# ASWT-SGNN: Adaptive Spectral Wavelet Transform-based Self-Supervised Graph Neural Network

arXiv: https://arxiv.org/abs/2312.05736 · HTML: https://mlsanity.com/paper/2312.05736/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 49 references that are in the map.
- First posted on arXiv 10 Dec 2023.

## Builds on (most cited first, 27 of 27)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [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)
- [Graph Contrastive Learning with Adaptive Augmentation](https://mlsanity.com/paper/2010.14945/) (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)
- [Adversarial Graph Augmentation to Improve Graph Contrastive Learning](https://mlsanity.com/paper/2106.05819/) (2021)
- [Self-Supervised Learning of Graph Neural Networks: A Unified Review](https://mlsanity.com/paper/2102.10757/) (2021)
- [Graph Neural Tangent Kernel: Fusing Graph Neural Networks with Graph Kernels](https://mlsanity.com/paper/1905.13192/) (2019)
- [From Canonical Correlation Analysis to Self-supervised Graph Neural Networks](https://mlsanity.com/paper/2106.12484/) (2021)
- [Graph Wavelet Neural Network](https://mlsanity.com/paper/1904.07785/) (2019)
- [Semi-Implicit Graph Variational Auto-Encoders](https://mlsanity.com/paper/1908.07078/) (2019)
- [Accelerating Training and Inference of Graph Neural Networks with Fast Sampling and Pipelining](https://mlsanity.com/paper/2110.08450/) (2021)
- [Accurate, Efficient and Scalable Graph Embedding](https://mlsanity.com/paper/1810.11899/) (2018)
- [Multi-Label Graph Convolutional Network Representation Learning](https://mlsanity.com/paper/1912.11757/) (2019)

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

- [SSTAG: Structure-Aware Self-Supervised Learning Method for Text-Attributed Graphs](https://mlsanity.com/paper/2510.01248/) (2025)
- [AS-GCL: Asymmetric Spectral Augmentation on Graph Contrastive Learning](https://mlsanity.com/paper/2502.13525/) (2025)
- [Multi-Modal Molecular Representation Learning via Structure Awareness](https://mlsanity.com/paper/2505.05877/) (2025)
- [Long-Range Graph Wavelet Networks](https://mlsanity.com/paper/2509.06743/) (2025)
- [InductWave: Inductive Multi-Hop Logical Query Answering on Knowledge Graphs](https://mlsanity.com/paper/2607.07422/) (2026)

## Abstract (arXiv)

Graph Comparative Learning (GCL) is a self-supervised method that combines the advantages of Graph Convolutional Networks (GCNs) and comparative learning, making it promising for learning node representations. However, the GCN encoders used in these methods rely on the Fourier transform to learn fixed graph representations, which is inherently limited by the uncertainty principle involving spatial and spectral localization trade-offs. To overcome the inflexibility of existing methods and the computationally expensive eigen-decomposition and dense matrix multiplication, this paper proposes an Adaptive Spectral Wavelet Transform-based Self-Supervised Graph Neural Network (ASWT-SGNN). The proposed method employs spectral adaptive polynomials to approximate the filter function and optimize the wavelet using contrast loss. This design enables the creation of local filters in both spectral and spatial domains, allowing flexible aggregation of neighborhood information at various scales and facilitating controlled transformation between local and global information. Compared to existing methods, the proposed approach reduces computational complexity and addresses the limitation of graph convolutional neural networks, which are constrained by graph size and lack flexible control over the neighborhood aspect. Extensive experiments on eight benchmark datasets demonstrate that ASWT-SGNN accurately approximates the filter function in high-density spectral regions, avoiding costly eigen-decomposition. Furthermore, ASWT-SGNN achieves comparable performance to state-of-the-art models in node classification tasks.