An adaptive higher-order neural networks (AHONN) and its approximation capabilities
Shuxiang Xu, Ming Zhang · 2004
The approximation capabilities of an adaptive higher-order neural network (AHONN) with a neuron-adaptive activation function (NAF) to any nonlinear continuous functional and any nonlinear continuous operator are studied. Universal approximation theorems of AHONN to continuous functionals and continuous operators are given, and learning algorithms are derived to tune the free parameters in NAF as well as connection weights between neurons. We apply the algorithms to approximate continuous dynamical systems (operators).