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.
The paper first summarizes a general approach to the training of recurrent neural networks by gradient-based algorithms, which leads to the introduction of four families of training algorithms. Because of the variety of possibilities thus available to the "neural network designer," the choice of the appropriate algorithm to solve a given problem becomes critical. We show that, in the case of process modeling, this choice depends on how noise interferes with the process to be modeled; this is evidenced by three examples of modeling of dynamical processes, where the detrimental effect of inappropriate training algorithms on the prediction error made by the network is clearly demonstrated.
The paper proposes a general framework which encompasses the training of neural networks and the adaptation of filters. It is shown that neural networks can be considered as general non-linear filters which can be trained adaptively, i.e. which can undergo continual training. A unified view of gradient-based training algorithms for feedback networks is proposed, which gives rise to new algorithms.
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