Biological Computation

Artificial Neural Networks    ◾    163

We have seen the limited computational powers of the simple single-

layered perceptron: it can classify only patterns that are linearly separable.

In their book Minsky and Papert (1969) showed that multilayered neural

networks can compute functions that cannot be computed by a single-layer

preceptron. For instance, it is enough to add one hidden layer to com-

pute the XOR function, which is not computable by a simple perceptron.

Multilayered networks’ greater computing power is an attractive property,

but they are much harder to engineer. Designing a suitable layout for a

multilayered network and nding the appropriate network weights can be

dicult. Finding an ecient learning rule for updating the wei