# Norm Augmented Graph AutoEncoders for Link Prediction

arXiv: https://arxiv.org/abs/2502.05868 · HTML: https://mlsanity.com/paper/2502.05868/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 30 references that are in the map.
- First posted on arXiv 9 Feb 2025.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [Hyperspherical Variational Auto-Encoders](https://mlsanity.com/paper/1804.00891/) (2018)
- [Neo-GNNs: Neighborhood Overlap-aware Graph Neural Networks for Link Prediction](https://mlsanity.com/paper/2206.04216/) (2022)
- [Cold Brew: Distilling Graph Node Representations with Incomplete or Missing Neighborhoods](https://mlsanity.com/paper/2111.04840/) (2021)
- [Linkless Link Prediction via Relational Distillation](https://mlsanity.com/paper/2210.05801/) (2022)
- [Variational Graph Normalized Auto-Encoders](https://mlsanity.com/paper/2108.08046/) (2021)
- [On Generalized Degree Fairness in Graph Neural Networks](https://mlsanity.com/paper/2302.03881/) (2023)
- [Bring Your Own View: Graph Neural Networks for Link Prediction with Personalized Subgraph Selection](https://mlsanity.com/paper/2212.12488/) (2022)
- [Simple and Effective Graph Autoencoders with One-Hop Linear Models](https://mlsanity.com/paper/2001.07614/) (2020)
- [ResNorm: Tackling Long-tailed Degree Distribution Issue in Graph Neural Networks via Normalization](https://mlsanity.com/paper/2206.08181/) (2022)
- [Challenging Low Homophily in Social Recommendation](https://mlsanity.com/paper/2401.14606/) (2024)
- [Disconnected Emerging Knowledge Graph Oriented Inductive Link Prediction](https://mlsanity.com/paper/2209.01397/) (2022)
- [Deepened Graph Auto-Encoders Help Stabilize and Enhance Link Prediction](https://mlsanity.com/paper/2103.11414/) (2021)

## Built on by (most cited first, 2 of 2)

- [Beyond the Academic Monoculture: A Unified Framework and Industrial Perspective for Attributed Graph Clustering](https://mlsanity.com/paper/2603.20829/) (2026)
- [Model Merging: Foundations and Algorithms](https://mlsanity.com/paper/2605.01580/) (2026)

## Abstract (arXiv)

Link Prediction (LP) is a crucial problem in graph-structured data. Graph Neural Networks (GNNs) have gained prominence in LP, with Graph AutoEncoders (GAEs) being a notable representation. However, our empirical findings reveal that GAEs' LP performance suffers heavily from the long-tailed node degree distribution, i.e., low-degree nodes tend to exhibit inferior LP performance compared to high-degree nodes. What causes this degree-related bias, and how can it be mitigated? In this study, we demonstrate that the norm of node embeddings learned by GAEs exhibits variation among nodes with different degrees, underscoring its central significance in influencing the final performance of LP. Specifically, embeddings with larger norms tend to guide the decoder towards predicting higher scores for positive links and lower scores for negative links, thereby contributing to superior performance. This observation motivates us to improve GAEs' LP performance on low-degree nodes by increasing their embedding norms, which can be implemented simply yet effectively by introducing additional self-loops into the training objective for low-degree nodes. This norm augmentation strategy can be seamlessly integrated into existing GAE methods with light computational cost. Extensive experiments on various datasets and GAE methods show the superior performance of norm-augmented GAEs.