City Research Online

Abstract

We examine the feasibility of rule extraction as a method of explanation for neural networks with an emphasis on deep neural networks. This is done by establishing a framework for neural-symbolic computing which gives precise meaning to notions such as fidelity, neural encoding, and rule extraction. Using this framework, we establish semantic and syntactic relationships between different classes of neural networks and different logical systems. This shows that there is nothing inherently different about the computations done by deep neural networks and logical systems. We use this to argue that complexity is the primary difference between neural and symbolic approaches. We develop a measure of complexity and two different rule extraction algorithms using M-of- N rules. The first extraction algorithm is a fast decompositional algorithm for Deep Belief Networks that builds on the optimal confidence extraction algorithm. The second algorithm is a parallel search for optimal M-of-N rules that implements a hyperparameter that controls the complexity of the extracted rules. We apply this algorithm to a variety of deep networks and find that although differences in architecture, dataset, and learning algorithm influence the complexity of extracted rules, generally only the final softmax layer can be represented simply and accurately with M-of-N rules. We conclude by experimenting with the combination of rule extraction from the final layer and importance methods to visualize the inputs to the final layer.

Publication Type:	Thesis (Doctoral)
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Departments:	Doctoral Theses School of Science & Technology > School of Science & Technology Doctoral Theses School of Science & Technology

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