On the stability properties of Gated Recurrent Units neural networks
This work addresses stability guarantees for GRU networks, which is crucial for reliable deployment in control and modeling applications, though it is incremental as it extends existing stability analysis to GRUs.
The paper tackled the problem of ensuring stability in Gated Recurrent Units (GRU) neural networks by deriving sufficient conditions for Input-to-State Stability (ISS) and Incremental Input-to-State Stability (δISS) through nonlinear inequalities on weights, which were tested on a Quadruple Tank benchmark system with satisfactory modeling results.
The goal of this paper is to provide sufficient conditions for guaranteeing the Input-to-State Stability (ISS) and the Incremental Input-to-State Stability (δISS) of Gated Recurrent Units (GRUs) neural networks. These conditions, devised for both single-layer and multi-layer architectures, consist of nonlinear inequalities on network's weights. They can be employed to check the stability of trained networks, or can be enforced as constraints during the training procedure of a GRU. The resulting training procedure is tested on a Quadruple Tank nonlinear benchmark system, showing satisfactory modeling performances.