Optimal noise-canceling networks

TL;DR

This paper investigates how to design network architectures that efficiently filter noise, revealing that increased input correlation leads to sparser, hierarchical structures, with implications for power grids and sensor networks.

Contribution

It provides an analytical and numerical framework for understanding optimal noise-canceling network topologies under cost constraints.

Findings

Optimal networks become sparser with more correlated noise.

Hierarchical organization emerges in optimal network structures.

Guidelines for designing robust power and sensor networks.

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 of question 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.