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Weight statistics controls dynamics in recurrent neural networks.

Patrick Krauss1,2, Marc Schuster2, Verena Dietrich2

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Network balance of excitatory and inhibitory connections is key to recurrent neural network dynamics. Fine-tuning this balance to the

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Area of Science:

  • Computational neuroscience
  • Complex systems

Background:

  • Recurrent neural networks (RNNs) exhibit complex dynamics, with properties determined by microscopic connection strengths.
  • The influence of coarse-grained statistical features of weight matrices on RNN dynamics remains underexplored.

Purpose of the Study:

  • Investigate how statistical parameters of weight matrices affect RNN dynamics.
  • Determine the role of density, balance, and symmetry in RNN network behavior.

Main Methods:

  • Simulated recurrent networks of Boltzmann neurons.
  • Computed a 'phase diagram' of network dynamics.
  • Analyzed the impact of connection density, excitatory-inhibitory balance, and weight symmetry.

Main Results:

  • Network balance emerged as the critical control parameter for dynamics.
  • Increasing balance shifted dynamics from oscillations to chaos, then to fixed points.
  • Rich, regular dynamics conducive to information processing were observed at the edge of chaos.

Conclusions:

  • The balance of excitatory and inhibitory connections is essential for controlling RNN dynamics.
  • Neural networks may operate at the 'edge of chaos' for optimal information processing.
  • Biological neural networks might be fine-tuned for balance, similar to findings in this study.