Backpropagation is the fundamental algorithm for training neural networks. It efficiently calculates gradients of the loss function with respect to network parameters. These gradients are then used to update weights and biases to minimize error. The algorithm works by propagating information forward through the network, then backward to compute gradients.
The forward pass is the first step in backpropagation. Input data enters the network and flows through each layer. At each neuron, the input is multiplied by weights, a bias is added, and an activation function is applied. This process continues layer by layer until the final output is produced. The mathematical operation at each neuron can be expressed as y equals f of W x plus b, where W represents weights, x is input, b is bias, and f is the activation function.
After the forward pass, we calculate the loss using a loss function that measures the difference between predicted and actual output. Then begins the backward pass, where the error propagates backward through the network. Using the chain rule of calculus, we calculate gradients that tell us how much each weight contributes to the total error. These gradients are then used to update the weights in a direction that minimizes the loss.
The final step is weight update using gradient descent. The algorithm uses the calculated gradients to update weights in the direction that reduces loss. The learning rate controls how big these updates are. This process repeats iteratively - forward pass, loss calculation, backward pass, and weight update - until the network learns to make accurate predictions. As we can see in the loss curve, the error decreases over iterations as the network improves.
To summarize what we have learned about backpropagation: It is the fundamental algorithm that efficiently trains neural networks. The forward pass produces predictions from input data. A loss function measures how accurate these predictions are. The backward pass calculates gradients using the chain rule of calculus. Finally, gradient descent uses these gradients to update weights and minimize error. This iterative process enables neural networks to learn complex patterns and make accurate predictions.