Having identified overfitting as a common challenge where models learn training data too well at the expense of performance on unseen data, we now turn to a direct approach to constrain model complexity: weight regularization. This chapter focuses on techniques that modify the learning objective by adding penalties based on the magnitude of the network's weights. The core idea is that simpler models, often characterized by smaller weight values, tend to generalize better.

You will learn about:

• The intuition behind penalizing large weights and its effect on model complexity.
• L2 Regularization (Weight Decay): How adding a penalty proportional to the squared magnitude of weights ($L_2$ norm) encourages smaller weights and its mathematical formulation.
• L1 Regularization: How adding a penalty proportional to the absolute magnitude of weights ($L_1$ norm) works, and how it can lead to sparse weight vectors (feature selection).
• A comparison of the effects and use cases for L1 versus L2 regularization.
• Elastic Net Regularization: A method combining both L1 and L2 penalties.
• How to practically implement these techniques within common deep learning frameworks using code examples.

By the end of this chapter, you'll understand how to apply these methods to reduce overfitting and improve the generalization capabilities of your neural networks.