Abstract
In this paper, we show how to design three-layer feedforward neural networks with hyperbolic sigma-pi units in the hidden layer in order to act as one-sided approximation and interpolation devices for regular gridded data. We obtain the concrete networks in real-time using a one-shot learning scheme based on special approximation operators which are generated by sampling the given discrete information on a regular grid. In this context, it is essential that we do not require any smoothness conditions regarding the underlying data function f. At the end of the paper we briefly discuss an application of our strategy.
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