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Diffusion Forcing: Next-Token Prediction Meets Full-Sequence Diffusion
Official Website of Diffusion Forcing
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The latest blog posts to take off on Hacker News. 2,851 posts.
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A practical introduction to constraint programming using CP-SAT and Python
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.
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How random are TOTP codes?
I'm pretty sure that the 2FA codes generated by my bank's TOTP app have a bias towards the number 8 - because eight is an auspicious number. But is that just my stupid meaty brain noticing patterns where none exist? The TOTP algorithm uses HMAC, which in turn uses SHA-1. My aforementioned brain is not clever enough to…
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Trying Kolmogorov-Arnold Networks in Practice
There's been a fair bit of buzz about Kolmogorov-Arnold networks online lately. Some research papers were posted around claiming that they offer better accuracy or faster training compared to traditional neural networks/MLPs for the same parameter count.
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A proof of proof by infinite descent
WARNING: the following contains a whole lot of pedantry about proving theorems at a level of detail such that you could likely convince a co...
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Conway's Game of Life for curved surfaces (2012)
Conway’s Game of Life is one of the most popular and iconic cellular automata. It is so famous that googling it loads up a working simulation right in your browser! The rules for the Game o…
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Convolutions, Fast Fourier Transform and polynomials (2022)
You may remember from high school what a polynomial is. If so, you may also remember how to multiply two of them. But what if I told you that the method you were taught is slow as F? In this post we will connect polynomials with the Fourier Transform and convolutions, and show you how to multiply polynomials with…
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Researchers develop the fastest possible flow algorithm
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.
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Quaternion Differentiation (2012)
I wanted to point someone to a short explanation of this today and noticed, with some surprise, that I couldn’t find something concise within 5 minutes of googling. So it seems worth writing …
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The Point of the Banach Tarski Theorem (2015)
One of my favourite Limited Audience Jokes (although technically it's actually a riddle) goes:
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A brief introduction to interval arithmetic
Why x^2 isn't always x*x.
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A reckless introduction to Hindley-Milner type inference (2019)
(I've been editing this post on and off for almost a year. I'm not really happy with it, but I suspect I never will be.)
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B-Trees Require Fewer Comparisons Than Balanced Binary Search Trees
A blog by and for database architects.
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A railroad simulation using discrete event simulation
In our previous post, we introduced how to utilize Discrete Event Simulation (DES) in PicoLisp. Now, let's explore another application: a railroad model…
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Solving puzzles faster than humanly possible
Can anyone solve 1000 Opus Magnum puzzles in 24 hours? What about with assistance from bots? Will the solutions be any good? Let's find out!
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How does a computer/calculator compute logarithms?
Summer of Math Exposition 3 - How does a computer/calculator compute logarithms?
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Reconstructing Public Keys from Signatures
One weird hobby of mine is reasonable properties of cryptographic schemes that nobody promised they do or don’t have. Whether that’s invisible salamanders or binding through shared secr…
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There's more to mathematics than rigour and proofs (2007)
The history of every major galactic civilization tends to pass through three distinct and recognizable phases, those of Survival, Inquiry and Sophistication, otherwise known as the How, Why, and Wh…
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Harvard Railroad Economics Exam (1906)
Final exam from Dr. Stuart Daggett's Harvard economics course on Railroad Practice taught in 1906-07.
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AI for math resources, and erdosproblems.com
This post contains two unrelated announcements. Firstly, I would like to promote a useful list of resources for AI in Mathematics, that was initiated by Talia Ringer (with the crowdsourced assistan…
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Exponentially Better Rotations (2022)
If you’ve done any 3D programming, you’ve likely encountered the zoo of techniques and representations used when working with 3D rotations. Some of them are better than others, depending on the situation.
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Does anybody know this fractal? (2012)
Experimenting with the "divisibility" of complex numbers, I stumbled across this thingy. It looks like a fractal. Although the formula does not do any iterations. It reminds me of something. But I dont know what. Doing a Google image search brings up a couple of galaxies :) This image shows the region from (-1/-1) to…
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Borges on Chaos Theory
About a weird, lovely short story
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Solving Probabilistic Tic-Tac-Toe
This morning, I came accross Cameron Sun’s Probabilistic Tic-Tac-Toe on HN . However, the comments were disappointing, with people proposing probabilistic models, linear programming, minimax algorithms, and heuristic evaluations to develop AI approaches for the game, none of which quite correct. In this post, I’ll…
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Feynman’s Razor
If an expert can't understand your explanation, you've dumbed it down too much!
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An animated introduction to Fourier series
This article will be part of an extensive series in which I plan to explore various aspects of Fourier Mathematics. I will take notes, create some visuals (a good pretext to learn more about graphics), and hope that it will be helpful to anyone looking for a clear, visual introduction to these concepts. The article…
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An intuitive guide to Maxwell's equations (2020)
An Intuitive and Visual Guide to Maxwell's Equations