Understanding How Intelligent Behavior Emerges from Learning

Hey, I'm Jorge — an applied mathematician and developer interested in the learning dynamics behind modern AI systems.

My work sits at the intersection of mathematics, machine learning, and mechanistic interpretability. I am especially interested in a broad scientific question:

What training conditions give rise to qualitatively new behaviors in learning systems?

This question appears in many forms: grokking, representation learning, long-horizon planning, tool use, coordination, and the emergence of structured internal circuits. I want to understand not only whether these behaviors appear, but when they appear, why they appear, and whether we can detect their precursors before they become visible in behavior.

Altered Chain is my research notebook. Here I write about papers, reproduce experiments, develop project ideas, and document my path toward a deeper mathematical understanding of learning systems.

Where to start

• Blog — essays and technical notes on learning dynamics, mechanistic interpretability, mathematics, and AI research.
• Projects — coding projects, research experiments, mathematical tools, and applied ML work.

Featured writing

These posts best represent what I have been thinking about recently:

• How a Transformer Learns Modular Addition — a technical exploration of how a small transformer discovers structure in a simple algorithmic task.
• Reading Grokking After Mechanistic Interpretability — reflections on delayed generalization, learning dynamics, and how mechanistic interpretability changes the way we read grokking.

Research direction

Modern AI systems often improve gradually in measured performance, yet their learned strategies can change qualitatively during training. A model may first memorize, then generalize. An agent may first act reactively, then begin planning over long horizons. A system may first learn local heuristics, then discover reusable internal structure.

I am interested in these transitions. My long-term goal is to combine mathematical modeling, controlled experiments, and interpretability tools to understand how complex behaviors emerge from simple training processes.

Thanks for visiting. I hope you find something here that makes you think differently about mathematics, learning, or intelligence.