Document Detail


What can a neuron learn with spike-timing-dependent plasticity?
MedLine Citation:
PMID:  16156932     Owner:  NLM     Status:  MEDLINE    
Abstract/OtherAbstract:
Spiking neurons are very flexible computational modules, which can implement with different values of their adjustable synaptic parameters an enormous variety of different transformations F from input spike trains to output spike trains. We examine in this letter the question to what extent a spiking neuron with biologically realistic models for dynamic synapses can be taught via spike-timing-dependent plasticity (STDP) to implement a given transformation F. We consider a supervised learning paradigm where during training, the output of the neuron is clamped to the target signal (teacher forcing). The well-known perceptron convergence theorem asserts the convergence of a simple supervised learning algorithm for drastically simplified neuron models (McCulloch-Pitts neurons). We show that in contrast to the perceptron convergence theorem, no theoretical guarantee can be given for the convergence of STDP with teacher forcing that holds for arbitrary input spike patterns. On the other hand, we prove that average case versions of the perceptron convergence theorem hold for STDP in the case of uncorrelated and correlated Poisson input spike trains and simple models for spiking neurons. For a wide class of cross-correlation functions of the input spike trains, the resulting necessary and sufficient condition can be formulated in terms of linear separability, analogously as the well-known condition of learnability by perceptrons. However, the linear separability criterion has to be applied here to the columns of the correlation matrix of the Poisson input. We demonstrate through extensive computer simulations that the theoretically predicted convergence of STDP with teacher forcing also holds for more realistic models for neurons, dynamic synapses, and more general input distributions. In addition, we show through computer simulations that these positive learning results hold not only for the common interpretation of STDP, where STDP changes the weights of synapses, but also for a more realistic interpretation suggested by experimental data where STDP modulates the initial release probability of dynamic synapses.
Authors:
Robert Legenstein; Christian Naeger; Wolfgang Maass
Publication Detail:
Type:  Comparative Study; Journal Article; Research Support, Non-U.S. Gov't    
Journal Detail:
Title:  Neural computation     Volume:  17     ISSN:  0899-7667     ISO Abbreviation:  Neural Comput     Publication Date:  2005 Nov 
Date Detail:
Created Date:  2005-09-13     Completed Date:  2005-11-21     Revised Date:  2006-11-15    
Medline Journal Info:
Nlm Unique ID:  9426182     Medline TA:  Neural Comput     Country:  United States    
Other Details:
Languages:  eng     Pagination:  2337-82     Citation Subset:  IM    
Affiliation:
Institute for Theoretical Computer Science, Technische Universitaet Graz, A-8010 Graz, Austria. legi@igi.tugraz.at
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MeSH Terms
Descriptor/Qualifier:
Action Potentials / physiology*
Animals
Learning / physiology*
Models, Neurological
Neuronal Plasticity / physiology*
Neurons / physiology*
Nonlinear Dynamics
Synapses / physiology*
Synaptic Transmission / physiology
Time Factors

From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine


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