Deep neural networks (DNN) are mainly black boxes, generally suffering from bad interpretability of their behavior and the results obtained. Hence, a human can not easily derive the relations modeled by the network. A reasonable way to provide interpretability for humans are logical rules. In this paper we propose neural logic rule layers (NLRL), which are able to represent arbitrary logic rules in terms of their conjunctive and disjunctive normal forms. Stacking various layers, we are theoretically able to represent arbitrary complex rules by the resulting neural network architecture. The NLRL are end-to-end trainable allowing to learn logic rules directly on the given data without needing any background information about the origin. We show in experiments, that NLRL-enhanced neural networks can model arithmetic and logical operations over the input values. Furthermore, we apply NLRL to image classification tasks and show that interpretability is provided without sacrificing classification performance by exchanging the fully-connected head of the network. We also apply NLRL to a real world industrial control problem where the task is to model the discrete control behaviour of a programmable logic controller (PLC), following a basic step sequence.(c) 2022 Elsevier Inc. All rights reserved.
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