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Graph degree sequence solely determines the expected hopfield network pattern stability.

Daniel Berend1, Shlomi Dolev, Ariel Hanemann

  • 1Department of Computer Science and Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, 84105 Israel berend@cs.bgu.ac.il.

Neural Computation
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Summary
This summary is machine-generated.

The network topology does not affect Hopfield neural network pattern stability. Instability depends only on the graph's degree sequence, not its specific structure.

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Area of Science:

  • Computational neuroscience
  • Network science
  • Graph theory

Background:

  • The Hopfield neural network is a recurrent neural network model known for its associative memory capabilities.
  • Pattern stability in neural networks is crucial for reliable information storage and retrieval.
  • Understanding the influence of network topology on system dynamics is a key challenge in complex systems research.

Purpose of the Study:

  • To investigate how different network topologies impact the pattern stability of Hopfield neural networks.
  • To quantify the relationship between graph properties and the occurrence of instability points.
  • To determine if network topology or other graph characteristics are the primary drivers of instability.

Main Methods:

  • Analysis of Hopfield neural network dynamics on general graphs.
  • Random selection of patterns from a uniform distribution.
  • Definition and measurement of instability points based on error propagation within the network.
  • Calculation of the expected total number of instability points across all patterns.

Main Results:

  • The study found that the instability of the Hopfield network is independent of the specific network topology.
  • Instability is solely determined by the degree sequence of the underlying graph.
  • A mathematical approximation for instability in large networks was derived, involving node degrees and a standard normal distribution function.

Conclusions:

  • The findings reveal a fundamental property of Hopfield networks: pattern stability is robust to topological variations.
  • The degree sequence of a graph is the critical factor governing the network's susceptibility to pattern instability.
  • The derived approximation offers a predictive tool for assessing instability in large-scale Hopfield networks.