Comments on local minima free conditions in multilayer perceptrons

IEEE Transactions on Neural Networks

Volumn 9, Issue 5, 1998, Pages 1051-1053

  Gori, Marco ^a   Tsoi, Ah Chung ^b  

^a UNIVERSITY OF SIENA   (Italy)

^b UNIVERSITY OF WOLLONGONG   (Australia)

Author keywords

Backpropagation; Computational capabilities of neural networks; Local mimma; Multilayer perceptrons; Positive weights canonical form

Indexed keywords

EID: 0007402218     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/72.712191     Document Type: Review

References (13)

1. M. Gori and A. Tesi, "On the problem of local minima in backpropagation," IEEE Trans. Pattern Anal. Machine Intell., vol. 14, pp. 76-86, Jan. 1992.
2. M. Bianchini, P. Frasconi, and M. Gori, "Learning without local minima in radial basis function networks," IEEE Trans. Neural Networks, vol. 6, pp. 749-756, May 1995.
3. M. Bianchini and M. Gori, "Optimal learning in artificial neural networks: A review of theoretical results," Neurocomputing, vol. 13, pp. 313-346, 1996.
4. P. Baldi and K. Hornik, "Neural networks and principal component analysis: Learning from examples without local minima," Neural Networks, vol. 2, pp. 53-58, 1989.
5. E. Sontag and H. Sussman, "Backpropagation separates when perceptrons do," in Int. Joint Conf. Neural Networks, vol. 1, Washington, DC, June 1989, pp. 639-642.
6. X. Yu and G. Chen, "On the local minima free condition of backpropagation learning," IEEE Trans. Neural Networks, vol. 6, pp. 1300-1303, Sept. 1995.
7. M. Brady, R. Raghavan, and J. Slawny, "Backpropagation fails to separate where perceptrons succeed," IEEE Trans. Circuits Syst., vol. 36, pp. 665-674, 1989.
8. E. Sontag and H. Sussman, "Backpropagation can give rise to spurious local minima even for networks without hidden layers," Complex Syst., vol. 3, pp. 91-106, 1989.
9. L. Hamey, "Xor has no local minima: A case study in neural-network error surface analysis," Neural Networks, Oct. 1998, to be published.
10. I. Sprinkhuizen-Kuyper and E. Boers, "The error surface of the simplest xor network has only global minima," Neural Comput., vol. 8, no. 6, pp. 1301-1320, 1996.
11. M. Bianchini, M. Gori, and M. Maggini, "On the problem of local minima in recurrent neural networks," IEEE Trans. Neural Networks, vol. 5, pp. 167-177, Mar. 1994 (Special Issue on Recurrent Neural Networks).
12. A. Chen, H. Lu, and R. Hecht-Nielsen, "On the geometry of feedforward neural networks," Neural Comput., vol. 5, no. 6, pp. 910-927, 1993.
13. J. Park and I. Sanderberg, "Universal approximation using radial basis functions," Neural Comput., vol. 3, no. 2, pp. 246-257, 1991.