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Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,391 posts.
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Continuous Diffusion Language Models (CDLM's)
Fully discrete methods dominated for a few years, but language models based on continuous diffusion are making a comeback.
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Solving LinkedIn Queens with SMT
For sure easier than solving it in SAT!
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Introduction to P vs. NP
Series Introduction In this series of articles I would like to share with you a set of ideas that are meant to help non-technical people build a better intuition as to what the current software and…
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Accidentally writing a SAT solver
where my words occasionally escape /dev/null
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Five Kinds of Nondeterminism
Or four kinds, or six kinds, I'm not picky about how you count them
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An overview of gradient descent optimization algorithms (2016)
Gradient descent is the preferred way to optimize neural networks and many other machine learning algorithms but is often used as a black box. This post explores how many of the most popular gradient-based optimization algorithms such as Momentum, Adagrad, and Adam actually work.
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Donut.c Without a Math Library
My little donut.c has been making the rounds again, after being featured in a couple YouTube videos (e.g., Lex Fridman and Joma Tech ). If I had known how much attention this code would get over the years, I would have spent more time on it.
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Elliptic Curve Cryptography: A Gentle Introduction – Part II
In the previous post , we have seen how elliptic curves over the real numbers can be used to define a group. Specifically, we have defined a rule for point addition : given three aligned points, their sum is zero ($P + Q + R = 0$). We have derived a geometric method and an algebraic method for computing point…
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Is mathematics about to enter the conservatory?
Math as cultural institution.
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Wolfram Language
Transcript of Stephen Wolfram's talk at SXSW 2015 on the present and future of computing: Wolfram Language, image recognition, language-design philosophy, tweetable programs, computational thinking for kids, natural language as input, symbolic programming, deployment, automation of programming, Internet of Things…
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Derivative at a Discontinuity
Alok Singh's Blog
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The Ruliology of Lambdas
Stephen Wolfram explains the rich ruliology of lambdas, made particularly significant by their connection to practical computing. Covers basic computations to undecidability to multiway graphs and evaluation strategies.
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Softmax, can you derive the Jacobian? And should you care?
Practice machine learning engineering with hands-on coding challenges. Implement neural network components, backprop, and more — from scratch.
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What does the Riemann zeta function have to do with the distribution of primes?
One of the oldest theorems in mathematics is that there are infinitely many primes. Euclid (the geometer!) proved this around 300 BCE, and for centuries afterwards the story ended there. There are infinitely many primes -- so what else is there to ask about them?
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Topologist's Map of the World
Reddit user xilefakamot created this in 2020 — a “topologist’s map of the world.” It depicts international borders and nothing else — the shapes, sizes, and distances between countries are forsaken in order to present the pattern of their borders as efficiently as possible. “No calculations per se – I sketched out a…
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Lemma for the Fundamental Theorem of Galois Theory
This post illustrates a key lemma that is used in proving the fundamental theorem of Galois theory (FTGT). Note that FTGT is not covered in this post. The focus of this post is on understanding and proving this lemma only. Here is the lemma from the book Galois Theory , 5th ed. by Stewart (2023):
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A shower thought turned into a Collatz visualization
I recently went on a nice long SCUBA diving trip with my wife and daughters. Lots of diving implies lots of showers, and lots of showers means lots of shower-thoughts! [1] An especially interesting one I had turned into a nice way to visualize some aspects of the Collatz Conjecture.
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Hardy, Ramanujan and Taxi No. 1729
In his book Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, G. H. Hardy tells this famous story: He could remember the idiosyncracies of numbers in an almost uncanny way. It …
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A Random Walk in 10 Dimensions (2021)
The geometry of random walks in high dimensions provides the power behind deep learning and may be the secret to intelligence.
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Advent of Code Python Solutions, Explained
I first participated in Advent of Code (AoC) in 2017. My co-workers at Formlabs introduced it to me. This year (2018), quite a lot of Formlabs folks are taking part and we have a nice private leaderboard going. I'm having a lot of fun with it. I've been staying up until midnight to work on the problems as soon as…
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Circulant Matrices, Eigenvectors, and the FFT
The eigenvectors of a circulant matrix do not depend on the matrix itself, only on the size, and the eigenvectors are columns of the FFT matrix.