mlsanityData to 7 Oct 2026

Training Stable Graph Neural Networks Through Constrained Learning

arXiv 2110.03576 ↗First posted 7 Oct 2021cs.LG eess.SPcited by 12

Not on the map. Why?

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.

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

Builds on

16 of 23 references.

References · 16

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2021Convex optimizationcited by 2,479
  3. 2018Graph Neural Networks: A Review of Methods and Applicationscited by 1,571
  4. 2015Convolutional Networks on Graphs for Learning Molecular Fingerprintscited by 751
  5. 2020Graph Structure Learning for Robust Graph Neural Networkscited by 368
  6. 2019Universal Invariant and Equivariant Graph Neural Networkscited by 182
  7. 2018Learning Human-Object Interactions by Graph Parsing Neural Networkscited by 176
  8. 2019On the equivalence between graph isomorphism testing and function approximation with GNNscited by 172
  9. 2020Learning to Drop: Robust Graph Neural Network via Topological Denoisingcited by 127
  10. 2019Stability Properties of Graph Neural Networkscited by 125
  11. 2020Graphon Neural Networks and the Transferability of Graph Neural Networkscited by 117
  12. 2018Convolutional Neural Network Architectures for Signals Supported on Graphscited by 94
4 more
  1. 2019Graph Neural Networks for Decentralized Multi-Robot Path Planningcited by 84
  2. 2020Probably Approximately Correct Constrained Learningcited by 47
  3. 2021Stability of Graph Convolutional Neural Networks to Stochastic Perturbationscited by 18
  4. 2021Space-Time Graph Neural Networkscited by 10

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 4; 2023: 3; 2024: 2; 2025: 0; 2026: 2.

12 papers.

  1. 2023Financial Fraud Detection using Quantum Graph Neural Networkscited by 35
  2. 2022A Lagrangian Duality Approach to Active Learningcited by 24
  3. 2022Automatic Data Augmentation via Invariance-Constrained Learningcited by 17
  4. 2021Robust Graph Neural Networks via Probabilistic Lipschitz Constraintscited by 10
  5. 2024Sparse Covariance Neural Networkscited by 6
  6. 2023Stability of Graph Convolutional Neural Networks through the lens of small perturbation analysiscited by 5
  7. 2024Graph neural networks and non-commuting operatorscited by 5
  8. 2022Learning Globally Smooth Functions on Manifoldscited by 4
  9. 2022Learning Stable Graph Neural Networks via Spectral Regularizationcited by 4
  10. 2023On the Trade-Off between Stability and Representational Capacity in Graph Neural Networkscited by 2
  11. 2026Stability of Flow Models for Graph Signalscited by 1
  12. 2026Graph Learning Should Move Beyond Restrictive Views of Spectral and Message-Passing GNNscited by 0