Kodwa ngexesha elinye, i-clawed back – i-stronger, i-sharpier, i-unstoppable. Kwaye kwakhona, i-clawed i-language ye-programming eyenza kakhulu – hhayi kuphela kwi-architectures zethu ze-von Neumann ezidlulileyo, okanye kuphela kwi-GPU computing race yamanje, kodwa ngenxa yeyona nto eninzi kunokufuneka kakhulu: i-optimizers eyenza i-heart yokubumba ye-AI ye-modern. Zifumaneka ukufa. Ukubumba ukuba kuhle. Zifumaneka ukufa. Ukubumba ukuba kuhle. Kodwa siphinde siphinde. I-DNA ye-1980 yaye i-DNA yaye i-DNA ye-1980 yaye i-DNA ye-1980 yaye i-DNA ye-1980 yaye yaye yaye yaye yaye i-DNA ye-1980 yaye yaye yaye yaye i-DNA ye-1900. The latest C++ release Izixhobo ezintsha ze-C++ 
 
 Iimpawu elinye, ezininzi ezaziwayo, inezinto ezininzi: iinkqubo monadic kwi-C++23 - std::expected, std::optional, kunye ne-std::variant ezisebenza ngokuxhomekeke. Ezi engabonakali i-functional programming i-sugar. Zihlanganisa isiseko sokwenza uhlobo olutsha le-optimization calculus curvature, nto leyo isixazululo esisiseko ukusuka kwi-limit-based calculus eyenza ukuthuthukiswa kwe-modernization kunye ne-AI. Iimpawu omnye, ezininzi ezaziwayo, inikeza iinkcukacha ezininzi: - Ukusuka   iimveliso   Ngokungafani. Kukho kuphela i-functional programming sugar. Zifumaneka isiseko yokusebenza uhlobo olutsha le-optimization calculus Ukukhangisa ngokugqithisileyo kwi-limit-based calculus eyenza i-optimization ezintsha kunye ne-AI advancement. monadic operations in C++23 std::expected , std::optional , std::variant Ukusebenza Ukucaciswa, oku I-Curious about the hidden side of technology? Find more on José Crespo, PhD's page I-Midlife Crisis ye-Optimizer - Yintoni i-C++23 i-Pure Gold Uya kuthatha lo ixesha elide, ngexesha, xa: i-Spotify ithatha i-20 iingoma efanayo. I-Instagram ithatha i-rage-bait. I-Tesla ifumaneka i-fire truck (i-hopefull ayikho ). I-model ifumaneka kwi-NaN emva kweiyure ze-72 kwi-$50k ye-GPUs. I-ChatGPT ibandakanya imini yabantu ngeengoma ezisixhenxe. Yintoni yintoni: iindawo ezahlukeneyo, ingxaki efanayo phantsi. Thina usebenzisa i-mathematics ye-1820 yokusebenza i-algorithms ngo-2025. Kwaye isixeko se-language yokuquka indlela yokulungisa. Yep, ngokufanelekileyo: i-C++ ye-modern (C++23). Inikeza izixhobo zokwenza i-step ye-optimizer yakho usebenzisa i-terrain, yaye isiseko se-one-size-fits-all. But you still need the right math tool—and, surprisingly for many, classical calculus is the wrong one for the new breed of truly smarter optimizers. : ibiza into efanayo kwindawo eyodwa xa isinyathelo esuka ku-zero. Oku kuthetha ukuba isakhiwo epheleleyo kwaye kunzima ukuyithatha xa izimo zihambe, njengoko ikhowudi efanelekileyo ifumaneka ngezinyathelo ezincinane, ezininzi, ezivela kwi-point. Yintoni? ngenxa yokungabonakali, inkqubo yethu yokucaciswa kwiminyaka ye-19 sifundiswa ngexesha lokuqala Yintoni? ngenxa yokungabonakali, inkqubo yethu yokucaciswa kwiminyaka ye-19 sifundiswa ngexesha lokuqala - i-alternative ye-calculus elidlulileyo - i-customized ye-AI systems ezisebenzisa i-billions ye-optimization updates ngeveki, ngaphezu kwe-manual oversight. Indawo yokufuneka isixhobo esahlukileyo Indawo yokufuneka isixhobo esahlukileyo Ngaphandle kwe-Curvature Numbers, i-Curvature Numbers (i-Curvature Numbers) yinkcukacha ze-Curvature Numbers (i-Curvature Numbers) ziyafumaneka ukuba i-Curvature Numbers (i-Curvature Numbers) ziyafumaneka ukuba i-Curvature Numbers (i-Curvature Numbers) zibonise inkqubo ye-Curvature kunye ne-Curvature Numbers (i-Curvature Numbers) kunye ne-Curvature Numbers. Nceda uqhagamshelane na umzekelo elula: I-calculus elidlulileyo ibonisa iimveliso ngaphambi kwe-forest, i-calculus entsha ebonakalayo ebonakalayo ebonakalayo ibonelela kwimveliso yokuqala, ngoko iimveliso kunye neengqongqo kwiimveliso. Ngoko ke, kwakhona - njengokuba kwiimeko ezininzi ezidlulileyo - kufuneka ukuguqulwa kwezobugcisa xa iimfuno ezisemthethweni, zebhizinisi kunye ne-technology zihlangene nemathematics ezintsha. Yintoni i-C++ inokukwazi ukwenza oku? Ukukhangisa i-hype, kwaye i-AI yeempawu ezininzi zihlangana kwi-optimization - ngokuvamile kwiiyure ezimbini: NaN explosion after expensive training: Uyavuma isinyathelo esininzi kakhulu ekugqibeleni elipheleleyo, okanye uye waya kwindawo engabonakaliyo kwi-computer's number grid. I-computers iye kuphela "i-number slots"; ukuba i-value yakho ivuma kakhulu okanye engabonakaliyo kakhulu kwi-slots ezininzi, i-mathematics ivela engabonakaliyo (NaN), kwaye i-run ibonakale. I-Copilot ibonisa i-bugs: I-Ironia epheleleyo - i-model inokufundisa i-pattern engabonakaliyo ngexabiso efanelekileyo ukuba isebenza ngexabiso efanelekileyo efuna ukuguqulwa. Kuyinto i-optimizer yokufaka kwi-minima engabonakaliyo ezibonakalayo-point-by-point, kodwa i-colapse xa ukuguqulwa kwimeko==.== Ndiyathanda indlela yokusebenza kunye nezibalo ze-curvature, nqakraza kwi-cows ezantsi. 
 
 
 Ubungakanani obungapheliyo: indlela elide (Hessian). Njengoko i-CT scan, iveza i-cow into ezincinane. Ezisetyenziselwa ukubonisa ngokukhawuleza, kodwa awukwazi ukufikelela ngokufanelekileyo umzimba wonke. Inani lokugqibela: Inani lokugqibela. Ngaphandle kweengxube, sinikezela i-cow ukuya kwiimveliso ezihlangeneyo. K1 inikeza i-envelope ye-yellow epheleleyo. K2 ibandakanya nge-halo ebomvu elibandayo kunye ne-surface. K3 ibandakanya nge-skin ye-green ebandakanya i-cow ukuba nathi. Indawo ngexesha elandelayo, i-skiz ye-rough iya kuba yi-mould efanelekileyo. 
 
 Yinto i-game-changer ethandwa ngexesha: i-moment optimizers kunokwenzeka ekugqibeleni kwi-automatic optimizers - akukho i-hacks ezincinane ezininzi ezininzi ezininzi ezidlulileyo ngexesha lokuphinda imeko. Yinto i-game-changer ethandwa ngexesha: i-moment optimizers kunokwenzeka ekugqibeleni kwi-automatic optimizers - akukho i-hacks ezincinane ezininzi ezininzi ezininzi ezidlulileyo ngexesha lokuphinda imeko. Ngiya i-revolution: ngeenombolo ze-curvature njenge-mathematics, kunye ne-C++23 njenge-engine, i-optimizer ayikho xa kuxhomekeke kwiingxaki ezincinane ze-human. I-optimizer iya kuba inkqubo enomgangatho-ukuguqulwa ngokugqithisileyo-ukuguqulwa ngokugqithisileyo-ukuguqulwa ngokugqithisileyo-ukuguqulwa ngokugqithisileyo. Yintoni oku kubaluleke? Ngenxa yokuba i-optimizers ayikho kuphela iinkcukacha ze-AI. Zininzi iinkqubo ezihambileyo ze-AI : every modern system 
 
 
 
 I-AI kunye ne-Machine Learning: ngaphandle kwe-optimizers, akukho ukuqeqeshwa, akukho ukufundisa, akukho intelligence. Yonke update ye-weight ithengisa kubo. I-Industry & Engineering: Ukusuka kwi-logistics ukuya kwi-energy grids, ukusuka kwi-robotics ukuya kwi-aerospace - zonke iinkqubo ze-automated zithunyelwe kwi-optimization under constraints. I-Economy at Large: I-Finance, i-manufacturing, nokuba i-drog discovery - zonke ziquka kwi-optimization loops, kwaye zonke ziquka ukuba ama-optimizers ezidlulileyo nangokufuneka ama-armies zeengcali ukuba baye-babysit ye-mathematics ye-19th century. Kuyinto ingxubevange. Yintoni i-automation epheleleyo ifumaneka. Ngaphandle kwe-automatic optimizers, iimveliso zihambe ezine-automatic: iimveliso ezibonisa ukuba zihambe, kodwa kwimveliso zihlanganisa ngokushesha kwi-hand-tuning yabantu. Ndingathanda ukuba uya kufumana ngoku ukuba oku ayikho upgrade emininzi. Kuyinto, ngaphandle kokuthintela, ingxubevange lwezobugcisa zobuchwepheshe-kufika ngexesha elincinci Iimpawu ze-curvature kwi-C++23 zibonisa i-optimization ngokufanelekileyo kwi-process ye-automated - i-hero ebonakalayo ayikho kwakhona, kodwa ngaphandle kwe-AI kunye ne-industry ayikwazi ukufikelela ukuba isebenze ngokupheleleyo. Ukukhishwa kwe-scepticism kwi-AI Ukukhishwa kwe-scepticism kwi-AI C++: Iilwimi kuphela enokufumana iinombolo ze-curvature ukuya ku-max Nceda nqakraza i-chart ezantsi. Oku kwakhona. Ukusuka kwakhona: (SGD, Adam, L-BFGS). Iingxowa zokusebenza ze-AI namhlanje. Emuva: classical optimizers ubungakanani ubungakanani (ε*) ku C++23. Uhlobo olungapheliyo lula kakhulu: I-Old Optimizers ihamba ngenxa yokusetyenziswa kwizinga ze-step, njenge-marching forward eyahlukileyo. Ukususela kwi-1980s, Ukubonisa ukuba ungayifumana ngcono ngokuvumelana ne-step ngokufanelekileyo kwi-slope ye-terrain. "Izixhobo ze-curvature" zithuthaza inkcazelo ezininzi: Ngaphandle kokucinga, usebenzisa i-derivatives ezifanelekileyo (kwiinombolo ze-dual / jet) kunye nezinyathelo ze-terrain-aware ezifanelekileyo kwi-machine. Kwaye nge-C++23 izixhobo ezifana: Ukucinga Yaye , unokufunda le optimizers ngexesha elula kwaye elula, phantsi kwexesha le-compiling. Uhlobo lweBarzilai-Borwein Ukucinga Ukucinga Ukulungele Uhlobo lweBarzilai-Borwein Kwaye akufutshane apho: ukhuseleko lwemememori, ukucaciswa kwe-noise, iinkcukacha ze-second-order, i-parallelism, iingcango ze-theoretical - inkqubo ye-curvature ibonelela kwi-board. Zonke i-bar ye-green ibonisa inkcazelo elifanayo: ama-optimizers ezidlulileyo akuyona kuphela ezidlulileyo; ziye zibonisa iindidi ezininzi. Yintoni iingoma ezininzi? Yintoni iingoma ezininzi? Umxholo we-Skeptic is a predictable: "Ngokuthi, i-C++ yaba ebalulekileyo kwihlabathi. Kodwa ayikho nje i-peer elidlulileyo ekubeni iilwimi ezintsha ezifana nePython, i-Rust, okanye i-Julia?" Nceda nqakraza i-chart apha. Nceda nqakraza okanye nqakraza ukubonisa umfanekiso epheleleyo Iinkcukacha ziyafumaneka ngokufanayo. 
 
 
 
 
 I-Python (i-yellow): Nangona ne-GPU accelerators efana ne-CuPy okanye ne-Numba, i-Python ibandakanya i-interpreter kwiinkalo ngamnye. I-Throughput i-collapses, i-latency spikes, i-memory efficiency tanks. It is a productivity tool for prototypes, akukho isiseko ye-civilization-scale optimizers. I-Rust (i-red): I-Brilliant ye-Safety kunye ne-Concurrent. Kodwa kwi-GPU computing ecosystems, i-Rust (i-red): Akukho i-stack epheleleyo yokusebenza ngqo kunye ne-CUDA/ROCm/SYCL. I-Cernels ikakhulukazi zithunyelwe kwi-clay layers. I-C++23 (i-green): I-operations ye-Monadic (std::expected, std::variant) zihlanganisa ngqo nge-GPU kernels. I-C++ 23 inokukwazi ukwakha i- "containers ye-math", i-containers ye-monadic, apho izicelo ze-calculus yakho entsha zihlanganiswa kwi-containers ngokwayo. Xa usebenzisa, imathematics efanelekileyo ibonakala ngokuzenzakalelayo - akukho abantu abavela ngexesha elandelayo, akukho izixeko ze-convergence, kuphela i-operations ze-algebraic ezisetyenziswa kwi-pipelines ye-monadic. Iimveliso zihlanganisa i-algebra ye-curvature ngexesha le-compilation. I-latency, i-precision, i-throughput, i-scaling, i-energy efficiency - kwi-cross every axis, i-C++23 ibekwe phambi. Yinto ayikho i-Nostalgia. Akukho malunga nokugqiba kwi-workhorse elidlulileyo. Yinto malunga ne-performance reality. Kwimeko ye-performance reality, i-C++23 ayikho kuphela kwi-competitive - nto leyo . miles ahead I-Call to Ownership I-C++ ayikho kufuneka ifumaneke. I-C++ yenzelwe ukuba ifumaneke ngokuhambelana nehlabathi ngelixa kwi-tools ezininzi, ezininzi, ezininzi. Kodwa umlando akuyona ngqo - kwaye apha siye, kunye ne-C++23 enikeza izixhobo ezininzi ezininzi ezivela kwi-civilization yethu yokusebenza ngokwenene. Ukufundwa kwakhona kulula: Ngaphandle kwabo, i-AI yindawo yokuzonwabisa. Ngeya, i-automation ivela kwimeko. Kwaye ngoku, ngenxa yokuqala, sincoma i-framework - iinombolo ze-curvature, ezivela kwi-C++23 - enza i-optimization kwi-automatic. optimizers are not side details. They are the hidden engines of everything that adapts, learns, and runs at scale. Ngoko ke, le ngxaki. Ngaba ukhangela ukuba i-Big Tech uye uye uyakuthanda "i-AI njengenkonzo." Ngaba ukhangela ukuba i-Python wrappers okanye i-Rust bindings ziyafumaneka. Faka izixhobo ngokufanayo. Wabelane iingcebiso. Thola iinombolo ze-curvature. Wabelane i-pipeline. yaye uya kufumana ngokufanayo ukuba i-automatization epheleleyo xa apha- Take ownership. Open the compiler. The future is yours to build.

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