About Me

Hi, I'm Jorge Guzman, an applied mathematician based in Atlanta, Georgia. I'm interested in understanding how intelligent behavior emerges from learning.

At first glance, my interests seem to span very different areas: dynamical systems, topology, mechanistic interpretability, reinforcement learning, and machine learning. To me, however, they all point toward the same question:

What causes learning systems to suddenly discover new ways of thinking?

Whether it's a transformer discovering an algorithm for modular arithmetic, a model undergoing grokking, or an agent transitioning from reactive behavior to long-horizon planning, I'm fascinated by the qualitative changes that appear during learning. Rather than treating these behaviors as isolated phenomena, I'm interested in understanding the mathematical principles that govern their emergence.

My background is in applied mathematics, where I worked on mathematical modeling, dynamical systems, and topological data analysis. More recently, my attention has shifted toward modern AI systems, particularly learning dynamics and mechanistic interpretability. I enjoy combining mathematical thinking with empirical experiments, using each to inform the other.

Altered Chain is my public research notebook. I use it to document papers I'm reading, reproduce experiments, write technical explanations, and develop research ideas. Rather than presenting polished conclusions, I try to make my thinking visible as it evolves.

Alongside my research interests, I enjoy building software. I've worked on machine learning tools, numerical simulations, full-stack web applications, and mathematical software using Python, PyTorch, Rust, TypeScript, Next.js, and other technologies. You can explore those projects on the Projects page.

Long term, I hope to contribute to a more principled scientific understanding of learning systems by combining mathematics, experiments, and interpretability. I plan to pursue a PhD and build research that helps explain not only what modern AI systems learn, but why they learn it.

If you'd like to collaborate, discuss research, or simply talk about mathematics and AI, feel free to reach out through GitHub or X.