# Towards a Unified Framework for Fair and Stable Graph Representation Learning

arXiv: https://arxiv.org/abs/2102.13186 · HTML: https://mlsanity.com/paper/2102.13186/

## Key facts

- Cited by 128 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 45 references that are in the map.
- First posted on arXiv 25 Feb 2021.

## Builds on (most cited first, 30 of 31)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [Heterogeneous Graph Transformer](https://mlsanity.com/paper/2003.01332/) (2020)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Fairness in Criminal Justice Risk Assessments: The State of the Art](https://mlsanity.com/paper/1703.09207/) (2017)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Adversarial Attacks on Graph Neural Networks via Meta Learning](https://mlsanity.com/paper/1902.08412/) (2019)
- [Modeling polypharmacy side effects with graph convolutional networks](https://mlsanity.com/paper/1802.00543/) (2018)
- [GNNGuard: Defending Graph Neural Networks against Adversarial Attacks](https://mlsanity.com/paper/2006.08149/) (2020)
- [Compositional Fairness Constraints for Graph Embeddings](https://mlsanity.com/paper/1905.10674/) (2019)
- [Subgraph Neural Networks](https://mlsanity.com/paper/2006.10538/) (2020)
- [From Parity to Preference-based Notions of Fairness in Classification](https://mlsanity.com/paper/1707.00010/) (2017)
- [SkipGNN: Predicting Molecular Interactions with Skip-Graph Networks](https://mlsanity.com/paper/2004.14949/) (2020)
- [Reliable Graph Neural Networks via Robust Aggregation](https://mlsanity.com/paper/2010.15651/) (2020)

## Built on by (most cited first, 30 of 128)

- [A Comprehensive Survey on Trustworthy Graph Neural Networks: Privacy, Robustness, Fairness, and Explainability](https://mlsanity.com/paper/2204.08570/) (2022)
- [Out-Of-Distribution Generalization on Graphs: A Survey](https://mlsanity.com/paper/2202.07987/) (2022)
- [EDITS: Modeling and Mitigating Data Bias for Graph Neural Networks](https://mlsanity.com/paper/2108.05233/) (2021)
- [Trustworthy Graph Neural Networks: Aspects, Methods and Trends](https://mlsanity.com/paper/2205.07424/) (2022)
- [Evaluating Explainability for Graph Neural Networks](https://mlsanity.com/paper/2208.09339/) (2022)
- [Graph Representation Learning in Biomedicine](https://mlsanity.com/paper/2104.04883/) (2021)
- [Fairness in Graph Mining: A Survey](https://mlsanity.com/paper/2204.09888/) (2022)
- [A Comprehensive Survey on Deep Graph Representation Learning](https://mlsanity.com/paper/2304.05055/) (2023)
- [DeAR: Debiasing Vision-Language Models with Additive Residuals](https://mlsanity.com/paper/2303.10431/) (2023)
- [Subgroup Generalization and Fairness of Graph Neural Networks](https://mlsanity.com/paper/2106.15535/) (2021)
- [Improving Fairness in Graph Neural Networks via Mitigating Sensitive Attribute Leakage](https://mlsanity.com/paper/2206.03426/) (2022)
- [Learning Fair Node Representations with Graph Counterfactual Fairness](https://mlsanity.com/paper/2201.03662/) (2022)
- [Rethinking Stability for Attribution-based Explanations](https://mlsanity.com/paper/2203.06877/) (2022)
- [Probing GNN Explainers: A Rigorous Theoretical and Empirical Analysis of GNN Explanation Methods](https://mlsanity.com/paper/2106.09078/) (2021)
- [FMP: Toward Fair Graph Message Passing against Topology Bias](https://mlsanity.com/paper/2202.04187/) (2022)
- [Releasing Graph Neural Networks with Differential Privacy Guarantees](https://mlsanity.com/paper/2109.08907/) (2021)
- [Augmentations in Hypergraph Contrastive Learning: Fabricated and Generative](https://mlsanity.com/paper/2210.03801/) (2022)
- [FairGT: A Fairness-aware Graph Transformer](https://mlsanity.com/paper/2404.17169/) (2024)
- [Unbiased Graph Embedding with Biased Graph Observations](https://mlsanity.com/paper/2110.13957/) (2021)
- [On Generalized Degree Fairness in Graph Neural Networks](https://mlsanity.com/paper/2302.03881/) (2023)
- [Fair Node Representation Learning via Adaptive Data Augmentation](https://mlsanity.com/paper/2201.08549/) (2022)
- [RawlsGCN: Towards Rawlsian Difference Principle on Graph Convolutional Network](https://mlsanity.com/paper/2202.13547/) (2022)
- [The Scales of Justitia: A Comprehensive Survey on Safety Evaluation of LLMs](https://mlsanity.com/paper/2506.11094/) (2025)
- [Towards Fair Graph Neural Networks via Graph Counterfactual](https://mlsanity.com/paper/2307.04937/) (2023)
- [Fairness and Explainability: Bridging the Gap Towards Fair Model Explanations](https://mlsanity.com/paper/2212.03840/) (2022)
- [Counterfactual Learning on Graphs: A Survey](https://mlsanity.com/paper/2304.01391/) (2023)
- [Fairness-Aware Graph Neural Networks: A Survey](https://mlsanity.com/paper/2307.03929/) (2023)
- [Data-centric Graph Learning: A Survey](https://mlsanity.com/paper/2310.04987/) (2023)
- [Fairness Amidst Non-IID Graph Data: A Literature Review](https://mlsanity.com/paper/2202.07170/) (2022)
- [A Survey on Fairness for Machine Learning on Graphs](https://mlsanity.com/paper/2205.05396/) (2022)

## Abstract (arXiv)

As the representations output by Graph Neural Networks (GNNs) are increasingly employed in real-world applications, it becomes important to ensure that these representations are fair and stable. In this work, we establish a key connection between counterfactual fairness and stability and leverage it to propose a novel framework, NIFTY (uNIfying Fairness and stabiliTY), which can be used with any GNN to learn fair and stable representations. We introduce a novel objective function that simultaneously accounts for fairness and stability and develop a layer-wise weight normalization using the Lipschitz constant to enhance neural message passing in GNNs. In doing so, we enforce fairness and stability both in the objective function as well as in the GNN architecture. Further, we show theoretically that our layer-wise weight normalization promotes counterfactual fairness and stability in the resulting representations. We introduce three new graph datasets comprising of high-stakes decisions in criminal justice and financial lending domains. Extensive experimentation with the above datasets demonstrates the efficacy of our framework.