Abstract
On-line Backpropagation has become very popular and it has been the subject of in-depth theoretical analyses and massive experimentation. Yet, after almost three decades from its publication, it is still surprisingly the source of tough theoretical questions and of experimental results that are somewhat shrouded in mystery. Although seriously plagued by local minima, the batch-mode version of the algorithm is clearly posed as an optimization problem while, in spite of its effectiveness, in many real-world problems the on-line mode version has not been given a clean formulation, yet. Using variational arguments, in this paper, the on-line formulation is proposed as the minimization of a classic functional that is inspired by the principle of minimal action in analytic mechanics. The proposed approach clashes sharply with common interpretations of on-line learning as an approximation of batch-mode, and it suggests that processing data all at once might be just an artificial formulation of learning that is hopeless in difficult real-world problems.
This is a preview of subscription content, log in via an institution to check access.
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
Bottou, L., Bousquet, O.: The tradeoffs of large-scale learning. Advances in Neural Information Processing Systems 20, 161–168 (2008)
Bryson, A., Ho, Y.C.: Applied optimal control: optimization, estimation, and control. Blaisdell Publishing Company (1969)
Gnecco, G., Gori, M., Sanguineti, M.: Learning with boundary conditions. Neural computation 25(4), 1029–1106 (2013)
Gori, M., Maggini, M.: Optimal convergence of on-line backpropagation. IEEE Transactions on Neural Networks 7(1), 251–254 (1996)
Gori, M., Tesi, A.: On the problem of local minima in backpropagation. IEEE Transactions on Pattern Analysis and Machine Intelligence 14(1), 76–86 (1992)
Herrera, L., Nunez, L., Patino, A., Rago, H.: A variational principle and the classical and quantum mechanics of the damped harmonic oscillator. American Journal of Physics 53(3), 273 (1985)
Hornik, K.: Approximation capabilities of multilayer feedforward networks. Neural Networks 4(2), 251–257 (1991)
Rumelhart, D.E., Hintont, G.E., Williams, R.J.: Learning representations by back-propagating errors. Nature 323(6088), 533–536 (1986)
Werbos, P.J.: Prediction and analysis in the behavioral sciences. Tech. rep., Harvard University (1974)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Frandina, S., Gori, M., Lippi, M., Maggini, M., Melacci, S. (2013). Variational Foundations of Online Backpropagation. In: Mladenov, V., Koprinkova-Hristova, P., Palm, G., Villa, A.E.P., Appollini, B., Kasabov, N. (eds) Artificial Neural Networks and Machine Learning – ICANN 2013. ICANN 2013. Lecture Notes in Computer Science, vol 8131. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40728-4_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-40728-4_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40727-7
Online ISBN: 978-3-642-40728-4
eBook Packages: Computer ScienceComputer Science (R0)