  Deep learning is widely used in tasks including image recognition and
generation, in learning dynamical systems from data and many more. It is
important to construct learning architectures with theoretical guarantees to
permit safety in the applications. There has been considerable progress in this
direction lately. In particular, symplectic networks were shown to have the non
vanishing gradient property, essential for numerical stability. On the other
hand, architectures based on higher order numerical methods were shown to be
efficient in many tasks where the learned function has an underlying dynamical
structure. In this work we construct symplectic networks based on higher order
explicit methods with non vanishing gradient property and test their efficiency
on various examples.
