Thoughts on software engineering, research, and technology.
The Monty Hall problem looks like a 50/50 coin flip but isn't. This post lets you play the game, watch the probability equation update live as you add doors, and run a Monte Carlo simulation of a hundred thousand games to see intuition and math collide.
Learning in high dimensions is impossible without assumptions. This post walks through the error decomposition behind every ML model, shows how the curse of dimensionality attacks each piece, and explains why exploiting geometry is the only known escape.
Graphs are everywhere — molecules, social networks, road maps — but most tutorials skip the basics and jump straight to GNNs. This post rebuilds the foundation: what a graph actually is, the properties that matter, and interactive tools to build and explore them yourself.
Message passing is the heartbeat of Geometric Deep Learning. This post breaks the loop into three moves — message, aggregate, update — with the math, the PyTorch, and an interactive playground where you inject a signal and watch it spread across a graph.
The retina is the only place in the body where you can directly observe neurons and blood vessels without a needle or a scalpel. AI is turning that biological accident into a revolution in non-invasive diagnostics.
If you've written a CLAUDE.md file, you're not prompting anymore — you're engineering context. Here's what that means and why everything is changing in 2026.
A world model is an agent's internal simulation of reality. Instead of just reacting to what it sees, it can imagine futures, plan inside its own mind, and act with foresight. Here's the foundation.
Before a graph neural network can learn anything, it needs to read the graph. That's where the adjacency matrix comes in — a compact, elegant way to encode who is connected to whom.
A gentle introduction to geometric deep learning, why symmetry matters, and how graph-based models help AI reason about connected data.
An interactive visual tour of why GANs use log, what min_G max_D means, and how the two-player game reaches Nash equilibrium.