Abstract
In the error-backpropagation learning algorithm for spiking neural networks, solving the differentiation of the firing time \(t^\alpha \) with respect to the weight \(w\) is essential. Bohte et al. see the firing time \(t^\alpha \) as a functional of the state variable x(t). But the differentiation of the firing time \(t^\alpha \) with respect to the state variable x(t) is impossible to perform directly. To overcome this problem, Bohte et al. assume that the state variable x(t) is a linear function of the time \(t\) around \(t=t^\alpha \). Then, it seems that the solution of Bohte et al. is used by all related Literatures. In particular, Ghosh-Dastidar and Adeli offer another explanation. In this paper, we consider the firing time \(t^\alpha \) as a function of the time \(t\) and the weight \(w\) and prove that the key formula for multiple spiking neural networks is in fact mathematically correct through the implicit function theorem.
Research funded by the Fundamental Research Funds for the Central Universities (2662013BQ049, 2662014QC011).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Maass, W.: Networks of spiking neurons: the third generation of neural network. Neural Networks 10, 1659–1671 (1997)
Voutsas, K., Adamy, J.: A biologically inspired spiking neural network for sound source lateralization. IEEE Trans. Neural Netw. 18(6), 1785–1799 (2007)
Wysoski, S.G., Benuscova, L., Kasabov, N.: Fast and adaptive network of spiking neurons for multi-view visual pattern recongnition. Neurocomputing 71, 2563–2575 (2008)
Ghosh-Dastidar, S., Adeli, H.: A new supervised learning algorithm for multiple spiking neural networks with application in epilepsy and seizure detection. Neural Networks 22, 1419–1431 (2009)
Liu, J., Perez-Gonzalez, D., Rees, A., Erwin, H., Wermter, S.: A biologically inspired spiking neural network model of the auditory midbrain for sound source localisation. Neurocomputing 74(1–3), 129–139 (2010)
Wysoski, S.G., Benuskova, L., Kasabov, N.: Evolving spiking neural networks for audiovisual information processing. Neural Networks 23, 819–835 (2010)
Wade, J., McDaid, L., Santos, J., Sayers, H.: SWAT: A spiking neural network training algorithm for classification problems. IEEE Trans. Neural Netw. 21(11), 1817–1830 (2010)
Wall, J.A., McDaid, L.J., Maguire, L.P., McGinnity, T.M.: Spiking neural network model of sound localization using the interaural intensity difference. IEEE Transactions on Neural Network and Learning System 23(4), 574–586 (2012)
Bohte, S.M., Kok, J.N., La Poutre, J.A.: Error-backpropagation in temporally encoded networks of spiking neurons. Neurocomputing 48(1–4), 17–37 (2002)
Ghosh-Dastidar, S., Adeli, H.: Improved spiking neural networks for EEG classification and epilepsy and seizure detection. Integrated Computer-Aided Engineering 14, 187–212 (2007)
Booij, O., Nguyen, H.T.: A gradient descent rule for spiking neurons emitting multiple spikes. Inf. Process. Lett. 95(6), 552–558 (2005)
McKennoch, S., Liu, D., Bushnell, L.G.: Fast modifications of the SpikeProp algorithm. In: Proceedings of the International Joint Conference on Neural Networks, pp. 3970–3977 (2006)
Wu, Q.X., McGinnity, T.M., Maguire, L.P., Glackin, B., Belatreche, A.: Learning under weight constraints in networks of temporal encoding spiking neurons. Neurocomputing 69, 1912–1922 (2006)
Xu, Y., Zeng, X.Q., Han, L.X., Yang, J.: A supervised multi-spike learning algorithm based on gradient descent for spiking neural networks. Neural Networks 43, 99–113 (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Yang, W., Yang, D., Fan, Y. (2014). A Proof of a Key Formula in the Error-Backpropagation Learning Algorithm for Multiple Spiking Neural Networks. In: Zeng, Z., Li, Y., King, I. (eds) Advances in Neural Networks – ISNN 2014. ISNN 2014. Lecture Notes in Computer Science(), vol 8866. Springer, Cham. https://doi.org/10.1007/978-3-319-12436-0_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-12436-0_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-12435-3
Online ISBN: 978-3-319-12436-0
eBook Packages: Computer ScienceComputer Science (R0)