Neural Networks: Using a Game Theoretic Derivative for Minimizing Maximal Errors and Designing Network Architecture
Mark Meltser, Moshe Shoham · 1995
In this short paper, we summarize (without proofs) the constructive method to approximate functions in the uniform (i.e. maximal error) norm, that was recently developed by the authors. [9] This is in contrast to other methods (e.g. back-propagation) that approximate only in the average error norm. We comment the novelty of the approach and possible extensions. The method includes a ~gradient descent method in the maximal error norm (i.e. a non-differentiable function) and a method to constructively add neurons on the fly to overcome the problem of local minima in the uniform norm. This is a realization of the approximation results of Cybenko, Hecht-Nielsen, Hornik, Stinchombe, White, Gallant, Funahasi, Leshno et al and others. The approximation in the uniform norm is both more appropriate for a number of examples, such as robotic arm control, and seems to