| Summary: | Back-propagation is a popular method for training feed-forward neural networks. This thesis extends the back-propagation technique to dispersive networks, which contain internal delay elements. Both the delays and the weights adapt to minimize the error at the output. Dispersive networks can perform many tasks, including signal prediction, signal production, channel equalization, and spatio-temporal pattern recognition. For comparison with conventional techniques, a dispersive network was trained to predict future values of a chaotic signal using only its present value as an input. With adaptable delays, the network had less than half the prediction error of an identical network with fixed delays, and about one-quarter the error of a conventional back-propagation network. Moreover, a dispersive network can simultaneously adapt and predict, while a conventional network cannot. After training as a predictor, the network was placed in a signal production configuration, where it autonomously generated a close approximation to the training signal. The power spectrum of the network output was a good reproduction of the training signal spectrum. Networks with fixed time delays produced much less accurate power spectra, and conventional back-propagation networks were unstable, generating high-frequency oscillations. Dispersive networks also showed an improvement over conventional techniques in an adaptive channel equalization task, where the channel transfer function was nonlinear. The adaptable delays in the dispersive network allowed it to reach a lower error than other equalizers, including a conventional back-propagation network and an adaptive linear filter. However, the improved performance came at the expense of a longer training time. Dispersive networks can be implemented in serial or parallel form, using digital electronic circuitry. Unlike conventional back-propagation networks, they can operate in a fully pipelined fashion, leading to a higher signal throughput. Their implementation in analog hardware is a promising area for future research.
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