Linear Separability the XOR Problem

To see what we mean by linear separability, we consider a simple problem that is not linearly separable the so-called XOR problem - to teach a neural net the exclusive-OR function (table 10.2). 

An appropriate perceptron model for this problem is one that has two input neurons (corresponding to inputs X and X2) and one output neuron, whose value 

In the more general case when there are N input neurons, the space of the Xi s 

0 as iV — 00. In other words, the set of linearly separable Boolean functions is a set of measure zero. 

Three-dimensional space, for example, would be divided into two regions by a two-dimensional plane. 

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