C++ Neural Networks and Fuzzy Logic: Preface

1

 = (1, 0, 1, 1),

1

 = (0, 1, 1), and X

2

 =

(0, 1, 1, 0), Y

2

 = (1, 0, 1). Naturally, the weight matrix is different, as is its transpose, correspondingly. As

stated before, the weights do not change during the operation of the network with whatever inputs presented to

C++ Neural Networks and Fuzzy Logic:Preface

Weights and Training

155

---

it. The results are as shown in Table 8.1 below.

Table 8.1 Results for the Example

Input vectoractivationoutput vector

X

1

 = (1, 0, 1, 1)(−4, 4, 2)(0, 1, 1) = Y

1

X

2

 = (0, 1, 1, 0)(2, −2, 2)(1, 0, 1) = Y

2

Y

1

 = (0, 1, 1)(2, −2, 2, 2)(1, 0, 1, 1) = X

1

Y

2

 = (1, 0, 1)(−2, 2, 2, −2)(0, 1, 1,0) = X

2

You may think that you will encounter a problem when you input a new vector and one of the neurons has

activation 0. In the original example, you did find this situation when you got the third output neuron’s

activation as 0. The thresholding function asked you to use the same output for this neuron as existed in the

earlier time cycle. So you took it to be 1, the third component in (0, 1, 1). But if your input vector is a new X

vector for which you are trying to find an associated Y vector, then you do not have a Y component to fall

back on when the activation turns out to be 0. How then can you use the thresholding function as stated?

What guidance do you have in this situation? If you keep track of the inputs used and outputs received thus

far, you realize that the Field B (where you get your Y vector) neurons are in some state, meaning that they

had some outputs perhaps with some training vector. If you use that output component as the one existing in

the previous cycle, you have no problem in using the thresholding function.

As an example, consider the input vector X