I-Error ye-Mathematics ye-Killing Every AI Architecture - Ngezinye ezintsha

LLMs are already museum pieces I-LLMs iyiphi imikhiqizo ye-museum Why JEPA, transformers, and LLMs all fail in the same Euclidean flatland, and the toroidal geometry that fixes them Yeah, ChatGPT, Claude, Gemini, bonke kubo. I-phossils emangalisayo ye-era ye-lingvistic eyenza. Zihlanganisa ngokubanzi, : amamodeli amakhulu, i-contexts engaphezulu, i-hallucinations engaphezu kwe-watt. izigidi ziye zithunyelwa ukuhlanzwa izikhwama zabo izigidi ziye zithunyelwa ukuhlanzwa izikhwama zabo izigidi ziye zithunyelwa ukuhlanzwa izikhwama zabo I-era ye-"predict-the-next-word" ye-LLM iyahora. I-killer entsha ebonakalayo isisekelo se-language, it is world modeling. Umthamo we-AI owaziwa ngokwemvelo njenge-puzzle ye-conceptual, lapho ungenza zonke izinhlayiya ukubona inkcazelo jikelele. Thina akuyona ama-stars ezindala ze-LLM emangalisayo. Uma ungenza ubudlelwane wakho ngokuvamile ngokuvimbela ama-chatbots, ungenza i-world eyenziwe. Thina akuyona ama-stars ezindala ze-LLM emangalisayo. Uma ungenza ubudlelwane wakho ngokuvamile ngokuvimbela ama-chatbots, ungenza i-world eyenziwe. Thina akuyona izibani ze-LLM ezidlulileyo emkhakheni. Uma ungenza ubudlelwane wakho ngokuvamile ngokuvumela chatbots, uzokufaka kwelanga elidlulile. Thina akufanele izinjini ezihambisa i-token njenge-paparazzi. Thina akufanele izinjini ezihambisa i-token. Ngiya Ngiya I-"Stochastically parroted" iyona enhle ngo-2023. It is not intelligence. It is probability cosplay. carry objects through time bind cause to effect keep the scene consistent Futhi lokhu kungcono ukuthi abaninzi tunamatheka ngaphambi kokufika kwebhizinisi le-tech: uma i-AI ibhizinisi Ngaphandle I-Industrial That Burned Ukwenza chatty cockatoos izibopho. Ngisho. likelihood reality 1 trillion dollars U-JEPA iyona i-AI ye-new hope? E-galactic e-Menlo Park, i-acronym entsha emangalisayo emanzini we-chatbot: JEPA! The promised one. The architecture was said to restore balance to the Force after the LLM wars. Ngaphambi kokuthumela isebe sokuthengisa ka-Meta ukhiphe njenge-Messiya elilandelayo, sicela ukhiphe i-acronym. Waze izici ezine ezinguqulo ezinguqulo ezinguqulo ezinguqulo ezinguqulo ezinguqulo ezinguqulo ezinguqulo ezinguqulo ezinguqulo ezinguqulo ezinguqulo: JEPA Joint Embedding Predictive Architecture - I-joint, ngenxa yokuhlanza amahlathi ezimbili ye-scene - eyodwa esibonakalayo, eyodwa e-masked - futhi ivimbele ukuxhumana emkhakheni eyahlukile. I-embedding, ngenxa yokuxhumana ne-pixels ashisayo noma ama-word efana ne-LLMs, isebenza ku-vector representations eqinile: indawo ebonakalayo lapho i-AI yesimanje. I-predictive, ngenxa yokuba i-trick yayo kuphela inikeza i-chunk eyenziwa kusuka ku-chunk eyenza. I-Architecture, ngenxa yokuba zonke izakhiwo ezintsha ze-AI zihlanganisa i-noun emangalisayo ekupheleni ukuze zibonele emangalisayo. Umbhali Olandelayo Olandelayo cult - like to put it, ngesiNgisi elula: As U-Yann LeCun - Imininingwane Ukulungiswa U-Yann LeCun U-Yann LeCun Imininingwane Intelligent is not a language, nor is it predicting the next word. Intelligent is predicting what will happen in the world. Intelligent is not a language, nor is it predicting the next word. Intelligent is predicting what will happen in the world. . It ufundisa ukuba — not by generating text or pixels, but by aligning internal representations so that . And that’s exactly what JEPA tries to do guess what’s missing in a world it only half perceives context can explain absence Futhi lokhu kuphela ukuthi JEPA inikeza ukwenza It is not writing; it completes. It is not imagining; it infers. It is not writing; it completes. It is not imagining; it infers. I-Too Good To Be True? Kodwa ungathanda ukuthi lokhu kuyinto ibhizinisi enhle - noma nje enye imikhiqizo ye-tech ebhekwe nge-LED emangalisayo kanye ne-intelligence enhle kakhulu Sishayele nge-great talk okungenani. Meta presents like a revelation eyenziwe silicon: usuku lwe "intelligent enhle", lokugqibela chatbots, ukuqala ama-world-model gods. JEPA Ngemuva kokuqala, kungcono ukuthi Thola lokhu - kuze kube Hlola i-halo ye-marketing, futhi uzothola ukuthi kukhona. Not quite the miracle LeCun sells, but still something valuable: , kodwa ungenza elide Ukusebenza Isinyathelo esisodwa esisodwa esisodwa Okwangoku, i-JEPA ibhekwa ikakhulukazi Nokho, lapho still leans heavily on the same zibonisa ukuthi ziye zihlale (bheka isithombe 1 ngezansi). videos and physical-world scenarios wording layer stochastic parrot LLMs Of course, Meta just prefers not to mention that part in the brochures. No surprise there So yes, in the blueprint, JEPA looks clever - new modules, shiny arrows, and a fresh sense of purpose, but underneath, we’re still stirring the same pot. The word-soup problem just got an upgrade to . Ubufakazi okuhlobene, okuhlobene okuhlobene. concept-soup Ukubuyekeza kanjani, Kuyinto yokuthengisa okuzenzakalelayo. Njengoba ibhayisikili elandelayo ibonisa - ngokumangalisayo eyenziwe nge-Meta's triumphal glow, it , , futhi form a clean little triad okuyinto ngokwenene isixazululo Imininingwane ye-LLMs JEPA context encoder target encoder predictor token tyranny Yini ungenza ngokwenene Nge Ngaba ufuna? Okwe, ungakwazi ukhawuleza i-wit , futhi ibonise isikhwama esithile not by painting pixels, but by . Kuyinto ukucindezeleka: do JEPA h half an image for you, reasoning in latent space perception over parroting. Futhi lapha lineup: Ukubuyiselwa Izinto eziningana kuphela amamodeli abacindezelwe, enhle. it still fails under fixed distractor noise and never touches language. I-JEPA Ukuhlobisa But I-JEPA I-JEPA Ukuqeqeshwa ngezividiyo ukufundisa ukuhambisa ukuhambisa, okuhambisa, lapho, futhi kanjani. isakhiwo esiyingqayizivele: ukuhlukaniswa, amandla, ukuxhumana okungenani. Then comes V-JEPA But Ngemuva kwalokho V-JEPA V-JEPA More into robotics? ** **Ukuhlola izindandatho ze-robot, ukuhlaziywa kanjani ama-objects ngaphambi kokusebenza. Ukubuyekeza abantu ku-benchmarks ye-physical futhi, i-irony ye-irony, inesidingo sokubuyekeza Ukusabela mayelana neNdlovukazi. V-JEPA 2 But LLM V-JEPA 2 So yes, progress, enough to declare LLM technology as a fossil in artificial life maintenance - but still flatland thinking dressed up as revelation. And that’s the part Meta doesn’t want you to see. Ngiyazi i-secret enhle esifundayo emzimbeni ze-JEPA ne-LeCun emangalisayo: zihlanganisa inkinga le-lingvistic ngokwenza inkinga le-architectural enhle emathemathemikhali. Wasehlukile i-word-prison kuphela ukwakha i-concept-prison nge amadolobha amancane. Ngiyazi i-secret enhle esifundayo emzimbeni ze-JEPA ne-LeCun emangalisayo: zihlanganisa inkinga le-lingvistic ngokwenza inkinga le-architectural enhle emathemathemikhali. IsiZulu Ukwakhiwa Wasehlukile i-word-prison kuphela ukwakha i-concept-prison nge amadolobha amancane. Yenziwe: I-LLM yaba enhle ngenxa yokuxhumana ne-reality njenge-sequence linear ye-token: isitimela esisodwa-dimensional nge-probability space. I-JEPA ithi. " ” futhi uxhumane endaweni high-dimensional representation, lapho izakhi zangaphakathi njengama-vectors . Thina ngcono kakhulu kunazo Umbala we-768-dimensional we’re smarter than that Ngingathanda kakhulu, hhayi? Wrong. Thina nje ukuhweba isixeko esihle isixeko esihle: uhlobo lapho . Izinsizakalo zomathematiki zihlanganisa isizukulwane I-Fatal Mathematical Doom ye-AI Architectures ezintsha: Bona Bona I-Flat World Futhi manje, uqhagamshelane, umbhali amangalisayo, ukufundisa ukuthi akuyona emangalisayo eminye. Indlela i-poison ye-matematics ihlukanise wonke isakhiwo se-AI - kusuka ku-Dinosaurs ye-LLM kuma-children ezintsha abalandeli ukuthi zithembisa konke. Stop. Breathe 😄 This is where the story gets dangerous. Kodwa unemibuzo, sinayo antidote. Futhi ungasebenzisa ku-friendly yakho. Ngaphambi kokufika, isixazululo encane. Uma ufuna ukujabulela ngaphezulu - ku-mathematics emangalisayo, emangalisayo, emangalisayo okuyinto ibonise ngaphandle kokubili ukuthi imodeli ye-toroidal ye-double-number ithatha imizila kanye ne-doom ye-myopic eyenza izakhiwo zokusebenza kwe-AI ezidumile - i-imeyili amahora amancane ezivela kuwe: → →__ __\→ JEPA-AI: Core Technologies & Programming Stack The Mathematical Myopia of New AI Architectures Mathematical Core Equations: AI JEPA’s Failures vs. AI-Toroidal Truth JEPA-AI: I-Core Technologies & Programming Stack JEPA-AI: Core Technologies & Programming Stack I-Mathematical Myopia ye-AI Architectures ezintsha I-Matematical Core Equations: I-AI JEPA I-Failures vs. I-AI-Toroidal Truth Mathematical Core Equations: AI JEPA’s Failures vs. AI-Toroidal Truth Thola isikhathi yakho lapho ufuna. Uma akuyona, sicela ushiye nathi. Thina uxhumane i-Event Horizon. Sishayele manje. Ungathanda ukuhanjiswa ibhizinisi lakho elikhulu yobuciko. Ungathanda zonke izincwadi zakho ku-mapping eyodwa elikhulu futhi ungathanda ukuthi ikhompyutha yakho ungathola ingxaki phakathi kwe- "Stairway to Heaven" ne- "Highway to Hell" ngokusekelwe ... i-vibes? Lokhu kubalulekile ukuthi i-JEPA ne-AI ezintsha izakhiwo zenza. Here’s the problem: these systems live in what mathematicians call “Euclidean space”, basically a flat, infinite spreadsheet where everything is a bunch of numbers floating around. Sounds reasonable, right? Wrong. Ngenxa yalokho, uzothola imvume yama-mathematical efanelekileyo efanelekileyo ezisetshenziselwa izinhlelo ze-inthanethi ye-inthanethi ye-”next generation”: ziye zithengiswa njenge-antidot ye-LLM poison. Ngenxa yalokho, uzothola imvume yama-mathematical efanelekileyo efanelekileyo ezisetshenziselwa izinhlelo ze-inthanethi ye-inthanethi ye-”next generation”: ziye zithengiswa njenge-antidot ye-LLM poison. Ngenxa yalokho, uzothola imvume efanayo ye-mathematical eyenziwe ngqo emzimbeni ye-inthanethi ye-AI ebizwa ngokuthi i-"next generation": ziye zithengiswa njenge-antidote ye-LLM poison. They promise salvation but inherit the same broken math. — Welcome again to the Hall of AI Shame. Here they are. — The Birthday Party Disaster Ingabe ufuna ukushumeka kokuthunyelwe kwebhizinisi? Qinisekisa 23 abantu abalandeli kwelinye ibhizinisi, futhi kunezimo se-50% ukuthi amabili abalandeli abalandeli. I-"White truck" ikakhulukazi ukubukeka cishe efanayo ne-"light sky" ngoba zihlala emkhakheni elifanayo kule supp ye-number giant, futhi lokhu kungcono ukuthi izitimela ze-Tesla ezimbonini ezimbonini. The Math says: Ukusabela Ukusabela The Math says: Ukusabela Ukusabela Ukusabela Ukusabela Kuyinto efanayo nokufunda ibhizinisi ngokushesha uketshe amabhuku emkhakheni futhi ukholelwa ukuthi ungakwazi ukufumana kwabo ngemva kokufunda izindlela zangaphakathi. The Gradient Descent Hamster Wheel Current AI architectures use something called “gradient descent” to find the minimum error given an error function, which is a fancy way of saying they stumble around in the dark, poking things with a stick, hoping to eventually find the exit. Ngaba awukwazi ukubona isakhiwo se-hill eyenza ukujula, kuphela isithombe esisodwa ngosuku. Kuyinto njengokufunda San Francisco nge-blindfold kanye ne-enlarging glass eyenza kuphela intshi ye-square ye-pathway. The problem? They use fake infinitesimals with point-wise myopic vision The problem? They use fake infinitesimals with point-wise myopic vision The problem? They use fake infinitesimals with point-wise myopic vision But wait, it gets dumber: you have to pick your epsilon (the step size) Ngaba uqala ukujabulela. Hlola enkulu kakhulu? Uyazi ukuthi omncane ngosuku, ukuthatha amaphuzu amakhulu futhi uxhumane emaphandleni. I-Too Small? Uyazi phambili njengama-sleeve e-paranoid, futhi uzame ubudala ngaphambi kokufika eminye indawo. Yup, lokhu yonke ingozi kusekelwe ku-19th century calculus kanye ne-epsilon-delta limit formalism. Kwangathi Kodwa okuhle kakhulu kunikeza ngesikhathi sokucwaninga: I-AI isebenza amabhayisikili yezinyathelo ze-tiptoeing zokusebenza ukuhlinzeka ukunciphisa umsebenzi yayo yokusabela. Amabhayisikili! Wonke okuvela emangalisayo njenge-robot buggy noma izivakashi njenge-Windows ngokushesha ku-1%. I-waste ye-computing kuyinto enhle kakhulu - konke ngoba le khasiwa elidlulileyo, eyenziwe ku-19th century, ikhulisa ukuba ukhethe inani le-epsilon ngaphambi. Kodwa okuhle kakhulu kunikeza ngesikhathi sokucwaninga: I-AI isebenza amabhayisikili yezinyathelo ze-tiptoeing zokusebenza ukuhlinzeka ukunciphisa umsebenzi yayo yokusabela. Amabhayisikili! Wonke okuvela emangalisayo njenge-robot buggy noma izivakashi njenge-Windows ngokushesha ku-1%. I-waste ye-computing kuyinto enhle kakhulu - konke ngoba le khasiwa elidlulileyo, eyenziwe ku-19th century, ikhulisa ukuba ukhethe inani le-epsilon ngaphambi. caused by this outdated way of doing infinitesimal calculus is the compounding effect of tiny approximation errors. You start with something like 10^-8 and think, “Eh, close enough to zero, right?” Wrong. Square it and you get 10^-16. Still. Not. Zero. After billions of iterations, these pretend infinitesimals pile up like compound interest from hell, spawning numerical explosions, instabilities, and rounding errors that eventually turn into full-blown AI hallucinations. The second error Yup, kukhona isixazululo elula: ukuguqulwa kwinkqubo ye-double-number elithakazelisayo kulo lonke le show ye-clown. Akukho izixazululo. Akukho imidlalo yokuthanda epsilon. Akukho amabhayisikili-step hamster wheel. Uma ε2 = 0 ngokuvumelana, akukho ukubuyekezwa, umthetho we-mathematics efanayo: izidakamizwa zihlanganisa, futhi i-topology nje ibonisa ukuthi konke kuhle. Akukho ukuchitha kufuneka. Yup, kukhona isixazululo elula: ukuguqulwa kwinkqubo ye-double-number eyenza kule umdlalo we-clown. No limits. No epsilon ukubuyekeza imidlalo. No billion-step hamster wheel. Uma ε2 = 0 ngokuvumelana, akukho ukubuyekeza, umthetho wekhwalithi real: derivatives zihlanganisa, futhi topology nje ushiye lapho yonke into. Akukho ukuchithwa kufuneka. Yup, kukhona isixazululo elula: ukuguqulwa kwinkqubo ye-double-number eyenza kule umdlalo we-clown. The Attention Apocalypse use something called “attention,” where every word looks at every other word. That’s N-squared complexity, which means if you double your text length, the computation goes up 4x. Transformers (the tech behind ChatGPT, not the robots) I-Transformers (u-tech esekelwe ku-ChatGPT, akukho ama-robots) Ngama-1000 i-word? Kuyinto i-million comparisons. Ngama-10,000 i-word? 100 million comparisons. I-AI yakho ikakhulukazi uyifunda ibhokisi ngokuvamile ngokuvamile ngokuvumelana nama-word ngamunye. I-exhausting kanye ne-expensive. How Our Toroidal Model Fixes the AI Flatland Doom Thola nami lapha. Instead of a flat spreadsheet, we use a donut (mathematically, a torus) Ngaphandle kokubili, sinikeza a I-DONUT donut (Ukuhlelwa kweMathematically, a torus) On a donut, you can wrap a string around it in different ways: around the hole, through the hole, or both. . It’s not probability, it’s topology. Different winding patterns are as different as a circle and a figure-8. They literally cannot become each other. These “winding patterns” give every concept a unique address that cannot collide These “winding patterns” give every concept a unique address that Ngikwazi cannot Ukuhlobisa The Real Infinitesimals - it’s the definition. This means our layers are separated by actual infinitesimals, not fake ones. No numerical explosions. No gradient descent needed. The topology just… works. We use dual numbers where ε² = 0 isn’t an approximation Ukusebenzisa izibalo ezimbini lapho ε2 = 0 ayidlulanga Sparse by Design Izixhumanisi amaningi zihlanganisa ngokucacileyo - akuyona "ngaphakathi ne-zero" kodwa . This drops complexity from N-squared to linear. That 100 million comparisons? I-Mechanism yethu ye-Attention iyahambisana kuphela ama-patterns eyenziwe I-Structural Impossible Ngaphezu kwe-10,000. I-Mechanism yethu ye-Attention iyahambisana kuphela ama-patterns eyenziwe Ngaphezu kwe-10,000. The Bottom Line The Bottom Line I-JEPA kanye nezakhiwo ezintsha ze-AI zihlanganisa indlela efanelekayo yokuguqulwa komhlaba lethu enhle ngokuvamile ku-AI enhle. Kodwa kunjalo, njenge-LLMs, zihlanganisa inkinobho efanayo ngokuchofoza ukuhlola emhlabeni enhle nge-compass enhle kanye ne-approximations. Ukuphakamisa okwenziwe ngempumelelo ku-Parameters.It ngeke kufinyeleleke ukusabela indawo ngokuvamile. The real leap won’t come from another tweak in parameters. It will come from changing the space itself. Thina kufuneka ukugcina isikhwama se-Euclidean enikezela ukuxhumana kwama-intelligence e-two-dimensional, futhi ukwakha ku-topology lapho umqondo angakwazi ukujabulela. Ngo-toroidal model yethu, izinhlelo zihlanganisa noma zihlukile. Zihlala ezivamile, izixazululo ezihambelana: zonke zihlukile ngokugcwele, zonke zihlukile kusuka ku-chaos ye-fake merges. Why Toroidal AI Is Not Being Built — Yet Okunye, umbhali omncane angathanda: "Uma okuhle kakhulu, ngakho-ke umuntu awukwazi ukwakha futhi?" "Uma okuhle kakhulu, ngakho-ke umuntu awukwazi ukwakha futhi?" Imibuzo efanelekayo - futhi impendulo ngokuvumelana. Ukubuyekezwa kwe-AI yonke i-trillions ku-Euclidean architectures. . Replacing that geometry would mean rebuilding the cathedral from its foundations - and few engineers dare shake the pillars of their own temple. 1. Institutional Inertia: Every framework, every GPU kernel, every optimization routine assumes a flat world Every framework, every GPU kernel, every optimization routine assumes a flat world Yonke framework, zonke i-GPU kernel, zonke izinga lokusebenza zokusebenza zihlanganisa indawo ephelele . Retraining them to reason with curvature, continuity, and dual numbers is not a weekend tutorial - it’s a civilizational shift in mathematical literacy. 2. The Workforce Barrier: __ A full generation of machine-learning engineers has been trained to think in gradients, not geometry I-generation ephelele ye-engineers ye-machine-learning eyenziwe ukufikelela ku-gradients, futhi akuyona ku-geometry Konke ukuhlangabezana kwe-geometric paradigm kuyimfuneko izindandatho ephelele ze-intellectual property kanye ne-licensing chains. I-system ayikho ku-truth-optimized - iyatholakala ku-control. 3. Patents and IP Locks: I-Big Tech Ayikho Inovative; I-Big Tech Yenza I-Defense Yayo I-Big Tech Ayikho Inovative; I-Big Tech Yenza I-Defense Yayo Ukusuka ku-cloud infrastructure kuya ku-AI chips, konke iyakhiwa ngenxa ye-flatland paradigm. Ngaphandle kwe-engineers it’s broken, the machinery keeps running - . 4. The Sunk-Cost Fallacy: Waze ngoba ukuhlangabezana kunikezela ukuhlangabezana izibane ezininzi kanye nezimo ezininzi because admitting it would collapse too many balance sheets and too many egos ngoba ukuhlangabezana kunikezela ukuhlangabezana izibane ezininzi kanye nezimo ezininzi Ngakho-ke - akuyona akuyona. Not because it’s wrong. But because it’s Okungenani, okungenani kakhulu, futhi okungenani kakhulu kumazwe omncane omncane. too right And that’s precisely why it will happen. Because math doesn’t care who resists it. Yenza kuphela - njalo. And soon, the new startups will notice the gap. You’ll watch Toroidal AI evolve exactly as every disruptive technology has before it: Okokuqala Ignored - Then ridiculed “crackpot” accusations from people who don’t understand topology. And finally, triumphantly accepted*“Of course! We always knew Euclidean space was wrong.” too threatening to a trillion dollars in sunk investments. Futhi ngokushesha, ama-startups ezintsha zihlole isixazululo. Uyahlola i-Toroidal AI ukukhula ngokufanayo ne-technology eyodwa esizayo: Okokuqala Ignored - Ngemuva kwalokho zihlukile ama-"crackpot" ama-accusations evela kumadoda abazi-topology. And finally, triumphantly accepted*“Of course! We always knew Euclidean space was wrong.” Zonke izinzuzo zihlanganisa izigidi ezingu-trillion. History doesn’t repeat itself. It curves. 😁 Top 10 Essential References On JEPA Architectures: (September 2025) 1.- LLM-JEPA: Large Language Models Meet Joint Embedding Predictive Architectures 1.- LLM-JEPA: Amamodeli amabhizinisi amakhulu zihlanganisa amabhizinisi amabhizinisi amabhizinisi 1.- LLM-JEPA: Amamodeli amabhizinisi amakhulu zihlanganisa amabhizinisi amabhizinisi amabhizinisi (Ukulungiselela ngo-2025) 2.- ACT-JEPA: I-New Joint-Embedding Predictive Architecture for Efficient Policy Representation Learning 2.- ACT-JEPA: Novel Joint-Embedding Predictive Architecture for Efficient Policy Representation Learning 2.- ACT-JEPA: I-New Joint-Embedding Predictive Architecture for Efficient Policy Representation Learning (February 2025) 3.- Point-JEPA: A Joint Embedding Predictive Architecture for Self-Supervised Learning on Point Cloud 3.- Point-JEPA: A Joint Embedding Predictive Architecture for Self-Supervised Learning on Point Cloud 3.- Point-JEPA: A Joint Embedding Predictive Architecture for Self-Supervised Learning on Point Cloud On Transformer Attention Complexity: (October 2024) 4.- The End of Transformers? On Challenging Attention and the Rise of Sub-Quadratic Architectures 4.- The End of Transformers? On Challenging Attention and the Rise of Sub-Quadratic Architectures 4.- Umphumela we-Transformers? Ngokusho Ukukhangisa nokuphuma kwe-Sub-Quadratic Architectures (Oktobha 2023, okwenziwe ngokubanzi ku-2024-2025) 5.- FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning 5.- I-FlashAttention-2: Ukukhishwa kwe-Attention nge-Better Parallelism ne-Work Partitioning 5.- I-FlashAttention-2: Ukukhishwa kwe-Attention nge-Better Parallelism ne-Work Partitioning On Toroidal / Topological Neural Networks: (Januwari 2022, Nature - okungenani isakhiwo 2024-25 umsebenzi) 6.- Toroidal Topology of Population Activity in Grid Cells 6.- Toroidal Topology of Population Activity in Grid Cells 6.- Toroidal Topology of Population Activity in Grid Cells (June 2022) 7.- Deep Networks on Toroids: Removing Symmetries Reveals the Structure of Flat Regions in the Landscape Geometry I-Deep Networks on Toroids: Ukukhishwa kwe-Symmetries Kubonise Isakhiwo se-Flat Regions ku-Landscape Geometry 7.- Deep Networks on Toroids: Removing Symmetries Reveals the Structure of Flat Regions in the Landscape Geometry Ngezansi ze-Dual Numbers ne-Automatic Differentiation: (Ukulungiselela ngoJanuwari 2025) 8-. Dual Numbers for Arbitrary Order Automatic Differentiation I-Dual Numbers I-Automatic Differentiation ye-Arbitrary Order I-Dual Numbers I-Automatic Differentiation ye-Arbitrary Order On LLM Hallucinations: (ngoMsombuluko 2025) I-Why Language Models I-Hallucinate I-Why Language Models I-Hallucinate I-Why Language Models I-Hallucinate I-Bonus - I-Vision yeYann LeCun: (April 2025) 10.- Navigation World Models 10.- Navigation World Amamodeli 10.- Navigation World Models