03.07.2025 Building animations in Manim with LLMs

Manim is a Python animation engine designed to build animated mathematical explainer videos (examples here) created by Grant Sanderson of the superb YouTube channel 3Blue1Brown.

A couple years ago I wanted to write my own mathematics explainer videos with Manim, but found the learning curve to be pretty steep at the outset.

The user experience has since improved dramatically - in large part because of the Manim Community Edition, but also because there’s now enough samples in recent LLM training runs that they can produce workable Manim code!

24.05.2025 Paper: Step-by-Step Diffusion: An Elementary Tutorial

I’ve been reading through Step-by-Step Diffusion: An Elementary Tutorial by Apple (arxiv). The mathematics underpinning diffusion language or image models is quite complex, but this walkthrough strikes a nice balance between concrete mathematical grounding and intuition.

18.04.2025 2025 Australian Election Forecast Model

My friend, Dania Freidgeim, created a probabilistic model of First Preference votes for the 2025 Australian Federal Election. Australia uses a Preferential voting (Instant-runoff) system, which makes this a really interesting exercise! Please go check it out!

11.03.2025 Inverse UMAP transforms

TIL that the dimensionality reduction algorithm UMAP¹ has support for inverse transforms!

Naturally, these are lossy inverses, but being able to generate novel examples of, for example, handwritten digits (yep, classic MNIST once again) is exceedingly cool.

The example images of handwritten digits here are sampled from the compressed planar space, and “inverted” into the original “image space”.

On a related note, the whole explanatory article for UMAP is a beautiful work of exposition, full of rich ideas that make one ponder deeply. I only wish I understood everything in here end-to-end.