Lasso regression for neural networks performs regularization during the training phase with the L1 norm, i.e. it adds a term which is the sum of the absolute values of the weights to the objective (loss) function being minimized. Thus, lasso regression minimizes the following during training: Objective = base_loss(weights) + alpha * (sum of absolute value of the weights). The base_loss will depend on the underling task (e.g. cross-entropy loss for classification) and alpha is generally adjusted during model validation, and is called the regularization parameter. Lasso stands for "least absolute shrinkage and selection operator."