Example 2: Binary Logic Unit

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 supervised learning using the perceptron learning algorithm. Using this applet, you can train the perceptron to act as a binary logic unit. It can compute or approximate most 2-input Boolean functions. However, a problem arises when trying to train the perceptron on the XOR (or XNOR) function. The applet provides a "work-around" for this problem by introducing an extra input.

Instructions:

To Train The Perceptron:

1. Select the desired Boolean function in the truth table.
2. Select the desired activation function by clicking the activation function image. You can also change some function parameters by holding down the <Shift> key and then clicking the image with your mouse.
3. Adjust the training parameters as desired. Legal values are as follows:
   • Learning Rate: 0.0 to 1.0
   • Iterations: 1 to 10000 (I wouldn't want to try this)
   • Error Threshold: 0.0 to 0.5
4. Click the Train button to begin a normal training session OR
5. Click the Step button repeatedly to single-step through the training session.

During Training:

1. To stop a training session (normal or single-step) in progress, click the Stop button.
2. A few notes:
   • The progress of the training session is displayed in the progress and status bars.
   • The error for the current input vector is displayed in the Current-Error text field.
   • The sum-squared error over all the input vectors is displayed in the Sum-Squared Error text-field
   • The perceptron's ability to classify the inputs into two classes (0 and 1) is shown in a graph in the top-right corner of the applet. Currently, this only works for the 2D graph.

To Test The Perceptron:

1. After training Click the Test button repeatedly to cycle through all four input vectors.
2. Some notes:
   • If the neuron output is correct (within the error threshold specified), the neuron output text-field is painted green otherwise it is red.
   • The current error and sum-squared error are updated and displayed in their text fields.

To Solve the Exclusive-OR (XOR) Problem:

1. Click the Show XOR Solution check box.
2. Set the truth table to the XOR function
3. Click the Train or Step button to start a training session.
4. Once the training is complete, click the Test button to check the results.