**Next message:**Murfitt G.R.: "Re: Categorisation and Prototypes"**Previous message:**Belcher, Ian: "Re: Algorithms and Creativity"**Maybe in reply to:**Saegusa, Mitu: "The Exclusive-Or (XOR) Problem"**Next in thread:**HARNAD Stevan: "Re: The Exclusive-Or (XOR) Problem"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

Exclusive Or (XOR) refers to a situation whereby a decision is based

on one, and only one, of two conditions being satisfied. For

instance, if I dislike crowds I may decide to go to the beach if it

is sunny, or if it is a bank holiday, but not both.

This is a Boolian logic function, and if each condition is assigned

a value of 1 if it is met, and 0 if it is not met, then a table can

be drawn up representing this, with values or 0 and 1 indicating

the decision:

1 0

1 0 1

0 1 0

This is a difficult concept for the human mind to grasp; we usually

function using and/or conditions. For a network, it constitutes the

basis of the XOR problem. How can a network be constructed so that

it will arrive at the the correct output when the input data is based

on XOR reasoning, and has nothing in common?

A network consists of a set of units that are each connected to all

the units of the next layer, but can only communicate with

each other by means of very simple signals.

The basic 2 layer perceptron is not capable of such processing, and

this was Minsky's critique. What is required to accomplish XOR

processing is a network such that

if the input is a pair of binary digits (which can be 0 or 1),

and the output is another binary pair, for the output value to be 1

of one of the inputs is 1, but 0 if neither or both is 1.

The answer to how this kind of decision can be made lies in the

network having one or more hidden layers between the input and output

layers. The units of the hidden layer are isolated from the networks

environment, and the connections pass from the input layer through

the hidden layer to the output layer. Each unit at a level is

connected to all units of the next higher layer.

The units can only transmit simple numerical values - the input

receives 1 or 0 and sends an output value of 1 or 0 along each of its

connections with other units. Each connection has a weight which is

either positive, negative or 0, and each unit has a bias. The

incoming value is multiplied by the weight on each of

its connections, and the sum of the products is added to the bias

that is associated with each unit. The resulting value is then

assigned an activation value of 0 or 1, according to the threshold of the

unit, and if the unit is thus activated it continues to propogate its

value to the output layer via another weighted connection.

Another advantage of this system is that changing the weights

allows a network to learn from past experience,

and thus improve its performance through the process of

backpropogation.

tion.

**Next message:**Murfitt G.R.: "Re: Categorisation and Prototypes"**Previous message:**Belcher, Ian: "Re: Algorithms and Creativity"**Maybe in reply to:**Saegusa, Mitu: "The Exclusive-Or (XOR) Problem"**Next in thread:**HARNAD Stevan: "Re: The Exclusive-Or (XOR) Problem"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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