L2 Regularization Penalty

Problem Statement

Calculate the L2 regularization term (weight decay) for a neural network.

Background

L2 regularization adds a penalty to the loss function based on the squared magnitude of weights:

$L2_{term} = \frac{\lambda}{2m} \sum ||W||^2$

Where:

• $\lambda$ (lambda) is the regularization strength
• $m$ is the number of training examples
• $||W||^2$ is the sum of squared weights (Frobenius norm squared)

This encourages smaller weights, reducing overfitting.

Your Task

Write a function l2_penalty(weights_list, lambda_reg, m) that computes the L2 regularization term.

weights_list is a list of weight matrices (each as a list of lists).

Output Format

Return a float rounded to 4 decimal places.