Ready, set , begin… (you don’t know how hard I tried to resist to making that pun). We begin our inquiry with the theory of sets. Set theory and category theory share many similarities. We can view category theory as a generalization of set theory. That is, it’s meant to describe the same thing as set theory…
The following is based upon systems of equations found in "Symmetry in Chaos, A Search for Pattern in Mathematics, Art, and Nature" (the second edition) by Michael Field and Martin Golubitsky. They ask the question whether there are aperiodic chaotic attractors that generate symmetric patterns? Can there be order…
I have been steeping myself in probabilistic exercises recently, because it’s an area where I feel like I could benefit from building better intuition. I have found a recurring key to solving many of them: conditioning on an intermediary state, and then computing the value of that intermediary state separately. This…
Erik van Zwet, Sander Greenland, Guido Imbens, Simon Schwab, Steve Goodman, and I write :
Apparently Randall Munroe gets a lot of messages saying that the “random” button on xkcd is biased.
The single most undervalued fact of linear algebra: matrices are graphs, and graphs are matrices
tl;dr: part 1 explains what an explanation algorithm is, and part 2 describes an open source SQL data differ.
From the highly eclectic blog of Mark Dominus
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…
A different view on two's complement math.
Suppose that we sample a large number N N N of independent random functions f i : R → R f_i \colon \R \to \R f i : R → R from a certain distribution F \Fc F and propose to solve a regression problem by choosing a linear combination f ˉ = ∑ i λ i f i . \bar{f} = \sum_i \lambda_i f_i. f ˉ = i ∑ λ i f i . For…
The definitons of the transform (to expansion coefficients) and the inverse transform are given below:
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…
This text presents a method for embedding a programmable, general-purpose, digital computer into Tetris. It describes the capabilities and performance of an implementation that runs Tetris on Tetris.
Prompted by your blog post this morning, I attach a plot from Figure 3 of They Still Haven’t Told You showing overnight and intraday returns to AIG (with logarithmic vertical scale, updated with data through the end of October).
High quality font rendering for WebGPU
Great. The fusion hype is bad enough already. Now its resurgence is going to interrupt the series of posts I’m in the middle of publishing in order for this post to be “timely.”
As a physicist, I’ve learned that the presence of 2 π 2\pi 2 π [▼] [ Or rather τ \tau τ , as it should actually be called . ] in a formula usually spells trouble. It’s kind of annoying to write by hand, easy to forget, and it’s dimensionless, so you can’t easily check if you forgot to divide or multiply by it…
a personal blog
Many years ago I've re-posted a Stack Overflow answer with Python code for a terse prime sieve function that generates a potentially infinite sequence of prime numbers ("potentially" because it will run out of memory eventually). Since then, I've used this code many times - mostly because it's short and clear. In this…
All large numbers are large, but some are larger than others
[Part of a series: Penrose and hats | Spectres | finite-state transducers | more transducers | refining tilings ]
This December I once again did the Advent of Code , in Rust. If you are interested, my solutions are on Github. I wanted to highlight one particular solution to the day 2 problem as it is both optimized completely beyond the point of reason yet contains a useful technique. For simplicity we’re only going to do part 1…
This is lobste.rs comment as an article, so expect even more abysmal editing than usual.
In the demoscene, there's never a boundary that can't be pushed. My recent 4k demo "Boo!" ( YouTube ), released at X 2023, is a humble attempt to contribute to this ongoing evolution. In particular, it pioneers a new way of computing lines.
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…
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…
Harvard Magazine printed the following chart that confirms a trend in undergraduate majors that we all know about: students are favoring STEM majors at the expense of humanities.
