connecting dots between mathematics, machines, and the mind.
developing a complete theoretical framework showing how low-rank structure creates spectral outliers that predict phase transitions, from fixed points to oscillations to chaos.
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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.
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a closer look at canonical path theory, the justification for rapid mixing in high-dimensional Markov chains.
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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 →