Title: R2DN: Scalable Parameterization of Contracting and Lipschitz Recurrent Deep Networks

Original: arXiv:2504.01250v2 Announce Type: replace

Abstract: This study introduces the Robust Recurrent Deep Network (R2DN), a scalable framework for parameterizing robust recurrent neural networks intended for machine learning and data-driven control applications. By configuring R2DNs as a feedback loop between a linear time-invariant system and a 1-Lipschitz deep feedforward network, we ensure that the models are inherently stable (contracting) and resilient to minor input disturbances (Lipschitz) through their architectural design. While R2DNs employ a structure akin to the previously introduced recurrent equilibrium network (REN), they eliminate the need to iteratively compute an equilibrium layer at every time step. This architectural advantage significantly accelerates both inference and backpropagation processes on GPUs, thereby enabling the scaling of network dimensions, batch sizes, and input sequence lengths far more effectively than RENs. In evaluations across three key nonlinear system identification, observer design, and learning-based feedback control tasks, R2DNs demonstrated training and inference speeds that are up to ten times faster than RENs, while maintaining comparable test set accuracy. Furthermore, R2DNs exhibited superior scalability regarding model expressivity.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC