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Low-dimensional dynamics of structured random networks.

Johnatan Aljadeff1,2, David Renfrew3, Marina Vegué4,5

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Summary
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This study links random recurrent neural network structure to low-dimensional dynamics using a mean-field approach. Chaotic network states emerge at a critical point, revealing structure-function relationships.

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Area of Science:

  • Computational Neuroscience
  • Statistical Physics
  • Network Science

Background:

  • Recurrent neural networks (RNNs) are crucial for modeling complex systems.
  • Understanding the relationship between network structure and dynamics is a key challenge.
  • Mean-field approaches offer insights into large-scale network behavior.

Purpose of the Study:

  • To investigate the connection between network connectivity structure and low-dimensional dynamics in generalized random RNNs.
  • To extend existing mean-field methods for analyzing network properties.
  • To establish a direct link between network structure and functional characteristics.

Main Methods:

  • Utilized a generalized random recurrent neural network model.
  • Extended a previously developed mean-field approach.
  • Analyzed the phase transition from silent to chaotic states based on connection properties.
  • Derived a critical point as a function of the connectivity variance function g.

Main Results:

  • Identified a phase transition in random RNNs from a silent to a chaotic state.
  • Derived the critical point governing this transition as a function of the connectivity variance function g.
  • Demonstrated that above the critical point, chaotic unit activations exhibit low-dimensional autocorrelation functions.
  • Established a direct link between network structure and functional dynamics.

Conclusions:

  • The study provides a theoretical framework linking network connectivity to emergent dynamics in random RNNs.
  • The findings offer insights into how network structure dictates functional properties like autocorrelation.
  • Applications in neuroscience (connectivity matrices) and ecology (food web stability) are discussed.