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This paper presents a new hybrid optimization strategy for training feedforward neural networks. The algorithm combines gradient-based optimization of nonlinear weights with singular value decomposition (SVD) computation of linear weights in one integrated routine. It is described for the multilayer perceptron (MLP) and radial basis function (RBF) networks and then extended to the local model network (LMN), a new feedforward structure in which a global nonlinear model is constructed from a set of locally valid submodels. Simulation results are presented demonstrating the superiority of the new hybrid training scheme compared to second-order gradient methods. It is particularly effective for the LMN architecture where the linear to nonlinear parameter ratio is large.

A software environment is described which provides facilities at a variety of levels for “animating” algorithms: exposing properties of programs by displaying multiple dynamic views of the program and associated data structures. The system is operational on a network of graphics-based, personal workstations and has been used successfully in several applications for teaching and research in computer science and mathematics. In this paper, we outline the conceptual framework that we have developed for animating algorithms, describe the system that we have implemented, and give several examples drawn from the host of algorithms that we have animated.

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