The latest blog posts to take off on Hacker News. 2,851 posts.
About eight years ago, I was playing a game of Codenames where the game state was such that our team would almost certainly lose if we didn't correctly guess all of our remaining words on our turn. From the given clue, we were unable to do this. Although the game is meant to be a word guessing game based on word…
I’ve been reading Pearl’s Causal Inference in Statistics , and one of the exercises poses this problem:
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…
When do music stars achieve fame, and how long does fame typically last?
We build complex mathematical formulas bottom-up using pure lambda calculus. Includes instructions of how to translate Taylor series and other approximations to lambda terms.
A family of infinite sums that evaluate to rational numbers, sometimes integers, and and effective algorithm for finding the sum.
Programmers on the internet often use Turing-completeness terminology. Typically, not being Turing-complete is extolled as a virtue or even a requirement in specific domains. I claim that most such discussions are misinformed --- that not being Turing complete doesn't actually mean what folks want it to mean, and is…
This is basically a compilation of the lecture notes I wrote when teaching 36-401, Modern Regression, in fall 2015 . I offer it here on the chance that it might be of interest to those learning, or teaching, linear regression. There's no shortage of resources on that, but I have tried to present the subject as though…
A ‘tritone substitution’ is a popular trick for making your music sound more sophisticated. I’ll show you a couple of videos with lots of examples. But since I’m mathematici…
A traditional subjective Bayesian will assume a data generating distribution (aka a likelihood when viewed as a function of the parameters). Then, conditional on this assumption, they encode their prior beliefs as a prior distribution over parameters. After this, they turn the crank on posterior inference and don’t…
Breakthrough models AlphaProof and AlphaGeometry 2 solve advanced reasoning problems in mathematics
Finding the median in a list seems like a trivial problem, but doing so in linear time turns out to be tricky. In this post I’m going to walk through one of my favorite algorithms, the median-of-medians approach to find the median of a list in deterministic linear time. Although proving that this algorithm runs in…
A guide on how to generate sudokus of any difficulty.
In 1890 Giuseppe Peano discovered a square-filling curve , and a year later David Hilbert published his variation . In those days people did not waste readers’ attention with dribble – Peano explained it all on 3 pages, and Hilbert on just 2 pages, with a picture!
Recently one of my colleagues was reading Alan Turing’s groundbreaking 1936 article “On Computable Numbers with an Application to the Entscheidungsproblem.” This is the article in…
I wrote a little book about entropy; here’s the current draft: • What is Entropy? If you see typos and other mistakes, or have trouble understanding things, please let me know! An altern…
Bézier curves are widely used for defining vector graphics. They are basically polynomial parametric curves, but given in the Bernstein basis, which enables us to define the curve using control points. The first and last control point define the start and endpoint of the curves, the intermediate control points kind of…
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.
Hugo Hadfield - Cross stack robotics engineer and computer vision researcher specializing in deep learning, sensor fusion, geometric algebra and applications in self-driving cars and robotic manipulation.
Can I make math operations run 100x faster on really, really big numbers?
Web site content explains the modern view of entropy change and the dispersal of energy in a process (at a specific temperature). It has been selected for instructors in general and physical chemistry by Dr. Frank L. Lambert, Professor Emeritus (Chemistry) of Occidental College, Los Angeles.
I’ve never been good at playing football 1 . I started playing again last year and I have scored more own goals than goals for my team. Also, I support the RCD Espanyol 2 , which has spent last season in the second division and has miraculously ascended to the first division last week. And to be honest, I only watch…
From gene regulatory networks to artificial neural networks
A programming model for spatial canvases
In Michael Sipser’s Introduction to the Theory of Computation textbook, he has one Platonically perfect homework exercise, so perfect that I can reconstruct it from memory despite not having …
“If you look at zero you see nothing; but look through it and you will see the world.”
How do you find near-duplicates in a massive collection of documents? An exploration of the Jaccard similarity metric, and the MinHash hashing trick used to efficiently approximate it at web scale.
In this post we will implement a data compression program in about 150 lines of Haskell. It will use Huffman coding and handle arbitrary binary files using constant memory for encoding and decoding.
