Mathematical Derivation of Wave Propagation Properties in Hierarchical Neural Networks with Predictive Coding...

Area of Science:

• Neuroscience
• Computational Neuroscience
• Systems Neuroscience

Background:

• Sensory perception involves hierarchical cortical processing with bidirectional neural activity.
• Neural signals manifest as forward and backward traveling waves, often with oscillatory patterns.
• The functional relationship between these activity patterns and perceptual system properties remains unclear.

Purpose of the Study:

• To develop a mathematical framework for investigating neural dynamics in hierarchical perceptual systems.
• To link system stability and neural signal propagation characteristics to predictive coding models.
• To explore how different neural assemblies exhibit independent dynamic properties.

Main Methods:

• Utilizing a mathematical framework inspired by predictive coding neural network models.
• Systematically analyzing hyper-parameters governing bottom-up, top-down, and error correction signals.
• Deriving continuous-limit versions of the system in time and neural space.
• Investigating the impact of transmission delays and analyzing emergent oscillations.

Main Results:

• System stability can be derived from hyper-parameter values controlling different neural signals.
• The direction and speed of neural activity propagation are determinable within the framework.
• Distinct neural assemblies can independently exhibit varied stability, propagation speed, and direction.
• Transmission delays can lead to the emergence of oscillations.

Conclusions:

• The developed mathematical framework provides insights into the functional properties of hierarchical perceptual systems.
• Predictive coding principles offer a basis for understanding neural signal propagation and system stability.
• The framework allows for the characterization of diverse dynamic behaviors within neural assemblies.