Abstract
This paper proposes an extension to the model of a spiking neuron for information processing in artificial neural networks, developing a new approach for the dynamic threshold of the integrate-and-fire neuron. This new approach invokes characteristics of biological neurons such as the behavior of chemical synapses and the receptor field. We demonstrate how such a digital model of spiking neurons can solve complex nonlinear classification with a single neuron, performing experiments for the classical XOR problem. Compared with rate-coded networks and the classical integrate-and-fire model, the trained network demonstrated faster information processing, requiring fewer neurons and shorter learning periods. The extended model validates all the logic functions of biological neurons when such functions are necessary for the proper flow of binary codes through a neural network.
Similar content being viewed by others
References
Bohte SM, Kok JN, La Poutr (2002) Spike-prop: error-backprogation in multi-layer networks of spiking neurons. In: Proceedings of the European symposium on artificial neural networks ESANN’2000 1:419–425
Bower J, Beeman D (1995) The book of genesis. Springer, New York
Haykin S (1999) Neural network: a comprehensive foundation. Prentice-Hall, New Jersey
Hodgkin AL, Huxley AF (1952) A quantitative description of ion currents and its application to conduction and excitation in nerve membranes. J Physiol 117:500–544
Izhikevich EM (2001) Resonate-and-fire neurons. J Neural Networks 14:883–894
Izhikevich EM (2004) Which model to use for cortical spiking neurons? IEEE Trans Neural Netw 5:1063–1070
Jolivet R, Rauch A, Lüscher HR, Gerstner W (2006) Integrate-and-fire models with adaptation are good enough: predicting spike times under random current injection. In: Advances in neural information processing systems 18, MIT, Cambridge, pp 595–602
Keener J, Sneyed J (2001) Mathematical physiology. Spinger, New York
Koch C, Segev I (1989) Methods in neuronal modeling. MIT Press, Cambridge
Latham P, Richmond B, Nelson P, Nirenberg S (2000) Intrinsic dynamics in neuronal networks. I Theory J Neurophysiol 83:808–827
Maass W (1997a) Noisy spiking neurons with temporal coding have more computational power than sigmoidal neurons. Adv Neural Inform Process Syst 9:211–217
Maass W (1997b) Network of spiking neurons: third generation of neural networks. IEEE Trans Neural Netw 10:1659–1671
Maass W, Bishop MC (2001) Pulsed neural networks. MIT, England
Maass W, Schnitger G, Sontag E (1991) On the computational power of sigmoid versus boolean threshold circuits. In: Proceedings of 32nd annual symposium on foundations of computer science, pp. 767–776
McCulloch WS, Pitts W (1943) A logical calculus of the ideas immanent in nervous activity. Bull Math Biophys Soc 5:115–133
Mehrtash N, Jung D, Hellmich HH, Schoenauer T, Lu VT, Klar H (2003) Synaptic plasticity in spiking neural networks. IEEE Trans Neural Netw 14:980–992
Minsky ML, Papert SA (1969) Perceptrons. MIT Press, Cambridge
Moore SM (2002) Back-propagation in spiking neural networks. Master’s Thesis, University of Bath. Available on line: http://www.simonchristianmoore.co.uk/back.htm
Remos O, Bard E (2001) Two dimensional synaptically generated traveling waves in a theta-neuron neural netwrok. Neurocomputing 38-40:789–795
Schrauwen B, Campenhout JV (2004) Extending SpikeProp. In: Proceedings of 2004 IEEE international joint conference on neural networks 1:471–475
Smith GD, Cox CL, Sherman SM, Rinzel J (2001) Fourier analysis of sinusoidally driven thalamocortical relay neurons and a minimal integrate-and-fire-or-burst model. J Neurophysiol 83:588–610
Smith LS, Hamilton A (1998) Neuromorphics systems: engineering silicon from neurobiology. World Scientific, Singapore
Trappenberg TP (2002) Fundamentals of computation neuroscience. Oxford University Press, New York
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Guerreiro, A.M.G., Paz de Araujo, C.A. An extended model for a spiking neuron class. Biol Cybern 97, 211–219 (2007). https://doi.org/10.1007/s00422-007-0169-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00422-007-0169-x