=================================================================================

In machine learning, the "norm" of parameters typically refers to a mathematical measure of the size or magnitude of the parameter vector in a model. It's a way to quantify how large or small the model's parameters are. Different types of norms can be used, but two of the most common are the L1 norm and the L2 norm.

1. L1 Norm (Manhattan Norm): The L1 norm of a parameter vector is the sum of the absolute values of its individual elements. Mathematically, for a parameter vector θ, the L1 norm is defined as:

   L1(θ) = ∑ |θ_i|

   Here, θ_i represents the individual elements of the parameter vector.

2. L2 Norm (Euclidean Norm): The L2 norm of a parameter vector is the square root of the sum of the squares of its individual elements. Mathematically, for a parameter vector θ, the L2 norm is defined as:

   L2(θ) = √(∑ θ_i²)

   Again, θ_i represents the individual elements of the parameter vector.

These norms are used in machine learning for various purposes, including:

• Regularization: Regularization techniques like L1 (Lasso) and L2 (Ridge) regularization add a penalty term to the loss function based on the norms of the model's parameters. This encourages smaller parameter values, which can help prevent overfitting and improve model generalization.

• Feature Selection: The L1 norm is often used to encourage sparsity in the parameter vector, effectively selecting a subset of the most important features.

• Convergence Analysis: The norms of parameter updates are sometimes used to monitor the convergence of optimization algorithms during model training.

• Model Interpretability: Understanding the magnitude of parameters can provide insights into the importance of different features or variables in the model's predictions.

============================================