I work on the theory of learning systems. Recently, I 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.
In the past, 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, affiliated with the Erlangen AI Hub.
arXiv, 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.
arXiv, 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.