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Neural Networks and Computational Learning Theory

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NeuroCOLT Technical Report NC-TR-96-030

Exponentially many local minima for single neurons

Peter Auer
University of California
Santa Cruz
USA

Mark Herbster
University of California Santa Cruz
USA

Manfred K. Warmuth
University of California Santa Cruz
USA

Abstract
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.

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