Backpropagation Solved Example - 4 | Backpropagation Algorithm in Neural Networks by Mahesh Huddar

Summary

This video tutorial explains the backpropagation algorithm using a neural network example with three layers. It details the process of input propagation from the input to the output layer, calculates the error, and updates the weights and biases accordingly. The video also covers the logistic activation function, error calculation, and weight update formulas, guiding viewers through each step to understand how backpropagation minimizes error in neural networks.

Takeaways

• 🌐 The video discusses the backpropagation algorithm using a neural network with an input layer, a hidden layer, and an output layer.
• 🔢 The neural network example has two neurons in each layer, with given weights and biases for the layers.
• 📈 The input values are 0.5 and 0.10, and the goal is to propagate these inputs through the network to calculate the output.
• 🧮 The net input for each neuron is calculated by summing the product of the weights and inputs, plus the bias.
• 📉 The logistic activation function is used to transform the net input into the output of the neurons.
• 🔄 The process is repeated for each neuron in the hidden and output layers to calculate their respective outputs.
• 📊 The error is calculated based on the difference between the target output and the calculated output using a specific formula.
• 🔧 The weights and biases are updated based on the error, using the delta (change in error) and the learning rate.
• 🔄 The process of calculating the output, error, and updating weights is repeated for each epoch until the error is minimized or reaches an acceptable level.
• 📚 The video aims to clarify the concept of the backpropagation algorithm for neural networks.

Q & A

What is the purpose of the backpropagation algorithm?

The backpropagation algorithm is used to train neural networks by adjusting the weights and biases to minimize the error between the predicted output and the actual target values.

How many layers does the neural network in the example have?

The neural network in the example has three layers: an input layer, a hidden layer, and an output layer.

How many neurons are there in each layer of the given neural network?

There are two neurons in the input layer, two neurons in the hidden layer, and two neurons in the output layer.

What are the roles of W1, W2, W3, and W4 in the neural network?

W1, W2, W3, and W4 are weights associated with the neurons in the hidden layer.

What activation function is used in this example?

The logistic activation function is used in this example, which is defined as f(x) = 1 / (1 + e^(-x)).

How is the net input for a neuron calculated?

The net input for a neuron is calculated as the sum of the products of the neuron's weights and the corresponding inputs plus the bias.

What is the formula used to calculate the error in the output layer?

The error in the output layer is calculated using the formula: error = 1/2 * (Target - Calculated Output)^2.

How is the weight update performed in the backpropagation algorithm?

The weight update is performed by adjusting the weights based on the error, using the formula: new weight = old weight + learning rate * error * output of the previous layer.

What is the significance of the biases B1, B2, B3, and B4?

B1 and B2 are biases for the hidden layer neurons, while B3 and B4 are biases for the output layer neurons. They are used to adjust the net input and help in the activation of the neurons.

How does the backpropagation algorithm handle the error?

The backpropagation algorithm calculates the error at the output layer, then propagates this error backward to update the weights and biases of the network.

What is the role of the learning rate in the backpropagation algorithm?

The learning rate is a hyperparameter that determines the step size at each iteration while moving toward a minimum of a loss function. It is used to update the weights during the training process.