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Moment neural network and an efficient numerical method for modeling irregular spiking activity.

Yang Qi1

  • 1Institute of Science and Technology for Brain-Inspired Intelligence, <a href="https://ror.org/013q1eq08">Fudan University</a>, Shanghai 200433, China; Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence (<a href="https://ror.org/013q1eq08">Fudan University</a>), Ministry of Education, Shanghai 200433, China; and MOE Frontiers Center for Brain Science, <a href="https://ror.org/013q1eq08">Fudan University</a>, Shanghai 200433, China.

Physical Review. E
|September 19, 2024
PubMed
Summary

This study introduces the moment neural network, a novel framework that models irregular neural spiking activity by extending firing rate models to capture second-order moments. This approach accurately models neural firing statistics and network dynamics.

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Area of Science:

  • Computational Neuroscience
  • Neural Network Modeling
  • Systems Neuroscience

Background:

  • Cortical circuits are often modeled using continuous rate-based neural networks.
  • However, these models fail to capture the irregular spiking activity and complex correlations of biological neurons, which are crucial for brain function.

Purpose of the Study:

  • To develop a computational framework that accurately models irregular spiking activity in neural networks.
  • To generalize existing rate models to incorporate higher-order statistical moments of neuronal firing.

Main Methods:

  • Introduction of the moment neural network framework, extending rate models to second-order moments.
  • Development of an efficient numerical method for evaluating moment mappings without solving the Fokker-Planck equation.
  • Simulation of large-scale neural circuits incorporating mean firing rate and firing variability.

Main Results:

  • The moment neural network accurately captures the firing statistics of spiking neural networks.
  • The framework allows for efficient simulation of coupled dynamics of firing rate and variability in large networks.
  • Demonstrated ability to explain diverse Fano factors in networks with quenched disorder and irregular oscillatory dynamics in excitation-inhibition networks.

Conclusions:

  • The moment neural network provides a powerful and analytically tractable method for modeling complex neural dynamics.
  • This framework bridges the gap between simplified rate models and the detailed statistics of spiking neural networks.
  • Offers new insights into phenomena like neural variability and network oscillations.