# Training Stable Graph Neural Networks Through Constrained Learning

arXiv: https://arxiv.org/abs/2110.03576 · HTML: https://mlsanity.com/paper/2110.03576/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 23 references that are in the map.
- First posted on arXiv 7 Oct 2021.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Universal Invariant and Equivariant Graph Neural Networks](https://mlsanity.com/paper/1905.04943/) (2019)
- [Learning Human-Object Interactions by Graph Parsing Neural Networks](https://mlsanity.com/paper/1808.07962/) (2018)
- [On the equivalence between graph isomorphism testing and function approximation with GNNs](https://mlsanity.com/paper/1905.12560/) (2019)
- [Stability Properties of Graph Neural Networks](https://mlsanity.com/paper/1905.04497/) (2019)
- [Learning to Drop: Robust Graph Neural Network via Topological Denoising](https://mlsanity.com/paper/2011.07057/) (2020)
- [Graphon Neural Networks and the Transferability of Graph Neural Networks](https://mlsanity.com/paper/2006.03548/) (2020)
- [Convolutional Neural Network Architectures for Signals Supported on Graphs](https://mlsanity.com/paper/1805.00165/) (2018)
- [Graph Neural Networks for Decentralized Multi-Robot Path Planning](https://mlsanity.com/paper/1912.06095/) (2019)
- [Probably Approximately Correct Constrained Learning](https://mlsanity.com/paper/2006.05487/) (2020)
- [Stability of Graph Convolutional Neural Networks to Stochastic Perturbations](https://mlsanity.com/paper/2106.10526/) (2021)
- [Space-Time Graph Neural Networks](https://mlsanity.com/paper/2110.02880/) (2021)

## Built on by (most cited first, 12 of 12)

- [Financial Fraud Detection using Quantum Graph Neural Networks](https://mlsanity.com/paper/2309.01127/) (2023)
- [A Lagrangian Duality Approach to Active Learning](https://mlsanity.com/paper/2202.04108/) (2022)
- [Automatic Data Augmentation via Invariance-Constrained Learning](https://mlsanity.com/paper/2209.15031/) (2022)
- [Robust Graph Neural Networks via Probabilistic Lipschitz Constraints](https://mlsanity.com/paper/2112.07575/) (2021)
- [Sparse Covariance Neural Networks](https://mlsanity.com/paper/2410.01669/) (2024)
- [Stability of Graph Convolutional Neural Networks through the lens of small perturbation analysis](https://mlsanity.com/paper/2312.12934/) (2023)
- [Graph neural networks and non-commuting operators](https://mlsanity.com/paper/2411.04265/) (2024)
- [Learning Globally Smooth Functions on Manifolds](https://mlsanity.com/paper/2210.00301/) (2022)
- [Learning Stable Graph Neural Networks via Spectral Regularization](https://mlsanity.com/paper/2211.06966/) (2022)
- [On the Trade-Off between Stability and Representational Capacity in Graph Neural Networks](https://mlsanity.com/paper/2312.02372/) (2023)
- [Stability of Flow Models for Graph Signals](https://mlsanity.com/paper/2607.07510/) (2026)
- [Graph Learning Should Move Beyond Restrictive Views of Spectral and Message-Passing GNNs](https://mlsanity.com/paper/2602.10031/) (2026)

## Abstract (arXiv)

Graph Neural Networks (GNN) rely on graph convolutions to learn features from network data. GNNs are stable to different types of perturbations of the underlying graph, a property that they inherit from graph filters. In this paper we leverage the stability property of GNNs as a typing point in order to seek for representations that are stable within a distribution. We propose a novel constrained learning approach by imposing a constraint on the stability condition of the GNN within a perturbation of choice. We showcase our framework in real world data, corroborating that we are able to obtain more stable representations while not compromising the overall accuracy of the predictor.