Through a couple of different avenues I wandered, yet again, down a rabbit hole leading to the topic of this post. The first avenue was through my main focus on a particular machine learning topic th
IBM Slapped the Buzzwords 'AI Interpretability' on Generalized Continued Fractions and their Series Transformations and was awarded a Patent
My journey implementing a new dithering algorithm in the Racket programming language.
A modest mathematical framing of language
Deriving the basic mathematical properties of the Smith chart from electrical engineering
Transformer-based large language models are relatively easy to understand. You break language down into a finite set of “tokens” (words or sub-word components…
An article about the John Coltrane Tone Circle, a 5-octave Circle of Fifths and a double-ring Hexatonic Circle as well. Interpretation, explanation ...
When you resize, rotate, or in any way transform an image; or more generally when you resample some discrete signal, the software you are using must _interpolate_ between the discrete points to produce a result. Linear and cubic interpolation are easy to explain, but Lánczos interpolation, one of the most popular…
With the concern that “Moore’s Law is dead,” new interest has grown for unconventional forms of computing. This includes:
In the comments on my recent post on books on the history of maths Fernando Q. Gouvêa jumped in to draw attention to the book Math Through the Ages: A Gentle History for Teachers and Othe…
A few weeks ago I was minding my own business, peacefully reading a well-written and informative article about artificial intelligence, when I was ambushed by a passage in the article that aroused …
Large language models like ChatGPT & Claude have become ubiquitous in today’s world. I visited a friend for the New years eve and was impressed by how ChatGPT was being extensively used within the family. The friend’s little kid is going to grow up in a world, where turning to large language models (LLM) for quick…
Update: this post was discussed on Hacker News I completed a Computer Science degree at uni, and bundled a lot of maths subjects in as electives: partial differential equations, vector calculus, discrete maths, linear algebra.
Chris Grossack's math blog and professional website.
Problem 1026 on the Erdős problem web site recently got solved through an interesting combination of existing literature, online collaboration, and AI tools. The purpose of this blog post is to try…
I'm the kind of person who thinks about the design and implementation of hash tables. One design which I find particularly cute, and I think deserves a bit more publicity, is Robin Hood open-addressing with linear probing and power-of-two table size. If you're not familiar with hash table terminology, that might look…
We published our video on zero-knowledge proofs! Surprisingly, making this video took a lot of work. Zero-knowledge proofs for coloring are one of those algorithms that, in hindsight, seem beautifu…
[Updated on 2020-09-03: Updated the algorithm of SARSA and Q-learning so that the difference is more pronounced. [Updated on 2021-09-19: Thanks to 爱吃猫的鱼, we have this post in Chinese].
Collaboratively editing strings of text is a common desire in peer-to-peer applications. For example, a note-taking app might represent each document as a single collaboratively-edited string of text.
Bézier curves are a core building block of text and 2D shapes rendering. There are several approaches to rendering them, but one especially challenging problem, both mathematically and technically, is computing the distance to a Bézier curve. For quadratic curves (one control point), this is fairly accessible, but for…
An explainer for people who don't know computer science and are mildly curious
Posts and writings by Julian Schrittwieser
This is the introduction to a series on Abstract Algebra. In particular, our focus will be on Galois Fields (also known as Finite Fields) and their applications in Computer Science. This is a project I've been excited about for many years now, but have been too busy to dedicate the adequate effort to meet my…
I can't remember where I first saw them, but ever since, I have been unable to forget them: abelian sandpiles. I'm far from the only one . They're remarkably simple, yet produce lovely symmetric patterns. I loved them so much that I adorned the title banner of this blog with an animation of an abelian sandpile. But…
These days, the most common question I get goes something like this: A decade ago, you told people that scalable quantum computing wasn’t imminent. Now, though, you claim it plausibly is immi…
My journey from building cricket bots to building “wind tunnels” with my collaborators — and finding the answer hidden in geometry.
Intel released the powerful Pentium processor in 1993, establishing a long-running brand of high-performance processors. 1 The Pentium incl...
The tools of linear algebra are extremely useful when working in Euclidean space (e.g. \mathbb{R}^3 ). Wouldn’t it be great if we could apply these tools to additional mathematical constructs, such as functions and sequences? Hilbert space allows us to do exactly this - apply linear algebra to functions.
Building on my previous post on sorting algorithms, I implemented the same algorithms using CUDA to explore performance improvements through parallel computing. The goal is to see how we can leverage the power of parallel computing to speed up our sorting algorithms. I went for a NVIDIA recruiting event some days ago…
This is a list of Unparalleled Misalignments, pairs of non-synonymous phrases where the words in one phrase are each synonyms of the words in the other. I've maintained this list since 2018; attributions (when known) can be seen on hover.
