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# Firing Rule

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ARTIFICIAL INTELLIGENCE: OVERVIEW OF NEURAL NETWORKS NAME: | | DATE: | | TOPIC: | FIRING RULE | SCHEDULE: | MH 04:30P – 06:00p |

OBJECTIVE: * To be familiarized with a neural network’s firing rule. * To demonstrate the implementation of Hamming Distance Technique (HDT)

PROBLEM:
A 3-input neuron is taught to output 1 when the input (X1, X2, and X3) is 111 or 101 and to output 0 when the input is 000 or 001.

PROCEDURES: 1. Take a collection of training patterns for a node which cause it to fire (the 1-taught set of patterns). | Case 1 | Case 2 | X1: | | | X2: | | | X3: | | | Out: | 1 | 1 |
Table 1.1 – 1-Taught Set of Patterns

2. Take a collection of training patterns for a node which prevent it from doing so (the 0-taught set). | Case 1 | Case 2 | X1: | | | X2: | | | X3: | | | Out: | 0 | 0 |
Table 1.2 - 0-Taught Set of Patterns

3. As of now, for the patterns from neither collections, the output stays unidentified (0/1).

| Input 1 | Input 2 | Input 3 | Input 4 | Input 5 | Input 6 | Input 7 | Input 8 | X1: | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | X2: | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | X3: | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | Out: | | | | | | | | |
Table 1.3 – Truth Table Accomplished without (HDT)

4. The patterns not in either collection is then compared with patterns of the given collection. a. If the pattern has less input elements different with the 'nearest' pattern in the 1-taught set than with the 'nearest' pattern in the 0-taught set, then the pattern will cause the node to fire. b. If the pattern has less input elements different with the 'nearest' pattern in the 0-taught set than with the 'nearest' pattern in the 1-taught set, then the pattern will not cause the node to fire. c. If the pattern is equally distant from two taught patterns that have different outputs, then the output stays undefined (0/1).

For example:

Table 1.4 – Differences in input elements between a specific pattern and other patterns of the given collection (000, 001, 101, 111)

Patterns | 000 | 001 | 101 | 111 | 010 | 1 | 2 | 3 | 2 | Result: | Nearest | - | - | - |

The pattern 010 differs from 000 in 1 element, from 001 in 2 elements, from 101 in 3 elements and from 111 in 2 elements. Therefore, the 'nearest' pattern is 000 which belongs in the 0-taught set. Thus the firing rule requires that the neuron should not fire when the input is 010.

5. Apply the HDT to accomplish the truth table below:

| Input 1 | Input 2 | Input 3 | Input 4 | Input 5 | Input 6 | Input 7 | Input 8 | X1: | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | X2: | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | X3: | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | Out: | | | | | | | | |
Table 1.3 – Truth Table Accomplished with (HDT)
(The difference between the two truth tables is called the generalization of the neuron.)

Derive the generalization of the neuron from the following scenarios: 1. A 3-input neuron is taught to output 0 when the input (X1, X2, and X3) is 001 or 110 and to output 1 when the input is 000 or 111. 2. A 2-input neuron is taught to output 1 when the input (X1 and X2) is 00 and to output 0 when the input is 10 and 11. 3. A 3-input neuron is taught to output 1 when the input (X1, X2, and X3) is 111 and to output 0 when the input is 101.…...

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