Analysis of neural networks through base functions

Problem statement. Despite their success-story, neural networks have one major disadvantage compared to other techniques: the inability to explain comprehensively how a trained neural network reaches its output; neural networks are not only (incorrectly) seen as a "magic tool" but possibly even more as a mysterious "black box" [1]. This is an important aspect of the functionality of any technology, as users will be interested in "how it works" before trusting it completely. Although much research has already been done to "open the box," there is a notable hiatus in known publications on analysis of neural networks. So far, mainly sensitivity analysis and rule extraction methods have been used to analyze neural networks. However, these can only be applied in a limited subset of the problem domains where neural network solutions are encountered.