Matt McWilliams

Projects and Blog

Hello there!

My name is Matt McWilliams.

I'm a dreamer.

I'm also a programmer, designer, reader, writer, tinkerer, builder, student, athlete, thinker, truth-seeker, and friend.


Projects and Writing

Guidance Scale Effects
AI
Writeup
December 2025

This project seeks to understand the effects of guidance scale on classifier-free sampling of conditional diffusion models. We trained a conditioned UNET diffusion model on the MNIST dataset and sampled using classifier-free guidance. Classifier-free guidance is essential for modern image generation diffusion models, allowing label-dependent features become more prominant simply by changing a variable, the guidance scale.

LemmaCraft
Math
Writeup
December 2025

LemmaCraft is a visual math proof engine with a custom parser and internal mathematical model. It allows its users to derive Peano-arithmetic results from only a few axioms. It consists of four chapters designed to teach users the software and introduce key lemmas: a tutorial chapter followed by three chapters that each cover a new mathematical domain: addition, multiplication, and exponentiation. In each chapter, players prove progressively more challenging lemmas about basic operations.

LemmaCraft

LemmaCraft is a math proof game in which you solve engaging math puzzles as you rebuild mathematics from the Peano axioms.

It also has a "story mode" if you'd like to solve math while participating in a cozy fantasy adventure.

Try it out →