On some relationships between hierarchies of quasiarithmetic means and neural networks

In this work, we establish the relations between neural networks and hierar chies of quasiarithmetic means. We show that a neural network with the same activation function in all the neurons gives an output that is isomorphic to the result that can be obtained with a hierarchy of quasiarithmetic mean s. From this result, we-show that hierarchies of quasiarithmetic means are universal approximations. (C) 1999 John Wiley & Sons, Inc.