Abstract
In a layered neural network, the error backpropagation method is generally used as the supervised learning procedure for the hidden layer, which cannot be observed from the outside. In order to apply the method, however, the output function of the neuron model must be differentiable. This paper proposes a supervised learning method for the hidden layer neurons in which the teaching signal is calculated for the hidden layer neurons, by utilizing the learning rule for the connection weight and the duality in the output layer neuron. The method is applicable so long as the neuron model contains duality, and it does not require that the output layer neurons or the hidden layer neurons be differentiable. As an example of a case in which the error backpropagation cannot be applied, a perceptron composed of neurons with a step output function is considered. The proposed method is applied, and the learning rule for the whole network is constructed. The XOR problem was actually learned by the network, and the same learning success rate was obtained as in the error backpropagation method for a perceptron composed of neurons with a sigmoid output function. Β© 2005 Wiley Periodicals, Inc. Syst Comp Jpn, 36(9): 34β42, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.20206