Charles London

DPhil Student

Department of Computer Science
University of Oxford
Wolfson Building, Parks Road, Oxford, OX1 3QD

E-mail: charles.london"at"cs.ox.ac.uk

About me

I am a DPhil student in computer science at the University of Oxford, supervised by Prof. Varun Kanade. I work mainly in machine learning theory, particularly theory of LLMs, and continual or open-ended learning. I am also interested in machine learning for mathematical reasoning. Before starting my DPhil I spent two years at Quantinuum, working on quantum machine learning with Bob Coecke, Stephen Clark and Dimitri Kartsaklis. Prior to this I completed my MSc degree in computer science at Oxford, graduating in early 2022, with my dissertation on generalization bounds supervised by Prof. Yarin Gal. I completed my BA in computer science at the University of Cambridge, graduating in 2019. My undergraduate dissertation was supervised by Prof. Pietro Liò and focused on semi-supervised machine learning methods for cancer classification.

Ideas and collaborations

I am always interested in discussing ideas and potential collaborations. I have more ideas than I have time, and a few of my current ideas are:

Dynamical theories of policy gradient training (similar to the RL Perceptron), to derive scaling laws for RLVR.
Teaching agents/RLMs to optimally decompose problems to avoid context rot.
Constructing benchmarks to measure continual learning capabilities. This would require constructing a good metric for efficiency of models, to measure improvements.
Mine GitHub for Lean proof patches, to train an LLM to construct proofs as in SWE-RL.
Anything to do with LLM theory, especially from a complexity theory perspective. See, for example, this paper on CoT and complexity classes, this paper on complexity-theoretic properties of multi-layer LLMs, or this paper on optimal space complexity for LLMs.
Anything to do with continual learning or continual RL theory, or applications to LLM agents. I'm particularly interested in the case of long time-horizons, where we see many tasks, some repeated, compute has some cost, and we want to minimize regret. I am also particularly interested in infinite memory, limited compute continual learning.

If any of these ideas sound interesting to you, or if you have your own ideas that you would like to discuss, please get in touch at the email address above. I'm also just happy to chat!

Research

Research interests:
Learning theory, LLM theory, continual learning, "agents", online learning, meta-learning, deep learning, generalization.

Selected publications:

Pause Tokens Strictly Increase the Expressivity of Constant-Depth Transformers (2025).
NeurIPS
[NeurIPS] [arXiv]
REAL: Benchmarking Autonomous Agents on Deterministic Simulations of Real Websites (2025).
NeurIPS Datasets and Benchmarks
[NeurIPS] [arXiv]
Solve Layerwise Linear Models First to Understand Neural Dynamical Phenomena (2025).
ICML Position Paper
[ICML] [arXiv]
Disentangling Feature Learning from Generalization in Neural Networks (2025).
ICML Workshop on High-Dimensional Learning Dynamics
[ICML] [arXiv]
Peptide Binding Classification on Quantum Computers (2024).
Springer Quantum Machine Intelligence
[QMI] [arXiv]

Preprints and submitted papers:

HorizonMath: Measuring AI Progress Toward Mathematical Discovery with Automatic Verification (2026).
[arXiv]
h1: Bootstrapping LLMs to Reason Over Longer Horizons via Reinforcement Learning (2025).
[arXiv]
Characterising the Inductive Biases of Neural Networks on Boolean Data (2025).
[arXiv]
Exploiting the Equivalence Between Quantum Neural Networks and Perceptrons (2024).
[arXiv]

Teaching

Departmental Tutor - Computational Learning Theory (Michaelmas 2023, 2024)

Miscellaneous

Other interests:
Economics of AI, theoretical CS, statistical physics, optimization, game theory, Arsenal football club, American football, spy novels, sci-fi.

Favourite fiction books (no particular order): Gorky Park, Blood Meridian, Brave New World, Leave it to Psmith, Do Androids Dream of Electric Sheep?, Moving Pictures, Berlin Game, All the Pretty Horses, Necropolis, Foundation, Catch-22, Neuromancer

Favourite films (no particular order):
In Bruges, No Country for Old Men, The Handmaiden, Shrek 2, Blade Runner, The Nice Guys

Favourite video games (no particular order):
Dragon Age: Origins, Super Mario Galaxy, Fallout: New Vegas, Hollow Knight, Baldur's Gate 3, Assassin's Creed: Black Flag, Metal Gear Solid V, Outer Wilds