Soft Computing

, Volume 13, Issue 12, pp 1219–1230 | Cite as

Second order spiking perceptrons

  • Xuyan Xiang
  • Yingchun Deng
  • Xiangqun Yang


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.


Integrate-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).


  1. Abbott LF, Varela JA, Sen K et al (1997) Synaptic depression and cortical gain control. Science 275:220–223CrossRefGoogle Scholar
  2. Bohte SM, Kok Joost NJN, La Poutre Han H (2002) Errorbackpropagation in temporally encoded networks of spiking neurons. Neurocomputing 48(1–4):17–37zbMATHCrossRefGoogle Scholar
  3. Brunel N (2000) Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J Comput Neurosci 8:183–208zbMATHCrossRefGoogle Scholar
  4. Fairhall AL, Lewen GD, Bialek W et al (2002) Efficiency and ambiguity in an adaptive neural code. Nature 412:787–792CrossRefGoogle Scholar
  5. Feng JF (2003) Computational neuroscience—a comprehensive approach. CRC Press, Chapman-HallGoogle Scholar
  6. Feng JF, Brown D (2000) Impact of correlated inputs on the output of the integrate-and-fire models. Neural Comput 12:671–692CrossRefGoogle Scholar
  7. Feng JF, Tuckwell HC (2003) Optimal control of neuronal activity. Phys Rev Lett 91:018101CrossRefGoogle Scholar
  8. Feng JF, Deng YC, Rossoni E (2006) Dynamics of moment neuronal networks. Phys Rev E 73:041906CrossRefMathSciNetGoogle Scholar
  9. Gerstner W, Kistler W (2003) Spiking neuron models. Cambridge University Press, CambridgeGoogle Scholar
  10. Leng G, Brown CH, Bull PM et al (2001) Responses of magnocellular neurons to osmotic stimulation involves coactivation of excitatory and inhibitory input: an experimental and theoretical analysis. J Neurosci 21:6967–6977Google Scholar
  11. Liu F, Feng JF, Wang W (2003) Impact of Poisson synaptic inputs with a changing rate on weak signal processing. Europhys Lett 64:131–136CrossRefMathSciNetGoogle Scholar
  12. Matthews PBC (1996) Relationship of firing intervals of human motor units to the trajectory of post-spike after-hyperpolarization and synaptic noise. J Physiol 492:596–628Google Scholar
  13. Pavlidis NG, Tasoulis DK, Plagianakos VP et al (2005) Neural network training using evolutionary algorithms. In: Proceedings of international joint conference on neural networks (IJCNN’05)Google Scholar
  14. Salinas E, Sejnowski TJ (2001) Correlated neuronal activity and the flow of neural information. Nat Rev Neurosci 2:539–550CrossRefGoogle Scholar
  15. Sompolinsky H, Yoon H, Kang KJ et al (2001) Population coding in neuronal systems with correlated noise. Phys Rev E 64(5): 051904CrossRefGoogle Scholar
  16. Tuckwell HC (1988) Introduction to theoretical neurobiology. Cambridge University Press, CambridgeGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.College of Mathematics and Computing ScienceHunan University of Arts and ScienceChangdePeople’s Republic of China
  2. 2.College of Mathematics and Computer ScienceHunan Normal UniversityChangshaPeople’s Republic of China

Personalised recommendations