Minimizing the Quadratic Training Error of a Sigmoid Neuron Is Hard

by Jiri Sima

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Datum	Value	Source
TITLE	Minimizing the Quadratic Training Error of a Sigmoid Neuron Is Hard	user correction - Legacy Corrections
AUTHOR NAME	Jiri Sima	user correction - Legacy Corrections
ABSTRACT	. We rst present a brief survey of hardness results for training feedforward neural networks. These results are then completed by the proof that the simplest architecture containing only a single neuron that applies the standard (logistic) activation function to the weighted sum of n inputs is hard to train. In particular, the problem of nding the weights of such a unit that minimize the relative quadratic training error within 1 or its average (over a training set) within 13=(31n) of its inmum proves to be NP-hard. Hence, the well-known back-propagation learning algorithm appears to be not ecient even for one neuron which has negative consequences in constructive learning. 1 The Complexity of Neural Network Loading Neural networks establish an important class of learning models that are widely applied in practical applications to solving articial intelligence tasks [13]. The most prominent position among successful neural learning heuristics is occupied by the back-prop...	user correction - Legacy Corrections
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