# Spectral Augmentation for Self-Supervised Learning on Graphs

arXiv: https://arxiv.org/abs/2210.00643 · HTML: https://mlsanity.com/paper/2210.00643/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 82 references that are in the map.
- First posted on arXiv 2 Oct 2022.

## Builds on (most cited first, 30 of 54)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [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)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Strategies for Pre-training Graph Neural Networks](https://mlsanity.com/paper/1905.12265/) (2019)
- [What Makes for Good Views for Contrastive Learning?](https://mlsanity.com/paper/2005.10243/) (2020)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Contrastive Multi-View Representation Learning on Graphs](https://mlsanity.com/paper/2006.05582/) (2020)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Deep Graph Contrastive Representation Learning](https://mlsanity.com/paper/2006.04131/) (2020)
- [Graph Contrastive Learning with Adaptive Augmentation](https://mlsanity.com/paper/2010.14945/) (2020)
- [GCC: Graph Contrastive Coding for Graph Neural Network Pre-Training](https://mlsanity.com/paper/2006.09963/) (2020)
- [InfoGraph: Unsupervised and Semi-supervised Graph-Level Representation Learning via Mutual Information Maximization](https://mlsanity.com/paper/1908.01000/) (2019)
- [Parameterized Explainer for Graph Neural Network](https://mlsanity.com/paper/2011.04573/) (2020)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)

## Built on by (most cited first, 30 of 39)

- [Data-centric Graph Learning: A Survey](https://mlsanity.com/paper/2310.04987/) (2023)
- [Embedding in Recommender Systems: A Survey](https://mlsanity.com/paper/2310.18608/) (2023)
- [Road Network Representation Learning with the Third Law of Geography](https://mlsanity.com/paper/2406.04038/) (2024)
- [A Survey on Self-Supervised Graph Foundation Models: Knowledge-Based Perspective](https://mlsanity.com/paper/2403.16137/) (2024)
- [Architecture Matters: Uncovering Implicit Mechanisms in Graph Contrastive Learning](https://mlsanity.com/paper/2311.02687/) (2023)
- [Hierarchical Topology Isomorphism Expertise Embedded Graph Contrastive Learning](https://mlsanity.com/paper/2312.14222/) (2023)
- [Graph Contrastive Learning with Cohesive Subgraph Awareness](https://mlsanity.com/paper/2401.17580/) (2024)
- [A Pure Transformer Pretraining Framework on Text-attributed Graphs](https://mlsanity.com/paper/2406.13873/) (2024)
- [Improving Expressive Power of Spectral Graph Neural Networks with Eigenvalue Correction](https://mlsanity.com/paper/2401.15603/) (2024)
- [Spectral-Aware Augmentation for Enhanced Graph Representation Learning](https://mlsanity.com/paper/2310.13845/) (2023)
- [Community-Invariant Graph Contrastive Learning](https://mlsanity.com/paper/2405.01350/) (2024)
- [Globally Interpretable Graph Learning via Distribution Matching](https://mlsanity.com/paper/2306.10447/) (2023)
- [Perfect Alignment May be Poisonous to Graph Contrastive Learning](https://mlsanity.com/paper/2310.03977/) (2023)
- [DropEdge not Foolproof: Effective Augmentation Method for Signed Graph Neural Networks](https://mlsanity.com/paper/2409.19620/) (2024)
- [MolEmb: Multimodal Large Language Models Can Be Strong Molecular Embedding Models](https://mlsanity.com/paper/2608.23646/) (2026)
- [Through the Dual-Prism: A Spectral Perspective on Graph Data Augmentation for Graph Classification](https://mlsanity.com/paper/2401.09953/) (2024)
- [Revisiting Edge Perturbation for Graph Neural Network in Graph Data Augmentation and Attack](https://mlsanity.com/paper/2403.07943/) (2024)
- [AugWard: Augmentation-Aware Representation Learning for Accurate Graph Classification](https://mlsanity.com/paper/2503.21105/) (2025)
- [Principled Data Augmentation for Learning to Solve Quadratic Programming Problems](https://mlsanity.com/paper/2506.01728/) (2025)
- [Self-supervision meets kernel graph neural models: From architecture to augmentations](https://mlsanity.com/paper/2310.11281/) (2023)
- [Graph Contrastive Learning with Low-Rank Regularization and Low-Rank Attention for Noisy Node Classification](https://mlsanity.com/paper/2402.09600/) (2024)
- [Rethinking Spectral Augmentation for Contrast-based Graph Self-Supervised Learning](https://mlsanity.com/paper/2405.19600/) (2024)
- [Data Augmentation in Graph Neural Networks: The Role of Generated Synthetic Graphs](https://mlsanity.com/paper/2407.14765/) (2024)
- [Exploring Consistency in Graph Representations:from Graph Kernels to Graph Neural Networks](https://mlsanity.com/paper/2410.23748/) (2024)
- [Graph Community Augmentation with GMM-based Modeling in Latent Space](https://mlsanity.com/paper/2412.01163/) (2024)
- [Edge Contrastive Learning: An Augmentation-Free Graph Contrastive Learning Model](https://mlsanity.com/paper/2412.11075/) (2024)
- [Graph Self-Supervised Learning with Learnable Structural and Positional Encodings](https://mlsanity.com/paper/2502.16233/) (2025)
- [Robust Graph Contrastive Learning with Information Restoration](https://mlsanity.com/paper/2307.12555/) (2023)
- [Hodge-Aware Contrastive Learning](https://mlsanity.com/paper/2309.07364/) (2023)
- [Balancing Augmentation with Edge-Utility Filter for Signed GNNs](https://mlsanity.com/paper/2310.16862/) (2023)

## Abstract (arXiv)

Graph contrastive learning (GCL), as an emerging self-supervised learning technique on graphs, aims to learn representations via instance discrimination. Its performance heavily relies on graph augmentation to reflect invariant patterns that are robust to small perturbations; yet it still remains unclear about what graph invariance GCL should capture. Recent studies mainly perform topology augmentations in a uniformly random manner in the spatial domain, ignoring its influence on the intrinsic structural properties embedded in the spectral domain. In this work, we aim to find a principled way for topology augmentations by exploring the invariance of graphs from the spectral perspective. We develop spectral augmentation which guides topology augmentations by maximizing the spectral change. Extensive experiments on both graph and node classification tasks demonstrate the effectiveness of our method in self-supervised representation learning. The proposed method also brings promising generalization capability in transfer learning, and is equipped with intriguing robustness property under adversarial attacks. Our study sheds light on a general principle for graph topology augmentation.