Backpropagation in Neural Networks

Backpropagation is a core algorithm for training neural networks, helping them learn from errors and improve their performance. It is a supervised learning method, which works by adjusting the weights of the network based on the error or loss calculated between the predicted output and the actual target.

How Backpropagation Works

Forward Pass

The input data is passed through the network layer by layer. Each neuron applies a weighted sum of its inputs and passes the result through an activation function (like ReLU or Sigmoid). This produces the output of the network (predictions).

Loss Calculation

After the forward pass, the predicted output is compared to the actual target (true values) using a loss function (such as Mean Squared Error for regression or Cross-Entropy Loss for classification). The difference between the predicted value and actual target is calculated as the loss.

Backward Pass (Backpropagation)

The goal is to minimize this loss. Backpropagation helps calculate how much each weight contributed to the error. It uses the chain rule of calculus to propagate the error backward from the output layer to the input layer.

Steps in the Backward Pass:

• Gradient of the Loss Function: Compute the gradient (partial derivatives) of the loss with respect to each weight and bias in the network. This tells you how to adjust the weights to reduce the error.
• Error Propagation: Starting from the output layer, the error is propagated backward to the earlier layers, adjusting weights layer by layer. Each layer’s weights are updated in the direction that minimizes the error.
• Gradient Descent: The gradients are used to update the weights using an optimization algorithm like gradient descent. The weights are adjusted by subtracting a fraction of the gradient (scaled by the learning rate) from the current weights.

Weight Update

The weights are updated using the formula:

w_new = w_old – η × ∂L∂w

Where:

• wold is the old weight
• η is the learning rate (a small value to control the step size)
• ∂L∂w is the gradient of the loss with respect to the weight

Repeat

This process (forward pass, loss calculation, backward pass, and weight update) is repeated for multiple iterations or epochs. As the network learns, the weights continue to adjust, and the loss reduces, improving the model’s accuracy.

 

Backpropagation helps the network learn by calculating the gradients of the loss function with respect to each weight and adjusting the weights to minimize the loss. It uses the chain rule to propagate the error back through the layers and updates weights using gradient descent or similar optimization techniques. This process allows neural networks to train efficiently and improve their performance over time!