The latest blog posts to take off on Hacker News. 2,851 posts.
KL-divergence is a topic which crops up in a ton of different places in information theory and machine learning, so it's important to understand well. Unfortunately, it has some properties which seem confusing at a first pass (e.g. it isn't symmetric like we would expect from most distance measures, and it can be…
Recent advances in quantum hardware and software have accelerated the timeline on which quantum attack might happen. Cloudflare is responding by moving our target for full post-quantum security to 2029.
Any Boolean function can be computed with Tofolli gates, and Tofolli gates are reversible, and so any Boolean function can be computed reversibly.
The Jazz of Physics: Albert Einstein and John Coltrane had a lot in common. The so-called “Coltrane circle” or “Circle of Fifths,” but incorporates Coltrane’s own innovations. Coltrane gave the drawing to saxophonist and professor Yusef Lateef in 1967, who included it in the Repository of Scales and
Actually building floating point from scratch!
We have been using Signals in production for years via several modern front-end frameworks like Solid, Vue, and others, but few of us are able to explain how they work internally. I wanted to dig into it, especially diving deep into the push-pull based algorithm, the core mechanism behind their reactivity.
In this chapter we will talk about types. This might be disappointing for you, if you expected to learn about as many new categories as possible (which you don’t even suspect are really categories till the unexpected reveal)—we’ve been talking about the category of types in a given programming language ever since the…
For those of you who haven’t seen, there were actually two “bombshell” QC announcements this week. One, from Caltech, including friend-of-the-blog John Preskill, showed how to do quantum faul…
Why the HJB is Bellman's equation in continuous time, why continuous time matters, and how to solve the resulting control problem with neural policy iteration.
How TurboQuant compresses the KV cache without losing accuracy, and what that could mean for memory stocks
A complete guide to quantization: how LLMs store parameters as floats, why shrinking them to 4 or 8 bits barely hurts accuracy, and how to measure the tradeoff.
Exploring the Weapon-Target Assignment problem: how missile defense connects to NP-completeness, SSPK probability calculations, and how saturation attacks exploit computational limits.
"A Ramsey-style Problem on Hypergraphs" — a problem from FrontierMath: Open Problems, Epoch AI's benchmark of unsolved research mathematics.
every regex engine that promises linear time breaks that promise the moment you ask for all matches. the problem has been there since the 70s, hiding in the iteration loop.
…symmetry isn’t just a preference for “pretty” shapes. Contents Introduction The HM-GM-AM-QM Inequality The two circles The Semicircle The Container The 3D container The Sum of Squares Inequality Nesbitt’s Inequality Conclusion Introduction While I was randomly browsing the web, I came across this nice picture: Roland…
When life gives you switches...
Bennett, an American physicist at IBM Research, and Brassard, a Canadian computer scientist at the Université de Montréal, are widely recognized as founders of quantum information science, a field at the intersection of physics and computer science that treats quantum mechanical phenomena not merely as properties of…
Calculus is the mathematics of approximations of continuous quantities ; number theory asks exact problems about discrete quantities. These seem, therefore, to be unrelated studies.
Mathematical research traditionally involves a small number of professional mathematicians working closely on difficult problems. However, I have long believed that there is a complementary way to …
JPEG is a clever image compression algorithm that exploits a human perceptual bias and the structure of natural images. It makes a change of basis before encoding so that the rewritten image representation concentrates the signal that humans are most perceptive to, and thus, the remaining details can be discarded…
Tutorials and articles of Inigo Quilez on computer graphics, fractals, math, art, demoscene, shaders and more.
When Mathematica seems to not to know how to simplify an expression, it may be doing the right thing, being more sophisticated than you expect.
A closer look at the tesseract and the ways we can render it on the screen.
In this post I’m going to cover a neat technique for rendering regions of fog with varying density. I’ll start by covering some of the basic principles behind fog rendering and a few co…
Interactive ternary chart of citrus ancestry
A hands-on introduction to elliptic curve cryptography. Start with curve geometry, build point addition and scalar multiplication, see why ECDLP is hard, and then use that math in ECDH, ECDSA, and ECIES.
An introduction to the Decision Trees, Entropy, and Information Gain.
An interactive exploration of quadtrees. Start with brute-force spatial search, build recursive space partitioning step by step, then use it for point lookups, range queries, nearest-neighbor search, collision detection, and image compression.
Just a brief announcement that I have been working with Quanta Books to publish a short book in popular mathematics entitled “Six Math Essentials”, which will cover six of the fundament…
