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This article proposes the use of a penalty function for pruning feedforward neural network by weight elimination. The penalty function proposed consists of two terms. The first term is to discourage the use of unnecessary connections, and the second term is to prevent the weights of the connections from taking excessively large values. Simple criteria for eliminating weights from the network are also given. The effectiveness of this penalty function is tested on three well-known problems: the contiguity problem, the parity problems, and the monks problems. The resulting pruned networks obtained for many of these problems have fewer connections than previously reported in the literature.

An algorithm for extracting rules from a standard three-layer feedforward neural network is proposed. The trained network is first pruned not only to remove redundant connections in the network but, more important, to detect the relevant inputs. The algorithm generates rules from the pruned network by considering only a small number of activation values at the hidden units. If the number of inputs connected to a hidden unit is sufficiently small, then rules that describe how each of its activation values is obtained can be readily generated. Otherwise the hidden unit will be split and treated as output units, with each output unit corresponding to an activation value. A hidden layer is inserted and a new subnetwork is formed, trained, and pruned. This process is repeated until every hidden unit in the network has a relatively small number of input units connected to it. Examples on how the proposed algorithm works are shown using real-world data arising from molecular biology and signal processing. Our results show that for these complex problems, the algorithm can extract reasonably compact rule sets that have high predictive accuracy rates.