The latest blog posts to take off on Hacker News. 2,851 posts.
Learn how modern image analysis and processing algorithms works under the hood with their C/C++ implementation on PixLab's APIs & FACEIO, facial recognition framework using the SOD Embedded Computer Vision Library.
In the demoscene, there's never a boundary that can't be pushed. My recent 4k demo "Boo!" ( YouTube ), released at X 2023, is a humble attempt to contribute to this ongoing evolution. In particular, it pioneers a new way of computing lines.
Mathematics Professor Gilbert “Gil” Strang taught his last class to thousands after teaching calculus, analysis, and linear algebra for more than 60 years at MIT and online. He reflects on his life at the Institute and as an instructor with MIT OpenCourseWare.
We’ve trained a model to achieve a new state-of-the-art in mathematical problem solving by rewarding each correct step of reasoning (“process supervision”) instead of simply rewarding the correct final answer (“outcome supervision”). In addition to boosting performance relative to outcome supervision, process…
Neel Nanda reverse engineers neural networks that have "grokked" modular addition, showing that they operate using Discrete Fourier Transforms and tr…
The discovery of the Higgs boson at CERN’s Large Hadron Collider (LHC) in 2012 marked a significant milestone in particle physics. Since then, the ATLAS and CMS collaborations have been diligently investigating the properties of this unique particle and searching to establish the different ways in which it is produced…
The myth A few years ago I saw a StackOverflow question (but I cannot find it now): allegedly Andrew Gelman blogged that Bayesian models would not overfit and would only underfit (I also cannot find Andrew’s blog post now but I think what he meant by “Bayesian models only underfits” is that you can never fully model…
A book I was recently reading mentioned a mathematical curiosity I haven't seen before - Tupper's self-referential formula . There are some resources about it online, but this post is my attempt to explain how it works - along with an interactive implementation you can try in the browser.
I recently read the article Beautiful Branchless Binary Search by Malte Skarupke. In it they discuss the merits of the following snippet of C++ code implementing a binary search :
On April 8, 2020, John Horton Conway developed symptoms of COVID-19. On April 11, 2020, he succumbed to the disease. 1 2 3 4
The definitons of the transform (to expansion coefficients) and the inverse transform are given below:
People always talk about "P vs NP" like P problems are easy and NP problems are hard. This is a useful day-to-day model but also an oversimplification....
When learning a new programming language, there is usually a table in the documentation that shows the various operators that can be used with numbers.
In a noisy world, it allows you to be heard.
A brief overview of the formal specification landscape
Diffusion models are trained to reverse a stochastic process through score matching. However, a lot of diffusion models rely on a small but critical implementation detail called thresholding. Thresholding projects the sampling process to the data support after each discretized diffusion step, stabilizing generation at…
A catalogue of software constructs, languages, or APIs which are unexpectedly Turing-complete; implications for security and reliability.
This tutorial is loosely based on a 46-page paper by Paul-Virak Khuong and Pat Morin “Array layouts for comparison-based searching” and describes one particular way of performing efficient binary search by rearranging elements of a sorted array in a cache-friendly way.
I read a blog post by Alex Muscar, “Beautiful Binary Search in D”. It describes a binary search called “Shar’s algorithm”. I’d never heard of it and it’s i…
A curious pattern in polar plots with prime numbers, together with discussion of Dirichlet's theorem
A self-contained introduction to Gröbner bases and solving polynomial systems
Some anomalies/questions which are not necessarily important, but do puzzle me or where I find existing explanations to be unsatisfying.
The uncanny resemblance between double descent and a 50 year old theory from psychology
Artificial intelligence, like machine learning before it, is making big money off what I call the “sell ∀ ∃ as ∃ ∀ scam.” The scam works as follows. Build a sy…
Tutorials and articles of Inigo Quilez on computer graphics, fractals, math, art, demoscene, shaders and more.
In 2005, id Software released the source code for their 1999 game Quake III Arena under the GPL-2 license. In the file code/game/q_math.c , there is a function for calculating the reciprocal square root of a number which at first glance seems to use a very peculiar algorithm:
