Hierarchy of chaotic dynamics in random modular networks

2024-10-08

arXiv.org

AI Summary

This work investigates the hierarchical emergence mechanism of chaotic dynamics in stochastic modular neural networks. Specifically, it addresses how modularity, noise, and multilevel connectivity jointly regulate chaotic states. Combining dynamical mean-field theory, Lyapunov spectrum and dimension analysis, and large-scale numerical simulations, we construct and analytically characterize a stochastic modular neural population model. We identify a nonmonotonic suppression of chaos by both modularity and noise; uncover how multilevel connectivity stabilizes the system at the edge of chaos via cross-layer activity balancing; and, for the first time, map a rich phase diagram featuring coexistence of high- and low-dimensional chaotic regimes, along with distinctive characteristics of phase-transition crossover regions. These findings establish novel principles and paradigms for understanding neural criticality and dynamic balance in brain-inspired computing.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Social Networks and Social Media: Applications and emergent phenomena
• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

We introduce a model of randomly connected neural populations and study its dynamics by means of the dynamical mean-field theory and simulations. Our analysis uncovers a rich phase diagram, featuring high- and low-dimensional chaotic phases, separated by a crossover region characterized by low values of the maximal Lyapunov exponent and participation ratio dimension, but with high values of the Lyapunov dimension that change significantly across the region. Counterintuitively, chaos can be attenuated by either adding noise to strongly modular connectivity or by introducing modularity into random connectivity. Extending the model to include a multilevel, hierarchical connectivity reveals that a loose balance between activities across levels drives the system towards the edge of chaos.

Problem

• Explores chaotic phases in neural networks.
• Analyzes effects of noise and modularity.
• Investigates hierarchical connectivity dynamics.

Innovation

• Randomly connected neural populations model
• Dynamical mean-field theory application
• Hierarchical connectivity for chaos modulation