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Memory capacity for sequences in a recurrent network with biological constraints.

Christian Leibold1, Richard Kempter

  • 1Institute for Theoretical Biology, Humboldt-Universität zu Berlin, Germany. c.leibold@biologie.hu-berlin.de

Neural Computation
|February 24, 2006
PubMed
Summary

This study develops a theoretical framework to understand how neural networks store sequential memories, finding that memory capacity can scale with network size under specific conditions.

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Area of Science:

  • Computational neuroscience
  • Neural network modeling
  • Memory systems

Background:

  • The CA3 region of the hippocampus is crucial for storing and replaying behavioral event sequences.
  • Recurrent neural networks face challenges in pattern storage due to limited active neurons and plasticity resources.

Purpose of the Study:

  • To develop a theoretical framework for calculating the sequence storage capacity of sparsely connected neural networks.
  • To optimize network parameters like pattern size and firing threshold for maximal sequence storage.

Main Methods:

  • Analytical mean field approach
  • Stochastic dynamics
  • Simulations of time-discrete McCulloch-Pitts networks with binary synapses

Main Results:

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  • Optimal pattern size is inversely proportional to mean connectivity for one-step associations.
  • Maximum storage capacity (P) is independent of network size (N) when synapses per neuron are fixed.
  • Storage capacity scales linearly with network size when synapses scale as N^(3/2), indicating scalable sequential memory.
  • An optimal ratio of silent to nonsilent synapses maximizes storage capacity.
  • Capacity for long sequences is lower than for minimal sequences but follows similar principles.

Conclusions:

  • Sequential memory in neural networks is scalable under specific synaptic scaling rules.
  • The brain may trade off error tolerance for information content in encoding sequential memories, deviating from theoretical optimality.