Abstract
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.
Highlights
Rule Extraction With Convolutional Rules complex to be understandable
We show that the decompositional rule extraction approach performs better than the approach that considers the network as a black box in terms of approximating the functionality of the neural network
Concerning the interpretability of convolutional neural networks, existing work can be divided into methods that merely visualize or analyze the trained convolutional filters (Simonyan et al, 2013; Zeiler and Fergus, 2014; Mahendran and Vedaldi, 2015; Zhou et al, 2016) and methods that influence the filters during training in order to force the CNN to learn more interpretable representations (Hu et al, 2016; Ross et al, 2017; Stone et al, 2017)
Summary
Rule Extraction With Convolutional Rules complex to be understandable. In this paper we propose convolutional rules for which the complexity is not related to the dimensionality of the input but only to the dimensionality of the convolutional filters. Thereby we aim to combine advantages from two fields: We make use of the NN’s ability to handle highdimensional data and we allow for model validation, not just through visualization and subjective assessment, but through rigorous logical rules. It is a wide-spread belief that shorter rules are usually better than longer rules, a principle known as Occam’s razor. Based on recent developments in deep learning with binary neural networks (BNNs) (Hubara et al, 2016), we propose an algorithm for decompositional rule extraction (Andrews et al, 1995), called Deep Convolutional DNF Learner (DCDL).
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