# MONET: Debiasing Graph Embeddings via the Metadata-Orthogonal Training Unit

arXiv: https://arxiv.org/abs/1909.11793 · HTML: https://mlsanity.com/paper/1909.11793/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Sep 2019.

## Built on by (most cited first, 11 of 11)

- [A Comprehensive Survey on Trustworthy Graph Neural Networks: Privacy, Robustness, Fairness, and Explainability](https://mlsanity.com/paper/2204.08570/) (2022)
- [EDITS: Modeling and Mitigating Data Bias for Graph Neural Networks](https://mlsanity.com/paper/2108.05233/) (2021)
- [Fairness in Graph Mining: A Survey](https://mlsanity.com/paper/2204.09888/) (2022)
- [Unbiased Graph Embedding with Biased Graph Observations](https://mlsanity.com/paper/2110.13957/) (2021)
- [A Survey on Fairness for Machine Learning on Graphs](https://mlsanity.com/paper/2205.05396/) (2022)
- [Graph Learning with Localized Neighborhood Fairness](https://mlsanity.com/paper/2212.12040/) (2022)
- [A Benchmark for Fairness-Aware Graph Learning](https://mlsanity.com/paper/2407.12112/) (2024)
- [Fair Graph Machine Learning under Adversarial Missingness Processes](https://mlsanity.com/paper/2311.01591/) (2023)
- [Fairness and/or Privacy on Social Graphs](https://mlsanity.com/paper/2503.02114/) (2025)
- [Self-Attention Based Multi-Scale Graph Auto-Encoder Network of 3D Meshes](https://mlsanity.com/paper/2507.05304/) (2025)
- [Schreier-Coset Graph Rewiring](https://mlsanity.com/paper/2607.27479/) (2026)

## Abstract (arXiv)

Are Graph Neural Networks (GNNs) fair? In many real world graphs, the formation of edges is related to certain node attributes (e.g. gender, community, reputation). In this case, standard GNNs using these edges will be biased by this information, as it is encoded in the structure of the adjacency matrix itself. In this paper, we show that when metadata is correlated with the formation of node neighborhoods, unsupervised node embedding dimensions learn this metadata. This bias implies an inability to control for important covariates in real-world applications, such as recommendation systems. To solve these issues, we introduce the Metadata-Orthogonal Node Embedding Training (MONET) unit, a general model for debiasing embeddings of nodes in a graph. MONET achieves this by ensuring that the node embeddings are trained on a hyperplane orthogonal to that of the node metadata. This effectively organizes unstructured embedding dimensions into an interpretable topology-only, metadata-only division with no linear interactions. We illustrate the effectiveness of MONET though our experiments on a variety of real world graphs, which shows that our method can learn and remove the effect of arbitrary covariates in tasks such as preventing the leakage of political party affiliation in a blog network, and thwarting the gaming of embedding-based recommendation systems.