Hello World

Hello world.

I study the mathematical foundations of machine learning - how models learn, why they generalize, and what makes that learning efficient. My work sits at the intersection of three subfields that I believe are more deeply connected than they are usually treated: mechanistic interpretability, learning theory, and machine learning systems. Understanding any one of them in isolation feels progressively insufficient; studying them together feels increasingly necessary.

The questions I find most compelling are ones that reach across these research areas. What internal computations does a model develop over the course of training, and why those rather than others? Which properties of data, architecture, and optimization determine what is learned, how efficiently, and how reliably it transfers? How do the representations that interpretability research uncovers relate to the generalization behavior that learning theory tries to bound? And how do these abstractions hold up when confronted with the constraints of real systems - memory, throughput, latency, scale? My intuition is that progress on any one of these questions is bottlenecked by the others and that the most informative answers come from working on them simultaneously.

My approach moves in directions between theory and experimentation. Sometimes I begin from formal claims and then design experiments to test whether the assumptions actually hold and the predictions actually appear in practice. Other times an empirical regularity emerges without an explanation, and the work becomes one of isolating the phenomenon, formalizing what is happening, and proving why. Usually, these are two halves of the same process.

This blog is meant to be a working notebook. Some posts will be sketches of arguments I am still trying to formalize. Others will be experimental notes - plots, ablations, anomalies - that I have not yet been able to fully explain. Occasionally there will be more developed pieces that bring theory and experiment together on a single question. None of these are intended as substitutes for full papers. The goal is to make the research process visible - not only the final result, but also the conjecture, the first failed attempt, and the partial understanding that motivated the next step.

I expect to be wrong in public here. Early feedback, disagreement, and refinement are how informal claims become reliable ones, and I would rather surface ideas while they can still be cheaply revised. Posts will aim for technical soundness and clarity even when they are short and for honesty about what is established versus what is still conjectural.

These notes are written by a researcher, for researchers, though I hope they remain accessible to anyone curious about why machine learning systems behave the way they do. If something here is useful, wrong, or incomplete, I would be glad to hear about it. Progress on these questions is not an individual undertaking; the field moves forward when its working drafts are shared, not only its finished ones.

Thanks for reading.