Example
A perceptron learns to perform a binary NAND function on inputs and .
Inputs:, with input held constant at 1.
Threshold : 0.5
Bias : 0
Learning rate : 0.1
Training set, consisting of four samples:
In the following, the final weights of one iteration become the initial weights of the next. Each cycle over all the samples in the training set is demarcated with heavy lines.
| Input | Initial weights | Output | Error | Correction | Final weights | |||||||||||
| Sensor values | Desired output | Per sensor | Sum | Network | ||||||||||||
| if then 1, else 0 | ||||||||||||||||
| 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | +0.1 | 0.1 | 0 | 0 |
| 1 | 0 | 1 | 1 | 0.1 | 0 | 0 | 0.1 | 0 | 0 | 0.1 | 0 | 1 | +0.1 | 0.2 | 0 | 0.1 |
| 1 | 1 | 0 | 1 | 0.2 | 0 | 0.1 | 0.2 | 0 | 0 | 0.2 | 0 | 1 | +0.1 | 0.3 | 0.1 | 0.1 |
| 1 | 1 | 1 | 0 | 0.3 | 0.1 | 0.1 | 0.3 | 0.1 | 0.1 | 0.5 | 0 | 0 | 0 | 0.3 | 0.1 | 0.1 |
| 1 | 0 | 0 | 1 | 0.3 | 0.1 | 0.1 | 0.3 | 0 | 0 | 0.3 | 0 | 1 | +0.1 | 0.4 | 0.1 | 0.1 |
| 1 | 0 | 1 | 1 | 0.4 | 0.1 | 0.1 | 0.4 | 0 | 0.1 | 0.5 | 0 | 1 | +0.1 | 0.5 | 0.1 | 0.2 |
| 1 | 1 | 0 | 1 | 0.5 | 0.1 | 0.2 | 0.5 | 0.1 | 0 | 0.6 | 1 | 0 | 0 | 0.5 | 0.1 | 0.2 |
| 1 | 1 | 1 | 0 | 0.5 | 0.1 | 0.2 | 0.5 | 0.1 | 0.2 | 0.8 | 1 | -1 | -0.1 | 0.4 | 0 | 0.1 |
| 1 | 0 | 0 | 1 | 0.4 | 0 | 0.1 | 0.4 | 0 | 0 | 0.4 | 0 | 1 | +0.1 | 0.5 | 0 | 0.1 |
| 1 | 0 | 1 | 1 | 0.5 | 0 | 0.1 | 0.5 | 0 | 0.1 | 0.6 | 1 | 0 | 0 | 0.5 | 0 | 0.1 |
| 1 | 1 | 0 | 1 | 0.5 | 0 | 0.1 | 0.5 | 0 | 0 | 0.5 | 0 | 1 | +0.1 | 0.6 | 0.1 | 0.1 |
| 1 | 1 | 1 | 0 | 0.6 | 0.1 | 0.1 | 0.6 | 0.1 | 0.1 | 0.8 | 1 | -1 | -0.1 | 0.5 | 0 | 0 |
| 1 | 0 | 0 | 1 | 0.5 | 0 | 0 | 0.5 | 0 | 0 | 0.5 | 0 | 1 | +0.1 | 0.6 | 0 | 0 |
| 1 | 0 | 1 | 1 | 0.6 | 0 | 0 | 0.6 | 0 | 0 | 0.6 | 1 | 0 | 0 | 0.6 | 0 | 0 |
| 1 | 1 | 0 | 1 | 0.6 | 0 | 0 | 0.6 | 0 | 0 | 0.6 | 1 | 0 | 0 | 0.6 | 0 | 0 |
| 1 | 1 | 1 | 0 | 0.6 | 0 | 0 | 0.6 | 0 | 0 | 0.6 | 1 | -1 | -0.1 | 0.5 | -0.1 | -0.1 |
| 1 | 0 | 0 | 1 | 0.5 | -0.1 | -0.1 | 0.5 | 0 | 0 | 0.5 | 0 | 1 | +0.1 | 0.6 | -0.1 | -0.1 |
| 1 | 0 | 1 | 1 | 0.6 | -0.1 | -0.1 | 0.6 | 0 | -0.1 | 0.5 | 0 | 1 | +0.1 | 0.7 | -0.1 | 0 |
| 1 | 1 | 0 | 1 | 0.7 | -0.1 | 0 | 0.7 | -0.1 | 0 | 0.6 | 1 | 0 | 0 | 0.7 | -0.1 | 0 |
| 1 | 1 | 1 | 0 | 0.7 | -0.1 | 0 | 0.7 | -0.1 | 0 | 0.6 | 1 | -1 | -0.1 | 0.6 | -0.2 | -0.1 |
| 1 | 0 | 0 | 1 | 0.6 | -0.2 | -0.1 | 0.6 | 0 | 0 | 0.6 | 1 | 0 | 0 | 0.6 | -0.2 | -0.1 |
| 1 | 0 | 1 | 1 | 0.6 | -0.2 | -0.1 | 0.6 | 0 | -0.1 | 0.5 | 0 | 1 | +0.1 | 0.7 | -0.2 | 0 |
| 1 | 1 | 0 | 1 | 0.7 | -0.2 | 0 | 0.7 | -0.2 | 0 | 0.5 | 0 | 1 | +0.1 | 0.8 | -0.1 | 0 |
| 1 | 1 | 1 | 0 | 0.8 | -0.1 | 0 | 0.8 | -0.1 | 0 | 0.7 | 1 | -1 | -0.1 | 0.7 | -0.2 | -0.1 |
| 1 | 0 | 0 | 1 | 0.7 | -0.2 | -0.1 | 0.7 | 0 | 0 | 0.7 | 1 | 0 | 0 | 0.7 | -0.2 | -0.1 |
| 1 | 0 | 1 | 1 | 0.7 | -0.2 | -0.1 | 0.7 | 0 | -0.1 | 0.6 | 1 | 0 | 0 | 0.7 | -0.2 | -0.1 |
| 1 | 1 | 0 | 1 | 0.7 | -0.2 | -0.1 | 0.7 | -0.2 | 0 | 0.5 | 0 | 1 | +0.1 | 0.8 | -0.1 | -0.1 |
| 1 | 1 | 1 | 0 | 0.8 | -0.1 | -0.1 | 0.8 | -0.1 | -0.1 | 0.6 | 1 | -1 | -0.1 | 0.7 | -0.2 | -0.2 |
| 1 | 0 | 0 | 1 | 0.7 | -0.2 | -0.2 | 0.7 | 0 | 0 | 0.7 | 1 | 0 | 0 | 0.7 | -0.2 | -0.2 |
| 1 | 0 | 1 | 1 | 0.7 | -0.2 | -0.2 | 0.7 | 0 | -0.2 | 0.5 | 0 | 1 | +0.1 | 0.8 | -0.2 | -0.1 |
| 1 | 1 | 0 | 1 | 0.8 | -0.2 | -0.1 | 0.8 | -0.2 | 0 | 0.6 | 1 | 0 | 0 | 0.8 | -0.2 | -0.1 |
| 1 | 1 | 1 | 0 | 0.8 | -0.2 | -0.1 | 0.8 | -0.2 | -0.1 | 0.5 | 0 | 0 | 0 | 0.8 | -0.2 | -0.1 |
| 1 | 0 | 0 | 1 | 0.8 | -0.2 | -0.1 | 0.8 | 0 | 0 | 0.8 | 1 | 0 | 0 | 0.8 | -0.2 | -0.1 |
| 1 | 0 | 1 | 1 | 0.8 | -0.2 | -0.1 | 0.8 | 0 | -0.1 | 0.7 | 1 | 0 | 0 | 0.8 | -0.2 | -0.1 |
This example can be implemented in the following Python code.
threshold = 0.5 learning_rate = 0.1 weights = training_set = def sum_function(values): return sum(value * weight for value, weight in zip(values, weights)) while True: print '-' * 60 error_count = 0 for input_vector, desired_output in training_set: print weights result = 1 if sum_function(input_vector) > threshold else 0 error = desired_output - result if error != 0: error_count += 1 for index, value in enumerate(input_vector): weights += learning_rate * error * value if error_count == 0: breakRead more about this topic: Perceptron
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