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Pattern Capacity of a Perceptron for Sparse Discrimination Vladimir Itskov and L. F. Abbott
 

Summary: Pattern Capacity of a Perceptron for Sparse Discrimination
Vladimir Itskov and L. F. Abbott
Department of Neuroscience, Department of Physiology and Cellular Biophysics, Columbia University Medical Center,
New York, New York 10032-2695, USA
(Received 20 January 2008; published 30 June 2008)
We evaluate the capacity and performance of a perceptron discriminator operating in a highly sparse
regime where classic perceptron results do not apply. The perceptron is constructed to respond to a
specified set of q stimuli, with only statistical information provided about other stimuli to which it is not
supposed to respond. We compute the probability of both false-positive and false-negative errors and
determine the capacity of the system for not responding to nonselected stimuli and for responding to
selected stimuli in the presence of noise. If q is a sublinear function of N, the number of inputs to the
perceptron, these capacities are exponential in N=q.
DOI: 10.1103/PhysRevLett.101.018101 PACS numbers: 87.19.ll, 87.18.Sn
Sparse coding is a useful and widespread strategy for
representing complex data [1]. Biological systems often
generate a high-dimensional representation of sensory data
at the initial receptor level but modify this to a sparse
representation at later processing stages. For example, in
the olfactory system of insects, Kenyon cells show odorant
selectivity to a much higher degree than do the projection

  

Source: Abbott, Laurence - Center for Neurobiology and Behavior & Department of Physiology and Cellular Biophysics, Columbia University

 

Collections: Biology and Medicine