  One obstacle that so far prevents the introduction of machine learning models
primarily in critical areas is the lack of explainability. In this work, a
practicable approach of gaining explainability of deep artificial neural
networks (NN) using an interpretable surrogate model based on decision trees is
presented. Simply fitting a decision tree to a trained NN usually leads to
unsatisfactory results in terms of accuracy and fidelity. Using L1-orthogonal
regularization during training, however, preserves the accuracy of the NN,
while it can be closely approximated by small decision trees. Tests with
different data sets confirm that L1-orthogonal regularization yields models of
lower complexity and at the same time higher fidelity compared to other
regularizers.
