Volume 12 Supplement 1

Twentieth Annual Computational Neuroscience Meeting: CNS*2011

Open Access

Plasticity and stability in recurrent neural networks

  • Friedemann Zenke1Email author,
  • Guillaume Hennequin1,
  • Henning Sprekeler1,
  • Tim P Vogels1 and
  • Wulfram Gerstner1
BMC Neuroscience201112(Suppl 1):P120

DOI: 10.1186/1471-2202-12-S1-P120

Published: 18 July 2011

Over the past 30 years, Bienenstock-Cooper-Munro (BCM) [1] type learning rules have shaped our understanding of synaptic plasticity. While they excel at explaining the emergence of receptive fields and stimulus selectivity in networks with feed-forward architecture, their impact on recurrent scenarios is less distinctive.

Here, we analyze general BCM-type synaptic plasticity rules with a homeostatic sliding threshold in the framework of recurrent networks of rate-based and spiking neurons. We begin by considering the effects of learning rate and homeostatic timescales on network stability in a non-linear firing rate model. We show how a sensible choice of timescales leads to stable weight dynamics, but other seemingly sensible parameter choices will inevitably lead to catastrophic run-away potentiation. We discuss under which conditions a stable fixed-point in a regime of Hebbian learning exists.

We then study the network's response to perturbations and quantify the critical point whereupon network stability is compromised. By viewing perturbation as a consequence of pattern storage in synaptic connections, we quantify the number of such patterns that can be learned safely in a given time.

Our model could provide simple explanations as to why memory intake capacity is limited and why learning becomes increasingly inefficient during intensive learning periods. We confirm these findings in numerical simulations of spiking neural networks and show that our analytical results apply to synapses subject to additive triplet-STDP [2].

Authors’ Affiliations

(1)
School of Computer & Communication Sciences and Brain-Mind Institute, École Polytechnique Fédérale de Lausanne

References

  1. Bienenstock E, Cooper L, Munro P: Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex. Journal of Neuroscience. 1982, 2 (1): 32-48.PubMedGoogle Scholar
  2. Pfister J-P, Gerstner W: Triplets of spikes in a model of spike timing-dependent plasticity. Journal of Neuroscience. 2006, 26 (38): 9673-82. 10.1523/JNEUROSCI.1425-06.2006.View ArticlePubMedGoogle Scholar

Copyright

© Zenke et al; licensee BioMed Central Ltd. 2011

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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