# Negative-Free Self-Supervised Gaussian Embedding of Graphs

arXiv: https://arxiv.org/abs/2411.01157 · HTML: https://mlsanity.com/paper/2411.01157/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 47 references that are in the map.
- First posted on arXiv 2 Nov 2024.

## Builds on (most cited first, 30 of 38)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Contrastive Multi-View Representation Learning on Graphs](https://mlsanity.com/paper/2006.05582/) (2020)
- [Deep Graph Contrastive Representation Learning](https://mlsanity.com/paper/2006.04131/) (2020)
- [A Theoretical Analysis of Contrastive Unsupervised Representation Learning](https://mlsanity.com/paper/1902.09229/) (2019)
- [Graph Contrastive Learning with Adaptive Augmentation](https://mlsanity.com/paper/2010.14945/) (2020)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Understanding Dimensional Collapse in Contrastive Self-supervised Learning](https://mlsanity.com/paper/2110.09348/) (2021)
- [Graph Self-Supervised Learning: A Survey](https://mlsanity.com/paper/2103.00111/) (2021)
- [Whitening for Self-Supervised Representation Learning](https://mlsanity.com/paper/2007.06346/) (2020)
- [Wiki-CS: A Wikipedia-Based Benchmark for Graph Neural Networks](https://mlsanity.com/paper/2007.02901/) (2020)
- [Graph Representation Learning via Graphical Mutual Information Maximization](https://mlsanity.com/paper/2002.01169/) (2020)
- [Large-Scale Representation Learning on Graphs via Bootstrapping](https://mlsanity.com/paper/2102.06514/) (2021)
- [From Canonical Correlation Analysis to Self-supervised Graph Neural Networks](https://mlsanity.com/paper/2106.12484/) (2021)
- [Augmentation-Free Self-Supervised Learning on Graphs](https://mlsanity.com/paper/2112.02472/) (2021)
- [Graph Barlow Twins: A self-supervised representation learning framework for graphs](https://mlsanity.com/paper/2106.02466/) (2021)
- [A Comprehensive Survey on Deep Graph Representation Learning](https://mlsanity.com/paper/2304.05055/) (2023)
- [Multi-Scale Contrastive Siamese Networks for Self-Supervised Graph Representation Learning](https://mlsanity.com/paper/2105.05682/) (2021)
- [Rethinking and Scaling Up Graph Contrastive Learning: An Extremely Efficient Approach with Group Discrimination](https://mlsanity.com/paper/2206.01535/) (2022)
- [COSTA: Covariance-Preserving Feature Augmentation for Graph Contrastive Learning](https://mlsanity.com/paper/2206.04726/) (2022)
- [Learning with Hyperspherical Uniformity](https://mlsanity.com/paper/2103.01649/) (2021)

## Built on by (most cited first, 5 of 5)

- [Bridging Academia and Industry: A Comprehensive Benchmark for Attributed Graph Clustering](https://mlsanity.com/paper/2602.08519/) (2026)
- [Learning Hierarchical Knowledge in Text-Rich Networks with Taxonomy-Informed Representation Learning](https://mlsanity.com/paper/2603.08159/) (2026)
- [Beyond the Academic Monoculture: A Unified Framework and Industrial Perspective for Attributed Graph Clustering](https://mlsanity.com/paper/2603.20829/) (2026)
- [Towards Anomaly-Aware Pre-Training and Fine-Tuning for Graph Anomaly Detection](https://mlsanity.com/paper/2504.14250/) (2025)
- [Self-Supervised Graph Learning via Spectral Bootstrapping and Laplacian-Based Augmentations](https://mlsanity.com/paper/2506.20362/) (2025)

## Abstract (arXiv)

Graph Contrastive Learning (GCL) has recently emerged as a promising graph self-supervised learning framework for learning discriminative node representations without labels. The widely adopted objective function of GCL benefits from two key properties: alignment and uniformity, which align representations of positive node pairs while uniformly distributing all representations on the hypersphere. The uniformity property plays a critical role in preventing representation collapse and is achieved by pushing apart augmented views of different nodes (negative pairs). As such, existing GCL methods inherently rely on increasing the quantity and quality of negative samples, resulting in heavy computational demands, memory overhead, and potential class collision issues. In this study, we propose a negative-free objective to achieve uniformity, inspired by the fact that points distributed according to a normalized isotropic Gaussian are uniformly spread across the unit hypersphere. Therefore, we can minimize the distance between the distribution of learned representations and the isotropic Gaussian distribution to promote the uniformity of node representations. Our method also distinguishes itself from other approaches by eliminating the need for a parameterized mutual information estimator, an additional projector, asymmetric structures, and, crucially, negative samples. Extensive experiments over seven graph benchmarks demonstrate that our proposal achieves competitive performance with fewer parameters, shorter training times, and lower memory consumption compared to existing GCL methods.