Information propagation in Gaussian processes on multilayer networks

TL;DR

This paper analyzes how the structure of multilayer networks influences the propagation of Gaussian process information across different timescales, revealing fundamental principles of interlayer interactions and their effects on system stability.

Contribution

It provides an analytical framework for understanding information flow in Gaussian processes on multilayer networks, extending previous discrete process results to continuous stochastic systems.

Findings

Interactions from fast to slow layers do not generate information.

Interactions from slow to fast layers create mutual information.

Identifies critical layers influencing information near stability edges.

Abstract

Complex systems with multiple processes evolving on different temporal scales are naturally described by multilayer networks, where each layer represents a different timescale. In this work, we show how the multilayer structure shapes the generation and propagation of information between layers. We derive a general decomposition of the multilayer probability for continuous stochastic processes described by Fokker-Planck operators. In particular, we focus on Gaussian processes, for which this solution can be obtained analytically. By explicitly computing the mutual information between the layers, we derive the fundamental principles that govern how information is propagated by the topology of the multilayer network. In particular, we unravel how edges between nodes in different layers affect their functional couplings. We find that interactions from fast to slow layers alone do not generate information, leaving the layers statistically independent even if they affect their dynamical evolution. On the other hand, interactions from slow to fast nodes lead to non-zero mutual information, which can then be propagated along specific paths of interactions between layers. We employ our results to study the interplay between information and instability, identifying the critical layers that drive information when pushed to the edge of stability. Our work generalizes previous results obtained in the context of discrete stochastic processes, allowing us to understand how the multilayer nature of complex systems affects their functional structure.