On the equivalence between predictive models for automatic speech recognition

This paper addresses the equivalence of input-output mapping functions between the Linked Predictive Neural Networks (LPNN, [5]) and the Hidden Control Neural Networks (HCNN, [2]). Two novel theoretical results supported with Mathematica experiments are presented. First, it is proved that for every HCNN model there exist an equivalent LPNN model. Second, it is shown that the set of input-output functions of an LPNN model is strictly larger than the set of functions of an equivalent HCNN model. Therefore, when using equal architecture of the canonical building blocks (MLPs) for the LPNN and HCNN models, the LPNN represent a superset of the approximation capabilities of the HCNN models.