not so sparse

connecting dots between mathematics, machines, and the mind.

IV / Fault Lines in Phase Space

developing a complete theoretical framework showing how low-rank structure creates spectral outliers that predict phase transitions, from fixed points to oscillations to chaos.
read more →

III/ A Ghost in the Machine

uncovering how a single spectral outlier eigenvalue can rise above chaotic bulk dynamics in recurrent neural networks, creating a clean computational channel hidden inside disorder.
read more →

II / The Slow Art of Fast Mixing

a closer look at canonical path theory, the justification for rapid mixing in high-dimensional Markov chains.
read more →

I / Walking the Quantum Line

tracing the shared formalism between classical random walks and quantum evolution on graphs, revealing how diffusion and interference arise from a common linear backbone. read more →