Optimal noise-canceling networks

From the cerebral cortex to large-scale power grids, natural and engineered networks face the challenge of converting noisy inputs into robust signals. The input fluctuations often exhibit complex yet statistically reproducible correlations that reflect underlying internal or environmental processes such as synaptic noise or atmospheric turbulence. This raises the practically and biophysically relevant question of whether and how noise-filtering can be hard-wired directly into a network's architecture. By considering generic phase oscillator arrays under cost constraints, we explore the design, efficiency and topology of noise-canceling networks. We find that when the input fluctuations become more correlated in space or time, optimal network architectures become sparser and more hierarchically organized, resembling the vasculature in plants or animals. Our results provide concrete guiding principles for designing more robust and efficient power grids and sensor networks.