A new class of neural networks based on approximate identities for approximation and learning

Learning a given input-output mapping can be regarded as a problem of approximating a multivariate function. A theoretical framework for approximation, based on sequences of functions named approximate identities, is developed. It is proved that such sequences are able to approximate a generally continuous function with a given error. This leads to a new class of three-layer networks that can efficiently be implemented in analog MOS VLSI.<>