Neural networks, despite their empirically-proven abilities, have been little used for the refinement of existing knowledge because this task requires a three-step process. First, knowledge in some form must be inserted into a neural network. Second, the network must be refined. Third, knowledge must be extracted from the network. We have previously described a method for the first step of this process. Standard neural learning techniques can accomplish the second step. In this paper, we propose and empirically evaluate a method for the final, and possibly most difficult, step. This method efficiently extracts symbolic rules from trained neural networks. The four major results of empirical tests of this method are that the extracted rules: (1) closely reproduce (and can even exceed) the accuracy of the network from which they are extracted; (2) are superior to the rules produced by methods that directly refine symbolic rules; (3) are superior to those produced by previous techniques fo...

Hybrid learning methods use theoretical knowledge of a domain and a set of classified examples to develop a method for accurately classifying examples not seen during training. The challenge of hybrid learning systems is to use the information provided by one source of information to offset information missing from the other source. By so doing, a hybrid learning system should learn more effectively than systems that use only one of the information sources. KBANN(Knowledge-Based Artificial Neural Networks) is a hybrid learning system built on top of connectionist learning techniques. It maps problem-specific "domain theories", represented in propositional logic, into neural networks and then refines this reformulated knowledge using backpropagation. KBANN is evaluated by extensive empirical tests on two problems from molecular biology. Among other results, these tests show that the networks created by KBANN generalize better than a wide variety of learning systems, as well as several t...

To Mom, Dad, and Susan, for their support and encouragement.

This article describes an approach to combining symbolic and connectionist approaches to machine learning. A three-stage framework is presented and the research of several groups is reviewed with respect to this framework. The first stage involves the insertion of symbolic knowledge into neural networks, the second addresses the refinement of this prior knowledge in its neural representation, while the third concerns the extraction of the refined symbolic knowledge. Experimental results and open research issues are discussed.

A distinct advantage of symbolic learning algorithms over artificial neural networks is that typically the concept representations they form are more easily understood by humans. One approach to understanding the representations formed by neural networks is to extract symbolic rules from trained networks. In this paper we describe and investigate an approach for extracting rules from networks that uses (1) the NofM extraction algorithm, and (2) the network training method of soft weight-sharing. Previously, the NofM algorithm had been successfully applied only to knowledge-based neural networks. Our experiments demonstrate that our extracted rules generalize better than rules learned using the C4.5 system. In addition to being accurate, our extracted rules are also reasonably comprehensible. 1 INTRODUCTION Artificial neural networks (ANNs) have been successfully applied to real-world problems as varied as steering a motor vehicle (Pomerleau, 1991) and learning to pronounce English tex...

Although neural networks have shown very good performance in many application domains, one of their main drawbacks lies in the incapacity to provide an explanation for the underlying reasoning mechanisms. The "explanation capability" of neural networks can be achieved by the extraction of symbolic knowledge. In this paper, we present a new method of extraction that captures nonmonotonic rules encoded in the network, and prove that such a method is sound. We start by discussing some of the main problems of knowledge extraction methods. We then discuss how these problems may be ameliorated. To this end, a partial ordering on the set of input vectors of a network is defined, as well as a number of pruning and simplification rules. The pruning rules are then used to reduce the search space of the extraction algorithm during a pedagogical extraction, whereas the simplification rules are used to reduce the size of the extracted set of rules. We show that, in the case of regular networks, the extraction algorithm is sound and complete. We proceed to extend the extraction algorithm to the class of non-regular networks, the general case. We show that non-regular networks always contain regularities in their subnetworks. As a result, the underlying extraction method for regular networks can be applied, but now in a decompositional fashion. In order to combine the sets of rules extracted from each subnetwork into the final set of rules, we use a method whereby we are able to keep the soundness of the extraction algorithm. Finally, we present the results of an empirical analysis of the extraction system, using traditional examples and real-world application problems. The results have shown that a very high fidelity between the extracted set of rules and the network can be achieved....

This paper presents a major revision of the Either propositional theory refinement system. Two issues are discussed. First, we show how run time efficiency can be greatly improved by changing from a exhaustive scheme for computing repairs to an iterative greedy method. Second, we show how to extend Either to refine M-of-N rules. The resulting algorithm, Neither (New Either), is more than an order of magnitude faster and produces significantly more accurate results with theories that fit the M-of-N format. To demonstrate the advantages of Neither, we present preliminary experimental results comparing it to Either and various other systems on refining the DNA promoter domain theory. 1 Introduction Recently, a number of machine learning systems have been developed that use examples to revise an approximate (incomplete and/or incorrect) domain theory [ Ginsberg, 1990; Ourston and Mooney, 1990; Towell and Shavlik, 1991; Danyluk, 1991; Whitehall et al., 1991; Matwin and Plante, 1991 ] . ...

This paper uses a special notation for specifying locations in a DNA sequence. The idea is to number locations with respect to a fixed, biologically-meaningful, reference point. Negative numbers indicate sites preceding the reference point (by biological convention, this appears on the left) while positive numbers indicate sites following the reference point. (Zero is not used.) Figure 9 illustrates this numbering scheme. Rules use this referencing scheme by stating a position with respect to the reference location, denoted by `@', and the giving a subsequence in the positive direction. For example @-4`GGT' refers to the three nucleotide long sequence in Figure 9 that begins at position-4 and ends at position-2. In addition to this notation for specifying locations a DNA sequence, Table 3 specifies a standard coding scheme for referring to any possible combination of nucleotides using a single letter (IUB Nomenclature Committee, 1985). This scheme is compatible with the codes used by the EMBL, GenBank, and PIR data libraries, three major collections of data for molecular biology. 4.2 Promoter recognition

This paper will give an overview of the various approaches to neurosymbolic integration. Roughly, these can be divided into two strategies: unified strategies aim at attaining neural and symbolic capabilities using neural networks alone, while hybrid strategies combine neural networks with symbolic models such as expert systems, case-based reasoning systems, 2 Chapter 2 and decision trees. These two approaches form the main subtrees of the classification hierarchy depicted in Figure 1. Symbol Proc. Neuronal Unified approach Symbol Proc. hybrids Connectionist Localist Hybrid approach Combined L/D Neurosymbolic integration Functional Chainprocessing Translational Subprocessing hybrids Metaprocessing Distributed Coprocessing Figure 1 Classification of integrated neurosymbolic systems.

We describe a method for using machine learning to refine algorithms represented as generalized finite-state automata. The knowledge in an automaton is translated into an artificial neural network, and then refined with backpropagation on a set of examples. Our technique for translating an automaton into a network extends kbann, a system that translates a set of propositional rules into a corresponding neural network. The extended system, FSkbann, allows one to refine the large class of algorithms that can be represented as state-based processes. As a test, we use FSkbann to refine the Chou-Fasman algorithm, a method for predicting how globular proteins fold. Empirical evidence shows the refined algorithm FSkbann produces is statistically significantly more accurate than both the original Chou-Fasman algorithm and a neural network trained using the standard approach. Introduction As machine learning has been increasingly applied to complex real-world problems, many researchers have...