Abstract
In usual spiking neural networks, the real world information is interpreted as spike time. A spiking neuron of the spiking neural network receives input vector of spike times, and activates a state function x(t) by increasing the time t until the value of x(t) reaches certain threshold value at a firing time t a. And t a is the output of the spiking neuron. In this paper we propose, and investigate the performance of, a modified spiking neuron, of which the output is a linear combination of the firing time t a and the derivative x′(t a). The merit of the modified spiking neuron is shown by numerical experiments for solving some benchmark problems: The computational time of a modified spiking neuron is a little greater than that of a usual spiking neuron, but the accuracy of a modified spiking neuron is almost as good as a usual spiking neural network with a hidden layer.
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References
Maass W (1997) Networks of spiking neurons: the thid generation of neural network. Neural Netw 10: 1659–1671
Funahashi K, Nakamura Y (1993) Approximation of dynamical systems by continuous time recurrent neural networks. Neural Network 6: 801–806
Maass W, Bishop CM (1999) Pulsed neural networks, MIT Press, Cambridge.
González-Nalda P, Cases B (2008) Topos: spiking neural networks for temporal pattern recognition in complex real sounds. Neurocomputing 71: 721–732
Wysoski SG, Benuscova L, Kasabov N (2008) Fast and adaptive network of spiking neurons for multi-view visual pattern recongnition. Neurocomputing 71: 2563–2575
Natschlager T, Berthold R (1999) Pattern analysis with spiking neurons using delay coding. Neurocomputing 26(27): 463–469
Wysoski SG, Benuskova L, Kasabov N (2010) Evolving spiking neural networks for audiovisual information processing. Neural Netw 23: 819–835
Ghosh-Dastidar S, Adeli H (2007) Improved spiking neural networks for EEG classification and epilepsy and seizure detection. Integr Comput Aided Eng 14: 187–212
Ghosh-Dastidar S, Adeli H (2009) A new supervised learning algorithm for multiple spiking neural networks with application in epilepsy and seizure detection. Neural Netw 22: 1419–1431
Hodgkin AL, Huxley AF (1952) A quantitative description of ion currents and its applications to conduction and excitation in nerve membranes. J Physiol 117: 500–544
Stein RB (1965) A theoretical analysis of neuronal variability. Biophys J 5: 173–194
Izhikevich EM (2003) Simple model of spiking neurons. IEEE Transac Neural Netw 14: 1569–1572
Izhikevich EM (2004) Which model to use for cortical spiking neurons?. IEEE Transac Neural Netw 15: 1063–1070
Gerstner W (1995) Time structure of the activity of neural network models. Phys Rev 51: 738–758
Kistler WM, Gerstner W, van Hemmen JL (1997) Reduction of Hodgkin–Huxley equations to a singlevariable threshold model. Neural Comput 9: 1015–1045
Wu OX, McGinnity TM et al (2006) Learning under weight constraints in networks of temproral encoding spiking neurons. Neurocomputing 69: 1912–1922
Bohte SM, Kok JN, La Poutré H (2002) Error-backpropagation in temporally encoded networks of spiking neurons. Neurocomputing 48: 17–37
Yang J, Yang W, Wu W (2012) A remark on the error-backpropagation learning algorithm for spiking neural networks. Appl Math Lett 25: 1118–1120
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Yang, W., Yang, J. & Wu, W. A Modified Spiking Neuron that Involves Derivative of the State Function at Firing Time. Neural Process Lett 36, 135–144 (2012). https://doi.org/10.1007/s11063-012-9226-0
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DOI: https://doi.org/10.1007/s11063-012-9226-0