# Input State Stability of Gated Graph Neural Networks

arXiv: https://arxiv.org/abs/2305.19235 · HTML: https://mlsanity.com/paper/2305.19235/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2023.

## Built on by (most cited first, 1 of 1)

- [Stable Transformer-Actor-Critic Model Predictive Control: A Contraction Analysis Approach](https://mlsanity.com/paper/2606.20197/) (2026)

## Abstract (arXiv)

In this paper, we aim to find the conditions for input-state stability (ISS) and incremental input-state stability (δISS) of Gated Graph Neural Networks (GGNNs). We show that this recurrent version of Graph Neural Networks (GNNs) can be expressed as a dynamical distributed system and, as a consequence, can be analysed using model-based techniques to assess its stability and robustness properties. Then, the stability criteria found can be exploited as constraints during the training process to enforce the internal stability of the neural network. Two distributed control examples, flocking and multi-robot motion control, show that using these conditions increases the performance and robustness of the gated GNNs.