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Abstract

Natural and artificial networks, from the cerebral cortex to large-scale power grids, 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 here analytically and numerically the design, efficiency,
and topology of noise-canceling networks. Specifically, 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. More broadly, our results provide concrete
guiding principles for designing more robust and efficient power grids and sensor networks.