# Learnable Spectral Wavelets on Dynamic Graphs to Capture Global Interactions

arXiv: https://arxiv.org/abs/2211.11979 · HTML: https://mlsanity.com/paper/2211.11979/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 44 references that are in the map.
- First posted on arXiv 22 Nov 2022.

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs](https://mlsanity.com/paper/1902.10191/) (2019)
- [Bottleneck Transformers for Visual Recognition](https://mlsanity.com/paper/2101.11605/) (2021)
- [Do Transformers Really Perform Bad for Graph Representation?](https://mlsanity.com/paper/2106.05234/) (2021)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [Representation Learning for Dynamic Graphs: A Survey](https://mlsanity.com/paper/1905.11485/) (2019)
- [CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters](https://mlsanity.com/paper/1705.07664/) (2017)
- [Representing Long-Range Context for Graph Neural Networks with Global Attention](https://mlsanity.com/paper/2201.08821/) (2022)
- [Vision GNN: An Image is Worth Graph of Nodes](https://mlsanity.com/paper/2206.00272/) (2022)
- [EquiBind: Geometric Deep Learning for Drug Binding Structure Prediction](https://mlsanity.com/paper/2202.05146/) (2022)
- [Graph Wavelet Neural Network](https://mlsanity.com/paper/1904.07785/) (2019)
- [DynGEM: Deep Embedding Method for Dynamic Graphs](https://mlsanity.com/paper/1805.11273/) (2018)
- [Learnable Fourier Features for Multi-Dimensional Spatial Positional Encoding](https://mlsanity.com/paper/2106.02795/) (2021)
- [dyngraph2vec: Capturing Network Dynamics using Dynamic Graph Representation Learning](https://mlsanity.com/paper/1809.02657/) (2018)
- [Dynamic Graph Convolutional Networks](https://mlsanity.com/paper/1704.06199/) (2017)
- [A Survey on Graph Representation Learning Methods](https://mlsanity.com/paper/2204.01855/) (2022)
- [A New Perspective on the Effects of Spectrum in Graph Neural Networks](https://mlsanity.com/paper/2112.07160/) (2021)
- [How Expressive are Transformers in Spectral Domain for Graphs?](https://mlsanity.com/paper/2201.09332/) (2022)
- [DynG2G: An Efficient Stochastic Graph Embedding Method for Temporal Graphs](https://mlsanity.com/paper/2109.13441/) (2021)
- [Learning to Evolve on Dynamic Graphs](https://mlsanity.com/paper/2111.07032/) (2021)

## Built on by (most cited first, 10 of 10)

- [A Comprehensive Survey of Dynamic Graph Neural Networks: Models, Frameworks, Benchmarks, Experiments and Challenges](https://mlsanity.com/paper/2405.00476/) (2024)
- [Spectral Invariant Learning for Dynamic Graphs under Distribution Shifts](https://mlsanity.com/paper/2403.05026/) (2024)
- [FUGNN: Harmonizing Fairness and Utility in Graph Neural Networks](https://mlsanity.com/paper/2405.17034/) (2024)
- [EasyDGL: Encode, Train and Interpret for Continuous-time Dynamic Graph Learning](https://mlsanity.com/paper/2303.12341/) (2023)
- [A General Graph Spectral Wavelet Convolution via Chebyshev Order Decomposition](https://mlsanity.com/paper/2405.13806/) (2024)
- [Beyond Spatio-Temporal Representations: Evolving Fourier Transform for Temporal Graphs](https://mlsanity.com/paper/2402.16078/) (2024)
- [GLADformer: A Mixed Perspective for Graph-level Anomaly Detection](https://mlsanity.com/paper/2406.00734/) (2024)
- [Evidential Spectrum-Aware Contrastive Learning for OOD Detection in Dynamic Graphs](https://mlsanity.com/paper/2506.07417/) (2025)
- [Long-Range Graph Wavelet Networks](https://mlsanity.com/paper/2509.06743/) (2025)
- [Dynamic Spectral Filtering for Temporal Graph Learning: Learning Evolving Propagation Operators](https://mlsanity.com/paper/2607.27891/) (2026)

## Abstract (arXiv)

Learning on evolving(dynamic) graphs has caught the attention of researchers as static methods exhibit limited performance in this setting. The existing methods for dynamic graphs learn spatial features by local neighborhood aggregation, which essentially only captures the low pass signals and local interactions. In this work, we go beyond current approaches to incorporate global features for effectively learning representations of a dynamically evolving graph. We propose to do so by capturing the spectrum of the dynamic graph. Since static methods to learn the graph spectrum would not consider the history of the evolution of the spectrum as the graph evolves with time, we propose a novel approach to learn the graph wavelets to capture this evolving spectra. Further, we propose a framework that integrates the dynamically captured spectra in the form of these learnable wavelets into spatial features for incorporating local and global interactions. Experiments on eight standard datasets show that our method significantly outperforms related methods on various tasks for dynamic graphs.