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.