SCXT 350
An exercise in perceptrons
Due: Friday, March 5 (in class)
Following the class discussion on Wednesday 2/25/04, discover weights on a two input perceptron (with bias) which will implement the following functions:
Perceptron #1:
| X | Y | Bias | Out |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 1 | 1 |
Perceptron #2:
| X | Y | Bias | Out |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 |
For each perceptron, sketch the equation of the line
w0 * bias + w1 * X + w2 * y = 0
where w0 is the weight you have placed on the bias (always 1), w1 is the weight you have placed on the input X, and w2 is the weight you have placed on the input Y.
Finally, consider the following truth function:
| X | Y | Bias | Out |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 0 |
Can you build a perceptron to do this? Try for a bit, but not too much. To see why it might not be possible, draw a line corresponding to one of your weight choices, and mark the (X,Y) points for which the perceptron fires, and the (X,Y) points for which the perceptron fails to fire, and see if something looks suspicious. This was the Minsky-Papert example that stopped research in perceptrons for twenty years.