L1 Regularization Penalty

L1 Regularization (Lasso)

L1 regularization adds a penalty proportional to the sum of absolute values of the weights:

Compared to L2 (Ridge):

| | L2 (Ridge) | L1 (Lasso) |

|---|---|---|

| Penalty | $\lambda \sum W_{ij}^2$ | $\lambda \sum |W_{ij}|$ |

| Effect | Shrinks weights evenly | Drives weights to exactly zero |

| Use case | General regularization | Feature selection / sparsity |

The L1 penalty encourages sparse solutions — many weights become exactly zero, which is useful for feature selection and model interpretability.

Your task:

Implement l1_penalty(W, lambda_) that returns the scalar L1 regularization term.