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UkuqambaAI Understanding ukwaziswa

Isifundo Sezibalo Esisizwa yi-AI Siqinisa Imingcele Ngokuhlala Okude

Ucwaningo lwecala lubika ukuthi uhlelo locwaningo lwe-AI lusize ukuthuthukisa imingcele ku-Grothendieck njalo, kuyilapho ababhali begcizelela ukuthi abacwaningi abangabantu bakhethe i-pivot eyinhloko futhi baqinisekisa ngokuzimela umphumela wezinga le-theorem kuphela.

6 min readRead the primary source
Idokhumenti yomthombo oyinhlokoUmthombo urekhodiwe
Umshicileli
Long-horizon AI mathematics case study on arXiv
Isixhumanisi somthombo
arxiv.orghttps://arxiv.org/abs/2608.11195
Uhlobo lomthombo
Idokhumenti eyisisekelo β€” isimemezelo esisemthethweni, iphepha, ukugcwalisa, noma ikhasi lomuntu wokuqala esilifunda ngokuqondile.
UmongoQonda lokhu ngemizuzwana engama-60

Qala lapha

Imigomo ebalulekile

I-API (I-Application Programming Interface)
Indlela ehlelekile yesistimu yesofthiwe eyodwa ukuthumela izicelo futhi yamukele izimpendulo ezivela kwenye isistimu.
Inkumbulo (Inkumbulo yomenzeli)
Ingqikithi egciniwe umenzeli we-AI usebenzisa ezinyathelweni zonke noma izikhathi ukuze athuthukise ukuqhubeka.
Ibhentshimakhi
Ukuhlolwa okujwayelekile noma isethi yedatha esetshenziselwa ukukala nokuqhathanisa ukusebenza kwemodeli.
ZihloleImibuzo ye-AI Agents

Kwenzekeni

Ucwaningo olusha lwe-arXiv luchaza ukuthi uhlelo locwaningo lwe-AI lusize kanjani izazi zezibalo ukuthi zithuthukise imingcele eyaziwayo ku-Grothendieck njalo, inkinga evulekile eyaqala ngo-1953. Iphepha lethula kokubili umphumela wezibalo kanye nerekhodi elinemininingwane yokuthi uhlelo lusebenze kahle kuphi, lapho abantu bekumele baluqondise, futhi yiziphi izimangalo ezihlala ziqinisekiswa ngomshini kunokuba ziqinisekiswe umuntu.

I-Grothendieck engaguquki ikala igebe phakathi kwenkinga enzima yokwenza kahle izinto ezihlanganisiwe kanye nokuphumula okulinganiselwe okufinyeleleka kalula. Ababhali babika isikhawu esisha esinomkhawulo ophansi we-6pi / 11, mayelana ne-1.7135, kanye nomkhawulo ongaphezulu mayelana ne-1.7818. Iphepha lezibalo elihambisana nalo linikeza ubufakazi. Umphumela wesibopho esiphansi uyaphawuleka ngoba akwakhi isimo esiqinile; esikhundleni salokho ithola isithiyo esisebenza kuzo zonke izikimu zokuqoqa ezifanele.

Uhlelo locwaningo luhlanganise imodeli yokucabanga ne-ejenti yokubhala ikhodi. Iphepha lithi ukugijima kusetshenziswe i-GPT-5.5-Pro ​​futhi kamuva i-GPT-5.6-Sol yokucabanga, i-Claude Code nge-Opus futhi kamuva i-Fable 5 ukuze kwenziwe, kanye ne-node ye-GPU emine yokusesha izinombolo. Amaseshini abe nokuqhubeka ngamafayela, okulotshiweyo, amalogi okuhlola, nesifinyezo esirekhode izimangalo njengezifakazelwe, ezisekelwe ngokwezinombolo, ezicatshangelwayo, noma eziphathelene ne-heuristic esikhundleni sokuthembela emongweni owodwa ongaphazamiseki.

Ukugijima kuhlanganisa cishe izikhathi zocwaningo ezingu-240 kusukela ngoJuni 16 kuya kuJulayi 24, nezingcingo eziyimodeli yokucabanga eziyi-2,091 kanye namathokheni alinganiselwa ezigidini eziyi-152 ngenani elilinganiselwa ku-$5,400 API. Iziqondiso zabantu ezingaba ngu-40 zadala umsebenzi. Lapho ukusesha okubheke phezulu kukhula, o-opharetha babone ukuthi ukwehluleka okuphindaphindiwe kungase kubonise ukuvinjelwa okujwayelekile futhi kuqondise kabusha isistimu ku-agumenti enesibopho esiphansi. Leli phepha lichaza lolo shintsho esiqondisweni socwaningo njengokungenelela komuntu, hhayi isinqumo esizimele.

Uhlelo lukhiqize kabusha i-central reframe kanye nobufakazi obuphelele be-6pi / 11 eboshiwe ephansi, ababhali base beyibuyekeza futhi baqinisekisa ngokuzimela. Iphinde yakhiqiza amakhandidethi ezinombolo aphezulu naphansi anamandla aphumelele iphrothokholi yokuhlola kwangaphakathi, kodwa ababhali abakaziqinisekisanga ngokuzimela lezo zitifiketi futhi abazisho njengezithiyori. Ngakho-ke iphepha lihlukanisa umphumela wezibalo oqinisekisiwe kokuphumayo kwesistimu okuqagelayo kakhulu noma okuhlolwe umshini.

Imininingwane yomthombo: Long-horizon AI mathematics case study on arXiv β†—

Kungani kubalulekile

Ucwaningo lunikeza ubufakazi obuphathekayo obungajwayelekile mayelana ne-AI obusetshenziswa kulo lonke uhlelo locwaningo kunomsebenzi owodwa wokulinganisa. Ukuthola kwayo okubaluleke kakhulu ukuhlukaniswa kwezabasebenzi: uhlelo lwaluqinile ekusebenzeni kobuchwepheshe, kuyilapho abacwaningi abangabantu behlala benesibopho sokusethwa kwe-ajenda, ukwahlulela, nokuqinisekisa okokugcina.

Ucwaningo lomkhathizwe lunzima ohlelweni lwe-AI ngoba inhloso ingashintsha njengoba kunqwabelana izindlela ezihlulekile. Umhleli owusizo kufanele agcine lokho okuzanyiwe, ahlukanise isiphetho esingenalutho embonweni ongaxazululiwe, futhi anqume lapho umbuzo omusha ubaluleke kakhulu kunokunye ukulungiselelwa kwendawo. Inkumbulo esekelwe efayeleni yababhali namalebula ezicelo kuwumzamo wokwenza leso simo socwaningo sibonakale futhi sifundeke kunokuvumela impendulo eshelelayo ukuthi ime ukuze iqhubeke.

Ukutholwa kwemingcele ephansi kubonisa ukuthi kungani ukwahlulela komuntu kusebalulekile ngisho nalapho umenzeli ekwazi ukwenza izibalo. Ama-opharetha aqaphele ukuthi imizamo eminingi yokwakha yahluleka ngendlela efanayo futhi anikezela nge-pivot yomqondo: fakazela ukuvinjelwa okuphindaphindiwe ngokwakho. Uhlelo lube selusiza ukwenza kube semthethweni kanye nokuqinisekisa ukungqubuzana. Lolo chungechunge luseduze nokuhlola okugadiwe kunesazi sezibalo somshini ozimele, futhi umehluko ubalulekile lapho uchaza lokho ubufakazi obusekelayo.

Ukuqinisekisa okuzimele kuyisango lokukhululwa lomphumela. Ucwaningo lwecala luthi umkhawulo ophansi uhlolwe ababhali nokuthi ubufakazi obuphelele buvela ephepheni elingumngane. Akusho ukuthi zonke izinombolo ezikhiqizwayo ngesikhathi sokugijima zilungile. Ukugcina izimangalo zeleveli ye-theoem, amakhandidethi ahlolwe ngomshini, kanye nokuqagela kuhlukene kunikeza abafundi indlela yokuhlola umnikelo ngaphandle kokwamukela ukuzethemba kwangaphakathi kwesistimu ye-AI njengobufakazi bezibalo.

Ezinhlanganweni zocwaningo, isifundo esisebenzayo siyasebenza. Uhlelo lwe-AI lungasesha izincwadi, lubhale amakhodi, luqhube izivivinyo, lugcine imizamo ehlulekile, futhi luphakamise izinguquko, kodwa ukuhamba komsebenzi okuzungezile kudinga ukuvela, ukubala okuphindaphindekayo, izindawo zokuhlola abantu ezicacile, nendlela yokwakha kabusha ukuthi kungani iqembu lishintshe indlela. Izindleko ezibikiwe nokubala futhi zenza kucace ukuthi ikhono le-horizon elide akuwona nje umbuzo wobuhlakani bemodeli; kuncike esikalini, isikhathi, kanye nokwengamela okuqhubekayo.

Interactive Mechanism

I-Interactive Mechanism: Indlela Esebenza Ngayo Ngempela

Hlola ubuchwepheshe obuyisisekelo ngemuva kwalokhu kuthuthukiswa ngokuhlanganyela.

Thinking Budget (Test-Time Tokens):1,024 tokens
Complex Accuracy79%Math & Code Logic
Latency3.2sTime to first full output
Inference Cost$0.0092Per query estimated
Reasoning StyleStep VerificationInternal chain depth
Active Thinking Trace:
1Deconstruct user problem into formal constraints
2Propose candidate hypotheses & step-by-step calculation
3Self-correction: Backtrack and refute subtle edge cases
4Exhaustive consistency check & final output synthesis
Core takeaway: Test-time compute fundamentally changes AI economics. Instead of only scaling during pre-training, giving reasoning models more tokens at inference time allows them to systematically solve PhD-level STEM problems.
I-Interactive Concept Check+10 Points
AI Agents Quiz

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Ongakubuka ngokulandelayo

Umbuzo olandelayo ukuthi ingabe le phethini yokubambisana ihlanganisa ngaphezu kwenkinga eyodwa nethimba, nokuthi abacwaningi abazimele bangakwazi yini ukukhiqiza kabusha umphumela oqinisekisiwe ngenkathi bekala izindleko nokuthembeka komnikelo ngamunye womuntu kanye ne-AI.

Ukuphindaphinda kufanele kuhlole ezinye izizinda zezibalo, izinhlobo zezinkinga, nezinhlelo zocwaningo ezinenkumbulo ehlukene kanye nemiklamo yamathuluzi. Inkinga ye-Grothendieck isivele iqhamuke nohlaka olwakhiwe ngabantu, amanothi anqwabelene, imishini yokunikeza izitifiketi, nezikhombisi-ndlela zekhandidethi. Leso sakhiwo sangaphambilini sisize ukusebenza, ngakho izifundo zesikhathi esizayo kufanele zibike ukuthi kungakanani isimo socwaningo esinikezwe kusengaphambili nokuthi imiphumela ishintsha kanjani lapho isistimu kufanele ichaze inkinga ngokwayo.

Abacwaningi kufanele futhi baqhathanise ukwenziwa kobuchwepheshe nokwahlulela kocwaningo besebenzisa izinyathelo ezingenzeka. Amamethrikhi awusizo angafaka ikhwalithi yezikhombisi-ndlela ezikhethiwe, isikhathi sokushiya indlela ehlulekayo, izinga lezimangalo ezingasekelwa, inani lokungenela kwabantu, kanye nengxenye yemiphumela esinda ekuhlolweni okuzimele. Icala elipholishiwe lingabonisa okwenzekile, kodwa ukuqhathanisa okulawulwayo kuyadingeka ukuze ulinganisele lapho umhlanganyeli we-AI ethuthukisa inqubo kunokumane wengeze esinye isendlalelo sokubuyekeza.

Umngcele phakathi kokuqinisekiswa komshini nokuqinisekiswa komuntu udinga ukunakwa okuqhubekayo. Izibalo zesikhawu, abasizi bobufakazi, izivivinyo, nokucwaningwa kwamabhuku okuphikisayo kungase kubambe amaphutha amaningi, kodwa isitifiketi sisengafaka ikhodi okuqondiwe okungalungile noma sincike ekuqageleni okungazange kuphikiswe. Umsebenzi wokulandelela kufanele ushicilele ama-artifact aphelele, uqalise kabusha imingcele engaqinisekisiwe eqine kakhulu, futhi wenze imiphumela ehlulekile noma ehoxisiwe ibonakale njengephumelele.

Okokugcina, izinguqulo zamamodeli, ukwaziswa, iziqondiso zokuqondisa, ikhodi, ukubala, nokulotshiwe kufanele kugcinwe lapho ukugunyazwa kwelayisensi nobumfihlo. Iphepha lamanje libalulekile ngokwengxenye ngenxa yokuthi libika lezo zimo futhi lichaza ubuthakathaka besistimu, okuhlanganisa ukumelela isimo socwaningo esintekenteke kanye nokuzimela okulinganiselwe ekwahluleleni. Kuze kube yilapho amanye amaqembu ekhiqiza kabusha iphethini, lobu ubufakazi obuqinile bokuqhubeka kwezibalo ezisizwa yi-AI, akubona ubufakazi bokuthi amasistimu e-AI angakwazi ukwenza ucwaningo oluvulekile ngokuzimela.

Imihlahlandlela ehlobene nemibuzo

Ama-AI AgentsAmamodeli e-AI AchaziweUkuqeqeshwa kwe-AIIzilinganiso ze-LLMHlola okwaziyo β€” zama imibuzo ye-AI yamahhalaBheka igama le-AI kuhlu lwethu lwamagamaLandela i-tracker yokukhishwa kwemodeli ye-AI
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