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An attractor-based complexity measurement for Boolean recurrent neural networks.

Jérémie Cabessa1, Alessandro E P Villa2

  • 1Neuroheuristic Research Group, Faculty of Business and Economics, University of Lausanne, Lausanne, Switzerland; Laboratory of Mathematical Economics (LEMMA), University of Paris 2 - Panthéon-Assas, Paris, France.

Plos One
|April 15, 2014
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Summary
This summary is machine-generated.

We introduce a new complexity measure for Boolean recurrent neural networks (BRNNs) based on attractor dynamics. This method assesses computational power by classifying BRNNs, offering insights into neural network capabilities and brain circuit complexity.

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Area of Science:

  • Computational Neuroscience
  • Theoretical Computer Science
  • Dynamical Systems

Background:

  • Boolean recurrent neural networks (BRNNs) are models of neural computation.
  • Assessing the computational power and complexity of BRNNs remains a challenge.
  • Attractor dynamics play a crucial role in the function of recurrent neural networks.

Purpose of the Study:

  • To develop a novel, refined complexity measurement for BRNNs.
  • To link the computational power of BRNNs to their attractor dynamics.
  • To provide a hierarchical classification of BRNNs based on complexity.

Main Methods:

  • Proving computational equivalence between BRNNs and a specific class of ω-automata.
  • Translating the refined classification of ω-automata to the context of BRNNs.
  • Applying the complexity measurement to a simplified basal ganglia-thalamocortical network model.

Main Results:

  • A novel, refined attractor-based complexity measurement for BRNNs was established.
  • A hierarchical classification of BRNNs based on their attractor dynamics was obtained.
  • The complexity measurement provides new theoretical insights into neural network computational and dynamical capabilities.

Conclusions:

  • The developed complexity measure offers a new way to understand the computational power of BRNNs.
  • The findings contribute to understanding the complexity of real brain circuits, exemplified by the basal ganglia-thalamocortical network model.
  • This work bridges theoretical computer science concepts with neural network dynamics.