The latest blog posts to take off on Hacker News. 221 posts.
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:
We present basic math related to computation and memory usage for transformers
In 1969, Marvin Minsky and Seymour Papert published Perceptrons: An Introduction to Computational Geometry. In it, they showed that a single-layer perceptron cannot compute the XOR function. The main argument relies on linear separability: Perceptrons are linear classifiers, which essentially means drawing a line to…
I've tried to write a blog post on tag systems for years now. Literally years, I think I first started drafting it out in 2018 or so? The problem is that...
From the highly eclectic blog of Mark Dominus
A brief introduction tutorial to Constraint Programming with Python, we introduce some relevant definitions and solve our old Pokémon Centers and Pokémon Gyms problem this time with CP!
We describe a graph-theoretic analogue of vector calculus. The linear operators of vector calculus (gradient, divergence, laplacian) correspond to the matrices naturally associated to graphs (incidence matrix, adjacency matrix). This analogy is useful for formalizing the discretization of some problems in image and…
When I first learned about Fourier series and integrals, I hated it because it seemed like a collection of many ad-hoc definitions, formally related but very different.
Posted by Matthew Streeter, Software Engineer, Google Research Derivatives play a central role in optimization and machine learning. By locally app...
Update (April 14): On the suggestion of my TA Justin Yirka, I gave GPT-4 problem 2 from the final exam, along with its own answers and my and Justin’s grading comments, and asked it whether i…
The unreasonable persistence of an old standard
[Part of a series: Penrose and hats | Spectres | finite-state transducers | more transducers | refining tilings ]
Lerp is the nickname for Linear Interpolation between two points. It's a fairly simple effect to implement but can really improve the look of your animations if you're moving an object from a point A to point B.
It’s April Cools again. For a few summers in high school and undergrad, I was a day camp counselor. I’ve written before about how it helped me develop storytelling skills, but recently I thought of it again because, while I was cleaning out a closet full of old junk, I happened upon a bag of embroidery thread. While…
Interactive article explaining the physics of a bicycle.
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…
Every Wordle solution laid out at once. Filter all 2,309 by letter, position, and gray/yellow/green clues to narrow down today's answer.
