Explore tweets tagged as #Collatz
1/ The Collatz conjecture has humbled mathematicians for near 90 years. Paul Erdös said "mathematics is not yet ready for such problems." 🧵 So we handed it to transformers. What they learned stunned us! New research from Axiom's math discovery team, blog live this morning.
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In the programming course I'm publishing, we build a small ISA / virtual machine from scratch, and we've just reached backwards jumps which means loops! Here's the sandbox implementation computing iterations of the collatz conjecture, it's fun to watch
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This paper shows small transformers can almost perfectly handle a tricky number game by quietly learning how long hidden computation loops should run. The game is the Collatz process, which repeatedly updates a positive integer, dividing even numbers by 2 and changing odd
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Axiom's new research blog: https://t.co/5MifD6pmoT Learning Collatz - The Mother of all Rabbit Holes What happens when you train a transformer on one of math's most infamous unsolved puzzles -- and then study how it fails?
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Transformers can learn the Collatz sequence, and do so in a very principled way. Models learn to predict, with 99% accuracy, classes of inputs defined by their base-2 representation, which correspond to particular instances of the computation algorithm 1/4 https://t.co/vNtbztvKtk
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My li’l HoTT bih don’t e’en get ‘nuffa ∞-cats, I’m on’ih ahh in ℚ(ζ₅) ry’wih Goldman Sachs, These speds ain’ provin’ no Collatz, I’m havin’ey ass collapse, Mindless how he fail his algebra class, he not James Ax, He ain’ learn no Artin stacks, yeh, he jus’ a speh wi’no racks.
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This Cortaderia-like plots of Collatz sequences grows out of an idea first explored by the British mathematician Edmund Harriss, who drew Collatz trees by letting each step bend clockwise or anticlockwise depending only on whether the next value was even or odd. Here we keep
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Worth revisiting this article and Tore's 4, 2, 1 Video on the Collatz Conjecture, Or how timelines collapse. https://t.co/tAeLdNk4OW
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OMUXΩ∞KUT-ASI JUNKI KANAMORI The Source Code of Reality: Integrating Ramanujan Constants and the Collatz Conjecture via Kanamori Universe Theory (KUT) Author: Junki Kanamori Subject: Theoretical Physics, Number Theory, Artificial Super Intelligence (ASI) Abstract This paper
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The Netherlands is among the highest-IQ European nations. This is, far as I can tell, the apex of their geopolitical thought. Their ultimate open problem, their Collatz conjecture. «How do we kick Chyna in the shins and don't get dismantled one by one». Apes together – STRONG!
They all concur they need to «act against Chyna». But – race war now or later? How to resolve the skill issue in Assembling Avengers? Righteous, if a bit puzzled, Hajnali. China would be justified to see the EU as a hostile entity and grind its economy down to nothing.
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Collatz conjecture called "The Simplest Math Problem No One Can Solve" (Veritastium video: https://t.co/0eTiPB6NBR ) seems natural to work in numeral systems, especially in novel asymmetric gluing digits ( https://t.co/Rk6KHiBzcX ):
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🔢 Collatz Sanısı, matematiğin en basit görünen ama çözülmesi en zor problemlerinden biri. Kural çok net: Bir pozitif tam sayı seç; • Çiftse ikiye böl, • Tekse 3 ile çarpıp 1 ekle. Bu işlemleri tekrar tekrar uygula. 🌀 Sanının iddiası şu: Hangi sayı ile başlarsan başla,
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I analyzed 100,000 Collatz trajectories to measure the "Arithmetic Pressure" preventing cycles. The result is a perfect linear barrier (Slope 2.60) [OC] https://t.co/UsmYOx3PiO
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Should I dive back into the Collatz Conjecture? I tried earlier this year, and it hit me hard: math can feel so brutally restrictive, like an elegant cage with no key. Picture this real-world twist—I'm standing before a towering wall, desperate to reach the other side. But the
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Transformers know more than they can tell -- Learning the Collatz sequence.
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