Artificial Neuron

Introduction

This applet demonstrates the basic structure and behaviour of an artificial neuron.

Credits

The original applet was written by Fred Corbett, and is available here.  These pages and applet were modified by Olivier Michel and Alix Herrmann.

Theory

The first computational model for an artificial neuron was proposed by McCulloch and Pitts in 1943.  The model neuron here is similar to the McCulloch and Pitts neuron, but they are not identical.

The general artificial neuron model has five components, shown in the following list. (The subscript i indicates the i-th input or weight.)

  1. A set of inputs, xi.
  2. A set of weights, wi.
  3. A threshold, u.
  4. An activation function, f.
  5. A single neuron output, y.

Applet

As you can see below, an artificial neuron is a very simple structure.  This neuron has only two inputs, but in general it could have many.

Click here to see the instructions.  You may find it helpful to open a separate browser window for the instructions, so you can view them at the same time as the applet window.

 

Questions

  1. Using the unit step activation function, determine a set of weights (and threshold value) that will produce the following classification:
    2. x1 x2 output
    -0.2 0.5 0
    0.2 -0.5 0
    0.8 -0.8 1
    0.8 0.8 1

    Try to do this by hand first, then check your answer with the applet.

  2. What might the different activation functions be used for?
  3. [Optional paper and pencil problem]
    This model has no dynamics: the output appears immediately. Suppose instead that the unit doesn't react instantly. What do you think will happen?
    Write down a differential equation describing a change in output proportional to the difference between the final value and the current value. Solve your equation.