There are few things I think about more than the essays on gwern.net, and there are few with as satisfying a theoretical payout to contemplate in my orb as his essay on “leaky pipelines”, aka log-normal distributions. The skulk: Say you’re working on a Laravel web app. You’re about 90% sure you know how to start the…
Space Engine ...
Stephen Wolfram explores minimal models and their visualizations, aiming to explain the underneath functionality of neural nets and ultimately machine learning.
A free, self-contained introduction to neural networks and differentiable programming, from automatic differentiation to transformers, with additional chapters on advanced topics.
An online book about collision detection using Processing.
A blog about math by Nic Ford
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.
Recently I came across a puzzling fact: the International Criminal Court hashes electronic evidence with MD5, even though MD5 is badly broken. So, why are lawyers using broken, outdated technology? The answer involves the common law system, cultural isolation, and a single man named Don L. Lewis.
Describes a simple Markov chain algorithm to generate reasonable-sounding but utterly nonsensical text, and presents some example outputs as well as a Python implementation.
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…
In my puzzle collection , there are many games in which you have to connect points together by edges, making a graph, and the puzzle rules say you must avoid making any loop in the graph. Examples are Net , Slant , and some configurations of Bridges (although not the default one). Loopy and Pearl also care about…
How I created a wall poster of knot diagrams.
EDIT: Be warned that this post is angry. If you’re easily offended when someone goes on a rant, then leave now because I’m very unforgiving in several places below. The tone of my writing is unusually harsh, but the people whose work I’m talking about deserve it, and here’s why. Even though I had been working with…
Achieving extreme video compression rates using the LivePortrait model for talking head videos.
A deep dive into spectral analysis of diffusion models of images, revealing how they implicitly perform a form of autoregression in the frequency domain.
Why x^2 isn't always x*x.
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…
About two years ago, I switched teams at Google to focus on fully homomorphic encryption (abbreviated FHE, or sometimes HE). Since then I’ve got to work on a lot of interesting projects, learning along the way about post-quantum cryptography, compiler design, and the ins and outs of fully homomorphic encryption. If…
Personal website of Dr. Peder M. Isager
From gene regulatory networks to artificial neural networks
This idea is particularly sticky because it was more or less true 50 years ago, and it's a passable mental model to use when learning sql. But it's an inadequate mental model for building new sql frontends, designing new query languages, or writing tools likes ORMs that abstract over sql.
Official Website of Diffusion Forcing
The Black–Scholes formula is the crown jewel of quantitative finance. The formula gives the fair price of a European-style option, and its success can ultimately be measured by its impact on option markets. Before the formula’s publication in 1973 (Black & Scholes, 1973; Merton, 1973) , option markets were relatively…
Intro to HM
An article about music and geometry, in particular about musical intervals and scales and their geometric equivalent ...
I have long struggled with understanding what probability-generating functions are and how to intuit them. There were two pieces of the puzzle missing for me, and we’ll go through both in this article.
