I work on the physics of learning systems. I'm especially interested in the nature of emergence, which is the observation that systems exhibit new behavior at different degrees of scale and complexity. For example: a cell is alive, but is only made of dead things. Water is wet, yet a single molecule is not.
I recently discovered and characterized a new type of phase transition in learning systems: Just as physical systems can transition between distinct phases of matter, I showed how learning systems transition between distinct phases characterized by the complexity of their internal patterns. I found that as deep neural networks transition from memorization of their training data to perfect generalization, there is a corresponding rise-and-fall of complexity in the network, as measured by the network's compressibility.
Previously, I did research in mathematics and physics. I've worked on projects in knot theory, neutrino physics, and quantum many-body localization. In industry, I've worked in computational geophysics, reinforcement learning for robotics, and natural language processing with LLMs at a startup I founded.
I have held a postdoctoral appointment in the Mathematical Institute at Oxford since autumn 2025. A brief statement on my research interests is available here.
Physica D: Nonlinear Phenomena (twitter thread, blog, link to talk)
We observe a complexity phase transition in grokking neural networks, which suddenly transition from memorization to perfect generalization. We find that during this transition, there is a corresponding rise and fall of complexity in the networks. We explain this phase transition using ideas from Kolmogorov complexity and rate-distortion theory, and derive a principled lossy compression framework for neural networks which allows us to track their complexity dynamics.
ICRA 2025, project page, twitter thread
We demonstrate robot policies trained purely offline in a world model transfer to the real world zero-shot. LUMOS is an upgrade to DITTO, adding planning in the learned world model latent space for improved long-horizon performance. LUMOS conditions on natural language commands to perform multi-task manipulation with a single network.
Normally when we train policies offline, it also means they learn off-policy. We use world models to enable safe offline training on-policy. We use reinforcement learning inside the latent space of a learned world model to induce imitation learning, using a robust reward defined in the learned latent space. On-policy RL in the world model transfers to robust imitation learning in the real environment.
First International Meeting for Applied Geoscience & Energy, 2021
A case study using a computer vision system I developed in conjunction with physical models which was led by a researcher at a customer seismic exploration company. The seismic visualizations on this page were produced around this time, as part of some experiments I ran to study generative and latent space modeling with GANs, which I explain here.
American Go E-Journal, Deutsche Go-Zeitung, 2020
An essay on the history of AI in the game of go. Republished by the American Go Association and the German Go Newspaper.
DUNE Collaboration Technical Report, 2016
I ran simulations of proposed changes to the beamline geometry for the DUNE experiment, to understand the effect of the changes on neutrino flavour production statistics. Published as a technical note to the internal DUNE collaboration.