Neural Network & Fuzzy Systems

Learning

Description:-Implementation of AND function in the neural network.

− There are 4 inequalities in the AND function and they must be satisfied.

w10 w2 0 <θ, w1 0 w2 1 < θ ,

w11 w2 0 <θ, w1 1 w2 1 > θ

− One possible solution:

if both weights are set to 1 and the threshold is set to 1.5, then

(1)(0) (1) (0) < 1.5 assign 0, (1) (0) (1) (1) < 1.5 assign 0

(1)(1) (1) (0) < 1.5 assign 0, (1) (1) (1) (1) > 1.5 assign 1

Although it is straightforward to explicitly calculate a solution to the AND function problem, but the question is "how the network can learn such a solution". That is, given random values for the weights can we define an incremental procedure which will cover a set of weights which implements AND function.

Example 1

AND Problem:-Consider a simple neural network made up of two inputs connected to a single output unit.

− The output of the network is determined by calculating a weighted sum of its two inputs and comparing this value with a threshold θ.

− If the net input (net) is greater than the threshold, then the output is 1, else it is 0.

− Mathematically, the computation performed by the output unit is

net = w1 I1 w2 I2 if net > θ then O = 1, otherwise O = 0.