Numerical methods for neural networks and applications

Neural Networks have been a trending topic in the latest years, because of their incredible capability of approximating any function. They could be considered big optimization problems, but their high complexity does not allow to use powerful algorithms, because of their computational cost. Thus the strategy adopted in Neural Networks' theory is to modify the classic Gradient Descent with some advices, deriving from heuristics. However this brings this family of problems to a not so rigorous environment. Thus the purpose of this work is to investigate the behaviour and results of Neural Networks through DLTI systems, that are well known mathematical models.