  This paper introduces recurrent equilibrium networks (RENs), a new class of
nonlinear dynamical models for applications in machine learning and system
identification. The new model class has "built in" guarantees of stability and
robustness: all models in the class are contracting -- a strong form of
nonlinear stability -- and models can have prescribed Lipschitz bounds. RENs
are otherwise very flexible: they can represent all stable linear systems, all
previously-known sets of contracting recurrent neural networks, all deep
feedforward neural networks, and all stable Wiener/Hammerstein models. RENs are
parameterized directly by a vector in R^N, i.e. stability and robustness are
ensured without parameter constraints, which simplifies learning since generic
methods for unconstrained optimization can be used. The performance of the
robustness of the new model set is evaluated on benchmark nonlinear system
identification problems.
