Classification approaches that allow to extract logical rules such as decision trees are often considered to be more interpretable than neural networks. Also, logical rules are comparatively easy to verify with any possible input. This is an important part in systems that aim to ensure correct operation of a given model. However, for high-dimensional input data such as images, the individual symbols, i.e. pixels, are not easily interpretable. Therefore, rule-based approaches are not typically used for this kind of high-dimensional data. We introduce the concept of first-order convolutional rules, which are logical rules that can be extracted using a convolutional neural network (CNN), and whose complexity depends on the size of the convolutional filter and not on the dimensionality of the input. Our approach is based on rule extraction from binary neural networks with stochastic local search. We show how to extract rules that are not necessarily short, but characteristic of the input, and easy to visualize. Our experiments show that the proposed approach is able to model the functionality of the neural network while at the same time producing interpretable logical rules. Thus, we demonstrate the potential of rule-based approaches for images which allows to combine advantages of neural networks and rule learning.

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