7. Design a Hebb net to implement logical AND function Soft Computing Machine Learning Mahesh Huddar

Summary

This video explains how to design a Hebbian network to implement the logical AND function using the Hebbian learning rule. The script demonstrates step-by-step how to initialize weights and bias, and adjust them based on training data to achieve the desired output. It covers the process of calculating weight updates using the Hebbian rule and modifying the weights for each input. By the end, the network's final weights and bias are derived, showing how the network models the logical AND function. The video is educational for those looking to understand Hebbian learning in neural networks.

Takeaways

• 😀 The video demonstrates how to design a web network to implement the logical AND function using Hebbian learning rule (HEB).
• 😀 The training data consists of two inputs (X1 and X2), a bias (B), and the target output (Y), with X1 and X2 taking values of +1 or -1.
• 😀 The target output Y is high (+1) only when both inputs X1 and X2 are high (+1), otherwise the output is low (-1).
• 😀 The weights and bias are initialized to zero at the beginning of the training process.
• 😀 Hebbian learning rule is applied to update the weights and bias: new weight = old weight + Δw, where Δw is the change in weight.
• 😀 Δw for each weight is calculated as the product of the input (X) and the target output (Y).
• 😀 The bias change (ΔB) is directly equal to the target output Y.
• 😀 The process of updating the weights and bias is illustrated with step-by-step examples, showing how the weights evolve after each iteration.
• 😀 After each training example, the weights and bias are adjusted accordingly, following the Hebbian rule, until the final weights are reached.
• 😀 The final weights for the AND function are found to be W1 = 2, W2 = 2, and Bias (B) = -2, which accurately represents the logical AND function.

Q & A

What is the Hebbian learning rule used for in the context of this video?

The Hebbian learning rule is used to modify the weights and bias in a network to implement a logical AND function. It adjusts the weights based on the inputs and the target output by calculating the change in weights (Delta W) using the formula ΔW = X * Y.

What are the initial values for the weights and bias before applying the Hebbian learning rule?

The initial values for the weights (W1, W2) and the bias (B) are all set to zero before applying the Hebbian learning rule.

How is the change in weights (Delta W) calculated?

The change in weights (Delta W) is calculated using the formula ΔW_i = X_i * Y, where X_i represents the input and Y represents the target output for a given example.

How does the Hebbian learning rule update the weights and bias?

The Hebbian learning rule updates the weights and bias by adding the change in weight (ΔW) to the old values. For example, the new weight W1 is calculated as W1_new = W1_old + ΔW1.

What are the inputs and target in the example used in the video?

In the example used in the video, the inputs X1 and X2 are both binary, with possible values of 1 or -1. The target output Y is 1 when both inputs are 1, and -1 otherwise.

What happens to the weights after applying the Hebbian rule to the first input (1, 1)?

After applying the Hebbian rule to the first input (X1=1, X2=1) with target Y=1, the weights W1, W2, and bias B are updated to 1, 1, and 1 respectively.

What is the change in weights when the second example input is (1, -1) with target -1?

For the second input (X1=1, X2=-1) with target Y=-1, the changes in weights are: ΔW1 = -1, ΔW2 = +1, and ΔB = -1. The new weights become W1=0, W2=2, and B=0.

How are the final weights calculated for the logical AND function?

The final weights for the logical AND function are calculated by applying the Hebbian learning rule to all four input-output pairs. After processing all examples, the final weights are W1=2, W2=2, and the bias B=-2.

Why is the bias included in the Hebbian learning process?

The bias is included in the Hebbian learning process to ensure that the network can adjust its output threshold. It helps shift the activation function's response, allowing it to model the logical function more accurately.

What does the final Hebbian network look like after all updates?

The final Hebbian network for the logical AND function has weights W1=2, W2=2, and bias B=-2. This network will output the correct results for the logical AND function based on the inputs X1 and X2.