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/*
 * L1 regularization.
 */

forward = function(matrix[double] X, double lambda)
    return (double reg_loss) {
  /*
   * Computes the forward pass for an L1 regularization function.
   *
   * Inputs:
   *  - X: Inputs, of shape (any, any).
   *  - lambda: Regularization strength.
   *      A typical value is 0.01.
   *
   * Outputs:
   *  - reg_loss: Total regularization loss.
   */
  reg_loss = lambda * sum(abs(X))
}

backward = function(matrix[double] X, double lambda)
    return (matrix[double] dX) {
  /*
   * Computes the backward pass for an L1 regularization function.
   *
   * Inputs:
   *  - X: Inputs, of shape (any, any).
   *  - lambda: Regularization strength.
   *
   * Outputs:
   *  - dX: Gradient wrt `X`, of same shape as `X`.
   */
  dX = lambda * sign(X)
}