论文信息 - Exponentially many local minima for single neurons

Exponentially many local minima for single neurons

We show that for a single neuron with the logistic function as the transfer function the number of local minima of the error function based on the square loss can grow exponentially in the dimension.

Peter Auer | Mark Herbster | Manfred K. Warmuth | P. Auer | M. Herbster

[1] J. Davenport. Editor , 1960 .

[2] Eric B. Baum,et al. Supervised Learning of Probability Distributions by Neural Networks , 1987, NIPS.

[3] John S. Denker,et al. Strategies for Teaching Layered Networks Classification Tasks , 1987, NIPS.

[4] Esther Levin,et al. Accelerated Learning in Layered Neural Networks , 1988, Complex Syst..

[5] Eduardo D. Sontag,et al. Backpropagation separates when perceptrons do , 1989, International 1989 Joint Conference on Neural Networks.

[6] Eduardo D. Sontag,et al. Backpropagation Can Give Rise to Spurious Local Minima Even for Networks without Hidden Layers , 1989, Complex Syst..

[7] J. Slawny,et al. Back propagation fails to separate where perceptrons succeed , 1989 .

[8] E. K. Blum,et al. Approximation of Boolean Functions by Sigmoidal Networks: Part I: XOR and Other Two-Variable Functions , 1989, Neural Computation.

[9] Alberto Tesi,et al. On the Problem of Local Minima in Backpropagation , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[10] Raymond L. Watrous. A Comparison between Squared Error and Relative Entropy Metrics Using Several Optimization Algorithms , 1992, Complex Syst..

[11] S. Hyakin,et al. Neural Networks: A Comprehensive Foundation , 1994 .