R2DN: Scalable Parameterization of Contracting and Lipschitz Recurrent Deep Networks

This paper presents the Robust Recurrent Deep Network (R2DN), a scalable parameterization of stable and robust recurrent neural networks for machine learning and data-driven control. We construct R2DNs as the feedback interconnection of a linear time-invariant system and a 1-Lipschitz deep feedforward network, and directly parameterize the weights so that our models are stable (contracting) and robust to input perturbations (Lipschitz) by design. Our parameterization uses a structure similar to the recurrent equilibrium network (REN), but without having to iteratively solve an equilibrium layer at each time-step. This speeds up model inference and training on GPUs, and makes it computationally feasible to scale up the network size and input sequence length in comparison to RENs. We compare R2DNs to RENs on representative problems in nonlinear system identification, observer design, learning-based feedback control, and sequential image classification. We find that training and inference are up to an order of magnitude faster with similar performance, and that they scale more favorably with respect to model expressivity.