 
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 100322695, 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 falsepositive and falsenegative 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 highdimensional 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
