Second order spiking perceptrons

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.

[1]  Jianfeng Feng,et al.  Responses of Magnocellular Neurons to Osmotic Stimulation Involves Coactivation of Excitatory and Inhibitory Input: An Experimental and Theoretical Analysis , 2001, The Journal of Neuroscience.

[2]  Henry C. Tuckwell,et al.  Introduction to theoretical neurobiology , 1988 .

[3]  Sander M. Bohte,et al.  Error-backpropagation in temporally encoded networks of spiking neurons , 2000, Neurocomputing.

[4]  Jianfeng Feng,et al.  Impact of Poisson synaptic inputs with a changing rate on weak-signal processing , 2003 .

[5]  T. Sejnowski,et al.  Correlated neuronal activity and the flow of neural information , 2001, Nature Reviews Neuroscience.

[6]  Jianfeng Feng,et al.  Dynamics of moment neuronal networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Adrienne L. Fairhall,et al.  Efficiency and ambiguity in an adaptive neural code , 2001, Nature.

[8]  L. Abbott,et al.  Synaptic Depression and Cortical Gain Control , 1997, Science.

[9]  V.P. Plagianakos,et al.  Spiking neural network training using evolutionary algorithms , 2005, Proceedings. 2005 IEEE International Joint Conference on Neural Networks, 2005..

[10]  Jianfeng Feng,et al.  Optimal control of neuronal activity. , 2003, Physical review letters.

[11]  Jianfeng Feng,et al.  Computational neuroscience , 1986, Behavioral and Brain Sciences.

[12]  Nicolas Brunel,et al.  Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons , 2000, Journal of Computational Neuroscience.

[13]  Jianfeng Feng,et al.  Impact of Correlated Inputs on the Output of the Integrate-and-Fire Model , 2000, Neural Computation.

[14]  P. Matthews Relationship of firing intervals of human motor units to the trajectory of post‐spike after‐hyperpolarization and synaptic noise. , 1996, The Journal of physiology.

[15]  Wulfram Gerstner,et al.  Spiking Neuron Models , 2002 .

[16]  H. Sompolinsky,et al.  Population coding in neuronal systems with correlated noise. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.