Research
Themes I'm working through, in prose. The structural view — papers, methods, open problems, and the relations between them — lives in the Shiplog.
Free probability and random matrices
Operator-algebraic and combinatorial tools for the spectral behaviour of large random matrices, and the structures (free independence, asymptotic freeness) that make their large-N limits tractable.
Free random projection
A construction that uses random orthogonal matrices as approximate free-group generators, injecting weak hierarchical bias into representations without changing model architecture. Open question: how well it transfers beyond synthetic / LSMDP-style environments to natural datasets.
Dynamical isometry
Conditions under which signal propagation in deep networks preserves norms and gradients. Free probability provides a tractable framework for analysing the input–output Jacobian spectrum at infinite width.
Self-attention at scale
Spectral and signal-propagation analysis of transformer self-attention layers, building on the dynamical-isometry literature.
Meta reinforcement learning
Algorithms that adapt to new tasks from limited interaction. Linearly-solvable MDPs admit closed-form value functions and serve as a controlled testbed.
VR research thread
Earlier exploratory work on virtual-reality interfaces and embodied interaction. Currently a stub — preserved for context rather than active development.