Wave Propagation Phenomena in Nonlinear Hierarchical Neural Networks with Predictive Coding Feedback Dynamics.

Area of Science:

• Computational Neuroscience
• Theoretical Neuroscience
• Mathematical Biology

Background:

• Predictive coding theories propose hierarchical neural processing where higher areas predict lower area activity.
• Understanding signal propagation dynamics in these networks is crucial for explaining perception and cognition.

Purpose of the Study:

• To develop a mathematical framework for analyzing propagation in nonlinear neural networks based on predictive coding.
• To determine conditions for upward, downward, and failed signal propagation.
• To investigate the influence of external input on network behavior and identify critical thresholds.

Main Methods:

• Mathematical modeling of continuous-time nonlinear neural networks with hierarchical processing areas.
• Analysis of propagation dynamics in bi-infinite and semi-infinite network idealizations.
• Numerical simulations of network long-time behavior under different external input conditions.

Main Results:

• Precise conditions for upward, downward, and propagation failure were determined.
• Numerical evidence of input amplitude thresholds for full network propagation was found.
• Parameter regions potentially associated with dysfunctional perceptions were identified.

Conclusions:

• The developed framework aligns with predictive coding principles.
• Input amplitude thresholds critically determine signal propagation in these neural networks.
• The study provides insights into potential neural mechanisms underlying perceptual dysfunction.