On the problem of applying AIC to determine the structure of a layered feedforward neural network

AIC (Akaike´s information criterion) has been thought to be effective to determine an optimal structure of layered feedforward neural networks. However, it has not been clarified from the theoretical point of view. On the other hand, it is known that a connection weight of the network can be nonunique in some cases. In this paper, we show that AIC can not be derived for three-layered networks due to the nonuniqueness of the connection weight. Through numerical simulations of data fitting with three-layered neural networks, we show that the structure determined by AIC tends to be more complex because of the inherent data fitting capability of the network.