Low-Rank Hypothesis of Complex Systems

A talk on the low-rank hypothesis of complex systems: how high-dimensional complex systems — ecosystems, neural networks, social structures — exhibit effective low-rank behavior, enabling dimension reduction and interpretable dynamics.

Covered singular value decomposition as a tool for analyzing low-rank structure, and empirical validation of the hypothesis across real and random networks, with implications for neural dynamics, epidemiology, and physics. Also addressed cases where the hypothesis fails, such as the brain’s criticality conjecture, and open challenges in predictive modeling of low-rank structures.

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