ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

15. Numerical Analysis and Scientific Computing

1991 MS Classification: 26, 41, 65, 68 Heinz, Alois P., Universität Freiburg, Germany Efficient function approximation by tree-structured neural networks. An algebra A of continuous functions from a compact K ⊂ IR^{n} to IR can be defined by tree-structured neural networks (TSNN) such that the uniform closure of A consists of all continuous functions from K to IR. Each TSNN has an equivalent representation as a feed-forward neural network with two hidden layers. It is shown that the average case time T (N) needed to evaluate a given TSNN function or its Jacobian matrix is in O(N^{q}), where N is the TSNN size and q ∈ [0, 1] depends on the TSNN and the distribution of query points. Reference: A. P. Heinz. A tree-structured neural network for real-time adaptive control. In S. Amari, L. Xu, L. -W. Chan, I. King, and K. -S. Leung, editors, Progress in Neural Information Processing, 926–931, Berlin, 1996, Springer.