Unit-growing learning optimizing the solvability condition for model-free regression

The universal approximation capability exhibited by one-hidden layer neural networks is explored to produce a supervised unit-growing learning for model-free nonlinear regression. The development is based on the solvability condition, which attests that the ability to learn a specific learning set increases with the number of nodes in the hidden layer. Since the training process operates the hidden nodes individually, a pertinent activation function can be iteratively developed for each node as a function of the learning set. The optimization of the solvability condition gives rise to neural networks of minimum dimension, an important step toward improving generalization.