Discontinuous Neural Networks and Discontinuity Learning

2In the framework of discontinuous function approximation and discontinuity interface detection, we consider an approach involving Neural Networks. In particular, we define a novel typology of Neural Network layers endowed with new learnable parameters and discontinuities in the space of the activations. These layers allow to create a completely new kind of Neural Networks, characterized to be discontinuous, not only able to approximate discontinuous functions but also to learn and detect the discontinuity interfaces. A sound theoretical analysis concerning the properties of the new discontinuous layers is performed, and some tests on discontinuous functions are proposed, in order to assess the potential of such instruments.noneopendella santa; pieracciniDella, Santa; Pieraccini, Sandr