Having explored how a neural network processes inputs to generate outputs via forward propagation, we now turn to the fundamental question: how does a network learn? This chapter introduces the mechanisms that allow networks to adjust their internal parameters based on prediction errors.

We will cover the essential components of the training process:

• Loss Functions: You'll learn how to quantify the network's prediction error using functions like Mean Squared Error (MSE) or Cross-Entropy. This measurement tells us how far off the network's predictions are from the true values.
• Gradient Descent: We will examine the core optimization algorithm used to minimize the calculated loss. The basic idea is to iteratively adjust the network's parameters in the direction that most steeply reduces the error.
• Backpropagation: This section explains the algorithm used to efficiently calculate the gradients of the loss function with respect to every weight and bias in the network. It relies on the chain rule from calculus to propagate the error signal backward through the layers.
• Parameter Updates: You will see how the computed gradients are used, along with a learning rate $\eta$, to update the weights $W$ and biases $b$ of the network, moving it closer to a state of lower error. A typical update looks like $W_{new} = W_{old} - \eta \frac{\partial Loss}{\partial W_{old}}$
• Learning Rate: Understanding the significance of the learning rate parameter and its effect on the training convergence.
• Optimization Variants: We will briefly introduce common variations like Stochastic Gradient Descent (SGD), Mini-batch Gradient Descent, and adaptive methods like Adam, which are widely used to improve training stability and speed.

By completing this chapter, you will grasp the mechanics behind how neural networks learn from data by minimizing a loss function through iterative adjustments guided by backpropagation and gradient descent.