Example 1: The Basic Neuron

The following is an applet and its instructions written by Fred Corbett. It is from his website Web Applets for Interactive Tutorials on Artificial Neural Learning. It is demonstrates our model of the simple neuron.

For this applet:

• x1 and x2 are the input values (ie n = 2)

• w1 and w2 are the multiplicative weights

• u is the thresholding function treated as another weighted input where the input value is -1 and the multiplicative weight for it can be treated as the thresholding value ø. (ie we are simply subtracting ø)

• y is the output of the Neuron.

• The box above the circle contains the activation function f_h(x). In the previous section we only referred to the unit step funtion as the activation function. Other functions may also be used as activation functions though and this applet allows you to use others such as the sigmoid, piecewise linear, and Gaussian.

  Sigmoid: f(x) = (1 + e^-ßx)^-1

  

  ^{Piecewise Linear: f(x) = 0 , if x <= x}_min

  ^{sfdf(x) = mx + b , if x}_min ^{< x < x}_max

  ^{sfdf(x) = 1 , if x >= x}_max

  

  Gaussian: f(x) = (2ó*Pi)^-1 * e^{-[(x-ù)(x-ù)/(2ó*ó)]}

  

Instructions:

Using this applet is straightforward, but a few points are in order:

1. Simply enter numeric values in the neuron input, weight, and threshold text fields, and press <Enter> or click the Calculate button to update the neuron output and weighted sum.
2. The text fields with a white background can be edited, while those with a grey background can not. However, you can scoll the grey (and white) text fields with your arrow keys to see more digits.
3. By clicking on the activation function image, you can scroll through the available functions.
4. By holding the <Shift> key down and then clicking your mouse on the activation function image, a small dialog is displayed that allows you to change some of the function parameters.
5. By pressing the <Tab> key, you can shift focus from one component to another.
6. To see a legend, labeling the neuron elements, simply check the Show Legend check box.
7. To clear the neuron fields and re-enable all of the text fields, click the Reset button.
8. Finally, to see how the neuron can approximate Boolean function, click one of the AND, OR, or NOT buttons. Note: the NOT button disables input 2 and weight 2. They can be re-enabled by pressing one of the Reset, AND, or OR buttons.