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...

A significant limitation of neural networks is that the representations they learn are usually incomprehensible to humans. We present a novel algorithm, Trepan, for extracting comprehensible, symbolic representations from trained neural networks. Our algorithm uses queries to induce a decision tree that approximates the concept represented by a given network. Our experiments demonstrate that Trepan is able to produce decision trees that maintain a high level of fidelity to their respective networks while being comprehensible and accurate. Unlike previous work in this area, our algorithm is general in its applicability and scales well to large networks and problems with high-dimensional input spaces.

Concepts learned by neural networks are difficult to understand because they are represented using large assemblages of real-valued parameters. One approach to understanding trained neural networks is to extract symbolic rules that describe their classification behavior. There are several existing rule-extraction approaches that operate by searching for such rules. We present a novel method that casts rule extraction not as a search problem, but instead as a learning problem. In addition to learning from training examples, our method exploits the property that networks can be efficiently queried. We describe algorithms for extracting both conjunctive and M-of-N rules, and present experiments that show that our method is more efficient than conventional search-based approaches. 1 INTRODUCTION A problem that arises when neural networks are used for supervised learning tasks is that, after training, it is usually difficult to understand the concept representations formed by the networks....

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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.

We propose and empirically evaluate a method for the extraction of expertcomprehensible rules from trained neural networks. Our method operates in the context of a three-step process for learning that uses rule-based domain knowledge in combination with neural networks. Empirical tests using real-worlds problems from molecular biology show that the rules our method extracts from trained neural networks: closely reproduce the accuracy of the network from which they came, are superior to the rules derived by a learning system that directly refines symbolic rules, and are expert-comprehensible.

A new methodology of extraction, optimization, and application of sets of logical rules is described. Neural networks are used for initial rule extraction, local, or global minimization procedures for optimization, and Gaussian uncertainties of measurements are assumed during application of logical rules. Algorithms for extraction of logical rules from data with real-valued features require determination of linguistic variables or membership functions. Context-dependent membership functions for crisp and fuzzy linguistic variables are introduced and methods of their determination described. Several neural and machine learning methods of logical rule extraction generating initial rules are described, based on constrained multilayer perceptron, networks with localized transfer functions or on separability criteria for determination of linguistic variables. A tradeoff between accuracy/simplicity is explored at the rule extraction stage and between rejection/error level at the optimization stage. Gaussian uncertainties of measurements are assumed during application of crisp logical rules, leading to “soft trapezoidal” membership functions and allowing to optimize the linguistic variables using gradient procedures. Numerous applications of this methodology to benchmark and real-life problems are reported and very simple crisp logical rules for many datasets provided.

: This paper presents a novel learning model Clarion, which is a hybrid model based on the twolevel approach proposed in Sun (1995). The model integrates neural, reinforcement, and symbolic learning methods to perform on-line, bottom-up learning (i.e., learning that goes from neural to symbolic representations). The model utilizes both procedural and declarative knowledge (in neural and symbolic representations respectively), tapping into the synergy of the two types of processes. It was applied to deal with sequential decision tasks. Experiments and analyses in various ways are reported that shed light on the advantages of the model. obstacles agent target Figure 1: Navigating Through A Minefield 1 Introduction This paper presents a model that unifies neural, symbolic, and reinforcement learning. It addresses the following three issues: (1) It deals with autonomous learning: It allows a situated agent to learn autonomously and continuously, from on-going experience in the world, w...

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...

This chapter provides an introduction to the field of hybrid neural systems. Hybrid neural systems are computational systems which are based mainly on artificial neural networks but also allow a symbolic interpretation, or interaction with symbolic components. In this overview, we will describe recent results of hybrid neural systems. We will give a brief overview of the main methods used, outline the work that is presented here, and provide additional references. We will also highlight some important general issues and trends.