# Beyond Spatio-Temporal Representations: Evolving Fourier Transform for Temporal Graphs

arXiv: https://arxiv.org/abs/2402.16078 · HTML: https://mlsanity.com/paper/2402.16078/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 60 references that are in the map.
- First posted on arXiv 25 Feb 2024.

## Builds on (most cited first, 30 of 35)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Spatial Temporal Graph Convolutional Networks for Skeleton-Based Action Recognition](https://mlsanity.com/paper/1801.07455/) (2018)
- [Self-Attentive Sequential Recommendation](https://mlsanity.com/paper/1808.09781/) (2018)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Temporal Graph Networks for Deep Learning on Dynamic Graphs](https://mlsanity.com/paper/2006.10637/) (2020)
- [Personalized Top-N Sequential Recommendation via Convolutional Sequence Embedding](https://mlsanity.com/paper/1809.07426/) (2018)
- [Inductive Representation Learning on Temporal Graphs](https://mlsanity.com/paper/2002.07962/) (2020)
- [EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs](https://mlsanity.com/paper/1902.10191/) (2019)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Session-based Recommendation with Graph Neural Networks](https://mlsanity.com/paper/1811.00855/) (2018)
- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (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)
- [How Powerful are Spectral Graph Neural Networks](https://mlsanity.com/paper/2205.11172/) (2022)
- [Recurrent Neural Networks with Top-k Gains for Session-based Recommendations](https://mlsanity.com/paper/1706.03847/) (2017)
- [Temporal Graph Benchmark for Machine Learning on Temporal Graphs](https://mlsanity.com/paper/2307.01026/) (2023)
- [DynGEM: Deep Embedding Method for Dynamic Graphs](https://mlsanity.com/paper/1805.11273/) (2018)
- [Hierarchical Gating Networks for Sequential Recommendation](https://mlsanity.com/paper/1906.09217/) (2019)
- [Filter-enhanced MLP is All You Need for Sequential Recommendation](https://mlsanity.com/paper/2202.13556/) (2022)
- [Streaming Graph Neural Networks](https://mlsanity.com/paper/1810.10627/) (2018)
- [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)
- [Dynamic Graph Neural Networks for Sequential Recommendation](https://mlsanity.com/paper/2104.07368/) (2021)
- [GC-LSTM: Graph Convolution Embedded LSTM for Dynamic Link Prediction](https://mlsanity.com/paper/1812.04206/) (2018)
- [Dynamic Graph Collaborative Filtering](https://mlsanity.com/paper/2101.02844/) (2021)
- [A Time-Vertex Signal Processing Framework](https://mlsanity.com/paper/1705.02307/) (2017)
- [Spatio-Temporal Graph Scattering Transform](https://mlsanity.com/paper/2012.03363/) (2020)
- [How Expressive are Transformers in Spectral Domain for Graphs?](https://mlsanity.com/paper/2201.09332/) (2022)

## Built on by (most cited first, 3 of 3)

- [Beyond Grid Data: Exploring Graph Neural Networks for Earth Observation](https://mlsanity.com/paper/2411.03223/) (2024)
- [A Dynamic Stiefel Graph Neural Network for Efficient Spatio-Temporal Time Series Forecasting](https://mlsanity.com/paper/2506.00798/) (2025)
- [Dynamic Spectral Filtering for Temporal Graph Learning: Learning Evolving Propagation Operators](https://mlsanity.com/paper/2607.27891/) (2026)

## Abstract (arXiv)

We present the Evolving Graph Fourier Transform (EFT), the first invertible spectral transform that captures evolving representations on temporal graphs. We motivate our work by the inadequacy of existing methods for capturing the evolving graph spectra, which are also computationally expensive due to the temporal aspect along with the graph vertex domain. We view the problem as an optimization over the Laplacian of the continuous time dynamic graph. Additionally, we propose pseudo-spectrum relaxations that decompose the transformation process, making it highly computationally efficient. The EFT method adeptly captures the evolving graph's structural and positional properties, making it effective for downstream tasks on evolving graphs. Hence, as a reference implementation, we develop a simple neural model induced with EFT for capturing evolving graph spectra. We empirically validate our theoretical findings on a number of large-scale and standard temporal graph benchmarks and demonstrate that our model achieves state-of-the-art performance.