We are introducing OpenAI o1, a new large language model trained with reinforcement learning to perform complex reasoning. o1 thinks before it answers—it can produce a long internal chain of thought before responding to the user.
Breakthrough models AlphaProof and AlphaGeometry 2 solve advanced reasoning problems in mathematics
Our AI system surpasses the state-of-the-art approach for geometry problems, advancing AI reasoning in mathematics
Note: These pages make extensive use of the latest XHTML and CSS Standards . They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in…
Knowing your ABCs is essential to academic success, but having a last name starting with A, B or C might also help make the grade.
Introduction You may have heard of the Kelly bet allocation strategy. It is a system for correctly exploiting information or bias in a gambling situation. It is also known as a maximally aggressive…
Rasmus Kyng has written the near-perfect algorithm. It computes the maximum transport flow at minimum cost for any kind of network – be it rail, road or electricity – at a speed that is, mathematically speaking, impossible to beat.
Avi Wigderson is the recipient of the 2023 ACM A.M. Turing Award for foundational contributions to the theory of computation, including reshaping our understanding of the role of randomness in computation, and for decades of intellectual leadership in theoretical computer science.
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Tog’s Paradox (also known as The Complexity Paradox or Tog’s ComplexityParadox) is an observation that products aiming to simplify a task for users tend toinspire new, more complex tasks. It’s one ...
We discuss constraint programming, an approach to solve discrete optimization problems, and illustrate how it works with a scheduling code example implemented in Python with the CP-SAT solver.
Note: These pages make extensive use of the latest XHTML and CSS Standards . They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in…
Every now and again you come across something that stretches your brain in a new direction. Last week I stumbled on a magic trick of a Choose Your Own Adventure: Al Leonardi’s Ace of Aces, a paper …
Automated reasoning and optimizations specific to CPU microarchitectures improve both performance and assurance of correct implementation.
A blog by and for database architects.
We estimate the magnitude of speed improvement for optimization solvers and computer hardware in the 35 years from 1989 to 2024.
The deficiencies of the Unit Sphere and an exploration of Lie groups.
Discover how prover-verifier games improve the legibility of language model outputs, making AI solutions clearer, easier to verify, and more trustworthy for both humans and machines.
GITHUB HUGGING FACE MODELSCOPE DISCORD 🚨 This model mainly supports English. We will release bilingual (English and Chinese) math models soon. Introduction Over the past year, we have dedicated significant effort to researching and enhancing the reasoning capabilities of large language models, with a particular focus…
A deep dive into the Probabilistic B-tree or Prolly Tree data structure including examples. Prolly Trees are used to create version controlled databases.
In a paper published in Physical Review X on May 13, a quartet of physicists and computer scientists expand the modern theory of the thermodynamics of computation. By combining approaches from statistical physics and computer science, the researchers introduce mathematical equations that reveal the minimum and maximum…
