Multilayered Perceptrons

Abstract

Before we enter into the discussion of how one can derive a learning rule for multilayered perceptrons, it is useful to consider a simple example. We choose the exclusive-or (xor) function, with which we are already familiar. In order to circumvent the “no-go” theorem derived for simple perceptrons in the previous section, we add a hidden layer containing two neurons which receive signals from the input neurons and feed the output neuron (see Fig. 6.1). We denote the states of the hidden neurons by the variables s _j , (j = 1,..., N _h ).¹ The synaptic connections between the hidden neurons and the output neurons are denoted by w _ij ; those between the input layer and the hidden layer by ${\bar w_{jk}}$. The threshold potentials of the output neurons are called ϑ _i ; those of the hidden neurons are called ${\bar \vartheta _j}$.