Abstract
An important task in practical applications of neural networks is to design a network architecture. Network parameters are usually determined for a fixed architecture which requires us to solve a non-linear optimization problem in a multidimensional parameter space. An alternative approach is to use a dynamically allocated architecture and determine the final set of network parameters in a series of steps, each taking place in a lower dimensional space. There have been considered various types of such architecture dynamics in which network units or connections are either added or deleted. The simplest type is incremental architecture where in each step an architecture is extended by adding one new unit.
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References
A. R. Barron. Neural net approximation. In Proceedings of the 7th Yale Workshop on Adaptive and Learning Systems (pp. 69–72 ), 1992.
A. R. Barron. Universal approximation bounds for superposition of a sigmoidal function. IEEE Transactions on Information Theory 39, 930–945, 1993.
B. Beliczynski. An almost analytical design of incremental discrete functions approximation by one-hidden-layer neural networks. In Proceedings of WCNN’96 (pp. 988–991 ). Lawrence Erlbaum, San Diego, 1996.
R. Courant and D. Hilbert. Methods of Mathematical Physics. Wiley, New York, 1989.
C. Darken, M. Donahue, L. Gurvits, and E. Sontag. Rate of approximation results motivated by robust neural network learning. In Proceedings of the 6th Annual ACM Conference on Computational Learning Theory (pp. 303–309 ). ACM, New York, 1993.
R. Devore, R. Howard, and C. Micchelli. Optimal nonlinear approximation. Manuscripta Mathematica 63, 469–478, 1989.
S. E. Fahlman and C. Lebiere. The cascade correlation learning architecture. Technical Report CMU-CS-90–100, 1991.
A. Friedman. Foundations of Modern Analysis. Dover, New York, 1982.
B. Fritzke. Fast learning with incremental RBF networks. Neural Processing Letters 1, 2–5, 1994.
F. Girosi. Approximation error bounds that use VC-bounds. In Proceedings of ICANN’95 (pp. 295–302). EC2 & Cie, Paris, 1995.
K. Hlavâckovâ, V. Knrkovâ, and P. Savickÿ. Representations and rates of approximation of real-valued Boolean functions by neural networks (manuscript).
Y. Ito. Finite mapping by neural networks and truth functions. Mathematical Scientist 17, 69–77, 1992.
L. K. Jones. A simple lemma on greedy approximation in Hilbert space and convergence rates for projection pursuit regression and neural network training. Annals of Statistics 20, 608–613, 1992.
V. Kůrkovâ. Dimension-independent rates of approximation by neural networks. In Computer-Intensive Methods in Control and Signal Processing: Curse of Dimensionality (Eds. M. Kdrnÿ, K. Warwick) (pp. 261–270 ). Birkhauser, Boston, 1997.
V. Kůrkovâ, P. C. Kainen, and V. Kreinovich. Estimates of the number of hidden units and variation with respect to half-spaces. Neural Networks,1997 (in press).
H. N. Mhaskar and C. A. Micchelli. Approximation by superposition of sigmoidal and radial basis functions. Advances in Applied Mathematics 13, 350–373, 1992.
C. A. Micchelli. Interpolation of scattered data: distance matrices and conditionally positive definite functions. Constructive approximation 2, 11–22, 1986.
J. Park and I. W. Sandberg. Approximation and radial-basis-function networks. Neural Computation 5, 305–316, 1993.
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© 1998 Springer-Verlag London Limited
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Kárný, M., Warwick, K., Kůrková, V. (1998). Incremental Approximation by Neural Networks. In: Kárný, M., Warwick, K., Kůrková, V. (eds) Dealing with Complexity. Perspectives in Neural Computing. Springer, London. https://doi.org/10.1007/978-1-4471-1523-6_12
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DOI: https://doi.org/10.1007/978-1-4471-1523-6_12
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