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The paper proposes a general framework which encompasses the training of neural networks and the adaptation of filters. We show that neural networks can be considered as general non-linear filters which can be trained adaptively, i. e. which can undergo continual training with a possibly infinite number of time-ordered examples. We introduce the canonical form of a neural network. This canonical form permits a unified presentation of network architectures and of gradient-based training algorithms for both feedforward networks (transversal filters) and feedback networks (recursive filters). We show that several algorithms used classically in linear adaptive filtering, and some algorithms suggested by other authors for training neural networks, are special cases in a general classification of training algorithms for feedback networks.

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