Mathematics

In the last years it was observed that Residual Neural Networks (ResNets) can be interpreted as discretizations of control systems. This observation can be a valuable tool for a further mathematical understanding of Machine Learning, since it bridges ResNets (and, more generally, Deep Learning) with Control Theory. This parallelism can be useful to study existing architectures and to develop new ones. In particular, in the present seminar we investigate ResNets obtained from linear-control systems. Despite their simplicity, recent theoretical results guarantee that they are surprisingly expressive. Moreover, owing to the linear dependence in the controls, the training strategies based on Pontryagin Maximum Principle can be carried out with low computational effort.