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Rule extraction from neural networks is a fervent research topic. In the last 20 years many authors presented a number of techniques showing how to extract symbolic rules from Multi Layer Perceptrons (MLPs). Nevertheless, very few were related to ensembles of neural networks and even less for networks trained by deep learning. On several datasets we performed rule extraction from ensembles of Discretized Interpretable Multi Layer Perceptrons (DIMLP), and DIMLPs trained by deep learning. The results obtained on the Thyroid dataset and the Wisconsin Breast Cancer dataset show that the predictive accuracy of the extracted rules compare very favorably with respect to state of the art results. Finally, in the last classification problem on digit recognition, generated rules from the MNIST dataset can be viewed as discriminatory features in particular digit areas. Qualitatively, with respect to rule complexity in terms of number of generated rules and number of antecedents per rule, deep DIMLPs and DIMLPs trained by arcing give similar results on a binary classification problem involving digits 5 and 8. On the whole MNIST problem we showed that it is possible to determine the feature detectors created by neural networks and also that the complexity of the extracted rulesets can be well balanced between accuracy and interpretability.

Characterization of Symbolic Rules Embedded in Deep DIMLP Networks: A Challenge to Transparency of Deep Learning