# On the stability properties of Gated Recurrent Units neural networks

arXiv: https://arxiv.org/abs/2011.06806 · HTML: https://mlsanity.com/paper/2011.06806/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2020.

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## Abstract (arXiv)

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.