# Control the GNN: Utilizing Neural Controller with Lyapunov Stability for Test-Time Feature Reconstruction

arXiv: https://arxiv.org/abs/2410.09708 · HTML: https://mlsanity.com/paper/2410.09708/

## Key facts

- Cited by 1 papers in the map (data through 7 Oct 2026).
- Builds on 20 of its 29 references that are in the map.
- First posted on arXiv 13 Oct 2024.

## Builds on (most cited first, 20 of 20)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Explainability in Graph Neural Networks: A Taxonomic Survey](https://mlsanity.com/paper/2012.15445/) (2020)
- [Neural Lyapunov Control](https://mlsanity.com/paper/2005.00611/) (2020)
- [Data Augmentation for Deep Graph Learning: A Survey](https://mlsanity.com/paper/2202.08235/) (2022)
- [Out-Of-Distribution Generalization on Graphs: A Survey](https://mlsanity.com/paper/2202.07987/) (2022)
- [Shift-Robust GNNs: Overcoming the Limitations of Localized Graph Training Data](https://mlsanity.com/paper/2108.01099/) (2021)
- [Generalizing Graph Neural Networks on Out-Of-Distribution Graphs](https://mlsanity.com/paper/2111.10657/) (2021)
- [Lyapunov-stable neural-network control](https://mlsanity.com/paper/2109.14152/) (2021)
- [Empowering Graph Representation Learning with Test-Time Graph Transformation](https://mlsanity.com/paper/2210.03561/) (2022)
- [Pointer Graph Networks](https://mlsanity.com/paper/2006.06380/) (2020)
- [Neural Lyapunov Control of Unknown Nonlinear Systems with Stability Guarantees](https://mlsanity.com/paper/2206.01913/) (2022)
- [Unleashing the Power of Graph Data Augmentation on Covariate Distribution Shift](https://mlsanity.com/paper/2211.02843/) (2022)
- [SizeShiftReg: a Regularization Method for Improving Size-Generalization in Graph Neural Networks](https://mlsanity.com/paper/2207.07888/) (2022)
- [Metropolis-Hastings Data Augmentation for Graph Neural Networks](https://mlsanity.com/paper/2203.14082/) (2022)
- [Are GATs Out of Balance?](https://mlsanity.com/paper/2310.07235/) (2023)
- [FRGNN: Mitigating the Impact of Distribution Shift on Graph Neural Networks via Test-Time Feature Reconstruction](https://mlsanity.com/paper/2308.09259/) (2023)

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

- [Feature Construction Using Network Control Theory and Rank Encoding for Graph Machine Learning](https://mlsanity.com/paper/2507.15195/) (2025)

## Abstract (arXiv)

The performance of graph neural networks (GNNs) is susceptible to discrepancies between training and testing sample distributions. Prior studies have attempted to mitigating the impact of distribution shift by reconstructing node features during the testing phase without modifying the model parameters. However, these approaches lack theoretical analysis of the proximity between predictions and ground truth at test time. In this paper, we propose a novel node feature reconstruction method grounded in Lyapunov stability theory. Specifically, we model the GNN as a control system during the testing phase, considering node features as control variables. A neural controller that adheres to the Lyapunov stability criterion is then employed to reconstruct these node features, ensuring that the predictions progressively approach the ground truth at test time. We validate the effectiveness of our approach through extensive experiments across multiple datasets, demonstrating significant performance improvements.