L1 term uses the sum of absolute values of weights. The regression model used for L1 regularization is also called *Lasso Regression* or L1 norm: $$w* \;=\; \sum_{i=0}^N (y_i-\sum_{j=0}^M {x_ij}{W_j})^2 + {\lambda}\sum_{j=0}^M {\vert{W_j}\vert}$$ The L2 term uses the sum of least square values of weights. The regression model used for L2 regularization is also called Ridge Regression or L2 norm:\
$$w* \;=\; \sum_{i=0}^N (y_i-\sum_{j=0}^M {x_ij}{W_j})^2 + {\lambda}\sum_{j=0}^M {W_j^2}$$

where *$\lambda$* is the regularization hyper-parameter. An overlarge *$\lambda$* will oversimplify the structure of the deep learning network because some weights are close to zero, whereas an undersized *$\lambda$* is not strong enough to reduce weights. In practice, L2 regularization is more widely used, mainly because of its computational efficiency; however, L1 regularization prevails over L2 on sparse properties [@yan16]. Models generated using L1 norm are simpler and interpretable, while L2 provides superior predictions. L1 and L2 have pros and cons, as shown in Table \[Table 1\] adapted from [@khandelwal18].\

                             L1                                               L2
  -------------------------------------------------------- -----------------------------------------
   [Penalizes the sum of the absolute value of weights]{}   [Penalizes the sum of square weights]{}
                    [Sparse solution]{}                             [Nonsparse solution]{}
                   [Multiple solution]{}                               [One solution]{}
               [Built-in feature selection]{}                      [No feature selection]{}
                   [Robust to outliers]{}                         [Not robust to outliers]{}
            [Unable to 