According to the diffusion approximation and usual approximation scheme, we present two more biologically plausible so called second order spiking perceptron (SOSP) and extended second order spiking perceptron (ESOSP) based on the integrate-and-fire model with renewal process inputs, which employ both first and second statistical representation, i.e., the means, variances and correlations of the synaptic input. We show through various examples that such perceptrons, even a single neuron, are able to perform various complex non-linear tasks like the XOR problem, which is impossible to be solved by traditional single-layer perceptrons. Here our perceptrons offer a significant advantage over classical models, in that they include the second order statistics in computations, specially in that the ESOSP considers the learning of variance in the training. Our ultimate purpose is to open up the possibility of carrying out a stochastic computation in neuronal networks.
KeywordsIntegrate-and-fire Renewal process input Second order statistics Non-linear discrimination
The authors would like to thank the any anonymous referees for their useful comments and suggestions. This work was partially supported by National Natural Science Foundation of China (10571051) and Scientific Research Fund of Hunan Provincial Education Department (08C588).
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