 0.1 chifukwa cha chitsanzo ichi.
Gawo 4: Bwerezani
Titakhala ndi mtengo wosinthidwa wa x, timabwereza Masitepe 2 ndi 3 pa chiwerengero chodziwikiratu cha kubwereza kapena mpaka kusintha kwa x kukhala kochepa, kusonyeza kusinthasintha.
Njirayi imawerengera gradient, imasintha mtengo wa x, ndikupitiriza ndondomekoyi nthawi iliyonse yobwereza, kuti ifike pafupi ndi yochepa.
Gawo 5: Kulumikizana
Njirayi imasinthasintha pakangobwereza pang'ono mpaka pomwe zosintha zina sizikhudza mtengo wa ntchitoyi.
Kwa ife, pamene kubwereza kumapitirira, x idzayandikira 0, yomwe ndi mtengo wochepa wa f (x) = x^2. Kuchulukitsa koyeneranso kophatikizana kumatsimikiziridwa ndi zinthu monga kuchuluka kwa maphunziro komwe kumasankhidwa komanso zovuta za ntchitoyo yomwe ikukongoletsedwa.
Kusankha Mlingo Wophunzirira ()
Kusankha mulingo wovomerezeka wophunzirira () ndikofunikira kwambiri pakuchita bwino kwa gradient descent algorithm. Monga tanenera kale, kuchepa kwa maphunziro kungayambitse kusinthasintha kwapang'onopang'ono, pamene kuchuluka kwa maphunziro kungayambitse kuwombera mopambanitsa ndi kulephera kuphatikizika.
Kupeza malire oyenera ndikofunikira kuti muwonetsetse kuti ma algorithm akusintha mpaka momwe angafunikire moyenera momwe angathere.
Kuwongolera kuchuluka kwa maphunziro nthawi zambiri kumakhala njira yoyesera ndi zolakwika pochita. Ofufuza ndi akatswiri amayesa nthawi zonse milingo yosiyanasiyana yophunzirira kuti awone momwe imakhudzira kusinthika kwa algorithm pazovuta zawo.
Kugwira Ntchito Zopanda Convex
Ngakhale chitsanzo chapitachi chinali ndi ntchito yosavuta ya convex, nkhani zambiri zokometsera zenizeni padziko lapansi zimaphatikizapo ntchito zopanda mawonekedwe ndi minima zambiri zakomweko.
Pogwiritsa ntchito kutsika kwa gradient muzochitika zotere, njirayo imatha kusinthana ndi malo ochepa m'malo mochepera padziko lonse lapansi.
Njira zingapo zapamwamba zotsika pansi zapangidwa kuti zithetse vutoli. Stochastic Gradient Descent (SGD) ndi njira imodzi yotere yomwe imayambitsa chisawawa posankha kagawo kakang'ono ka data (kotchedwa mini-batch) kuti awerengere kuchuluka kwake pakubwereza kulikonse.
Zitsanzo zachisawawazi zimalola ma aligorivimu kuti apewe minima yakumaloko ndikuwunika magawo atsopano azomwe zimagwirira ntchito, kukulitsa mwayi wopeza zochepa zabwinoko.
Adam (Adaptive Moment Estimation) ndi mtundu winanso wodziwika bwino, womwe ndi njira yosinthira yophunzirira yomwe imaphatikiza zabwino zonse za RMSprop komanso kuthamanga.
Adam amasintha mulingo wophunzirira pagawo lililonse motengera zomwe zidachitika kale, zomwe zitha kupangitsa kuti pakhale kulumikizana kwabwinoko pazida zomwe sizili ndi ma convex.
Kusiyanasiyana kwamakono kotereku kwakhala kothandiza pakuwongolera ntchito zomwe zikuchulukirachulukira ndipo zakhala zida zodziwika bwino pakuphunzirira kwamakina ndi kuphunzira mozama, pomwe zovuta zosasinthika ndizofala.
Khwerero 6: Onani M'maganizo Kupita Kwanu
Tiyeni tiwone mayendedwe a gradient descent algorithm kuti timvetsetse bwino njira yake yobwerezabwereza. Ganizirani graph yokhala ndi x-axis yoyimira kubwereza ndi y-axis kuyimira mtengo wa f(x).
Momwe ma algorithm akuchulukirachulukira, mtengo wa x ukuyandikira zero ndipo, chifukwa chake, mtengo wantchito umatsika ndi sitepe iliyonse. Zikakonzedwa pa graph, izi zitha kuwonetsa kutsika kosiyana, kuwonetsa kupita patsogolo kwa algorithm yofikira pakuchepera.
Khwerero 7: Kukonza Bwino Mlingo wa Maphunziro
Mlingo wophunzirira () ndichinthu chofunikira kwambiri pakuchita bwino kwa algorithm. M'zochita zake, kudziwa mlingo woyenera wa maphunziro nthawi zambiri kumafuna kuyesa ndi kulakwitsa.
Njira zina zokometsera, monga ndandanda ya kuchuluka kwa maphunziro, zimatha kusintha kuchuluka kwa maphunziro panthawi yamaphunziro, kuyambira ndi mtengo wapamwamba ndikuchepetsa pang'onopang'ono momwe ma algorithm akuyandikira kulumikizana.
Njirayi imathandiza kuti pakhale mgwirizano pakati pa chitukuko chofulumira kumayambiriro ndi kukhazikika pafupi ndi mapeto a kukhathamiritsa.
Chitsanzo china: Kuchepetsa Quadratic Function
Tiyeni tiwone chitsanzo china kuti timvetse bwino za kutsika kwa gradient.
Ganizirani za mbali ziwiri za quadratic function g(x) = (x - 5)^2. Pa x = 5, ntchitoyi imakhalanso ndi zochepa. Kuti tipeze zochepa izi, tidzagwiritsa ntchito kutsika kwa gradient.
1. Kuyambitsa: Tiyeni tiyambe ndi x0 = 8 monga poyambira.
2. Weretsani gradient ya g(x): g'(x) = 2(x – 5). Tikalowetsa x0 = 8, gradient pa x0 ndi 2 * (8 - 5) = 6.
3. Ndi = 0.2 monga momwe timaphunzirira, timasintha x motere: x = x₀ - α * g' (x₀) = 8 - 0.2 * 6 = 6.8.
4. Kubwerezabwereza: Timabwereza masitepe 2 ndi 3 nthawi zambiri momwe tingathere mpaka mgwirizano ufikire. Kuzungulira kulikonse kumabweretsa x pafupi ndi 5, mtengo wocheperako wa g (x) = (x - 5)2.
5. Convergence: Njirayi pamapeto pake idzasintha kukhala x = 5, yomwe ndi mtengo wochepa wa g(x) = (x - 5)2.
Kuyerekeza kwa Mitengo Yophunzirira
Tiyeni tifananize liwiro la kusinthika kwa kutsika kwa gradient pamitengo yosiyana yophunzirira, nenani α = 0.1, α = 0.2, ndi α = 0.5 mu chitsanzo chathu chatsopano. Titha kuwona kuti kuchuluka kwa maphunziro otsika (mwachitsanzo, = 0.1) kudzapangitsa kuti pakhale kulumikizana kwanthawi yayitali koma kuchepera kolondola.
Maphunziro apamwamba (mwachitsanzo, = 0.5) amalumikizana mwachangu koma amatha kuwombera kapena kusuntha pang'ono, zomwe zimapangitsa kusalondola bwino.
Chitsanzo cha Multimodal cha Non-Convex Function Handling
Ganizirani h (x) = sin(x) + 0.5x, ntchito yopanda mawonekedwe.
Pali ma minima angapo am'deralo ndi maxima pa ntchitoyi. Kutengera ndi komwe tidayambira komanso kuchuluka kwa maphunziro, titha kusinthira ku minima iliyonse yakumaloko pogwiritsa ntchito kutsika kotsika.
Titha kuthetsa izi pogwiritsa ntchito njira zotsogola kwambiri monga Adam kapena stochastic gradient descent (SGD). Njirazi zimagwiritsa ntchito milingo yophunzirira yosinthika kapena zitsanzo mwachisawawa kuti zifufuze madera osiyanasiyana a momwe ntchitoyi ikuyendera, ndikuwonjezera mwayi wopeza zochepa.
Kutsiliza
Ma gradient descent algorithms ndi zida zamphamvu zokhathamiritsa zomwe zimagwiritsidwa ntchito kwambiri m'mafakitale osiyanasiyana. Amapeza chotsikitsitsa (kapena chokwera) cha ntchito pokonzanso magawo ang'onoang'ono kutengera komwe akulowera.
Chifukwa cha kubwereza kwa ma aligorivimu, imatha kugwira ntchito zazikuluzikulu ndi ntchito zovuta, zomwe zimapangitsa kuti ikhale yofunika kwambiri pakuwerenga kwamakina ndi kukonza deta.
Kutsika kwa gradient kumatha kuthana ndi zovuta zenizeni padziko lapansi ndipo kumathandizira kwambiri kukula kwaukadaulo komanso kupanga zisankho motsogozedwa ndi deta posankha mosamala kuchuluka kwa maphunziro ndikugwiritsa ntchito kusiyanasiyana kwapamwamba monga kutsika kwa stochastic gradient ndi Adamu.
Siyani Mumakonda