Design a Hebb net to implement OR function (consider bipolar inputs and targets)

**Hebb Net to Implement OR Function**

**Introduction:**

A Hebb net is a type of artificial neural network that can be used to implement simple logical functions. In this example, we will design a Hebb net to implement the OR function using bipolar inputs and targets.

**Bipolar Inputs and Targets:**

Bipolar inputs and targets take on values of -1 and 1, respectively. For the OR function, the truth table is as follows:

Input 1 | Input 2 | Target |
---|---|---|

-1 | -1 | -1 |

-1 | 1 | 1 |

1 | -1 | 1 |

1 | 1 | 1 |

**Hebb Net Architecture:**

A Hebb net consists of a layer of input neurons and a layer of output neurons. The input neurons are connected to the output neurons with weighted connections. The weights are updated based on the Hebb learning rule.

**Hebb Learning Rule:**

The Hebb learning rule states that the weight between two neurons is increased if the neurons are both active (i.e., have a value of 1) and decreased if the neurons are both inactive (i.e., have a value of -1).

**Design:**

To design a Hebb net to implement the OR function, we need to set the weights between the input neurons and the output neuron as follows:

- w1 = 1
- w2 = 1
- Î¸ = -1

**Operation:**

When the input neurons are activated with bipolar inputs, the output neuron will calculate the weighted sum of the inputs and compare it to the threshold Î¸. If the weighted sum is greater than or equal to Î¸, the output neuron will be activated and output a value of 1. Otherwise, the output neuron will be inactive and output a value of -1.

**Example:**

Let’s consider the input pattern (-1, 1). The weighted sum of the inputs is:

w1 * Input 1 + w2 * Input 2 = 1 * (-1) + 1 * 1 = 0

Since the weighted sum is less than the threshold Î¸, the output neuron will be inactive and output a value of -1. This matches the target value for the OR function.