# Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networks

arXiv: https://arxiv.org/abs/2107.10234 · HTML: https://mlsanity.com/paper/2107.10234/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 151 of its 287 references that are in the map.
- First posted on arXiv 21 Jul 2021.

## Builds on (most cited first, 30 of 151)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translation](https://mlsanity.com/paper/1609.08144/) (2016)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [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)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Effective Approaches to Attention-based Neural Machine Translation](https://mlsanity.com/paper/1508.04025/) (2015)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)

## Built on by (most cited first, 19 of 19)

- [Parallel and Distributed Graph Neural Networks: An In-Depth Concurrency Analysis](https://mlsanity.com/paper/2205.09702/) (2022)
- [Learn from Global Correlations: Enhancing Evolutionary Algorithm via Spectral GNN](https://mlsanity.com/paper/2412.17629/) (2024)
- [A Survey on Graph Condensation](https://mlsanity.com/paper/2402.02000/) (2024)
- [A Comprehensive Benchmark on Spectral GNNs: The Impact on Efficiency, Memory, and Effectiveness](https://mlsanity.com/paper/2406.09675/) (2024)
- [Rethinking Spectral Graph Neural Networks with Spatially Adaptive Filtering](https://mlsanity.com/paper/2401.09071/) (2024)
- [Demystifying Higher-Order Graph Neural Networks](https://mlsanity.com/paper/2406.12841/) (2024)
- [Tackling Size Generalization of Graph Neural Networks on Biological Data from a Spectral Perspective](https://mlsanity.com/paper/2305.15611/) (2023)
- [Transfer Entropy in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2406.06632/) (2024)
- [Rethinking Over-Smoothing in Graph Neural Networks: A Perspective from Anderson Localization](https://mlsanity.com/paper/2507.05263/) (2025)
- [Spatio-Temporal Graph Structure Learning for Earthquake Detection](https://mlsanity.com/paper/2503.11215/) (2025)
- [Convexified Message-Passing Graph Neural Networks](https://mlsanity.com/paper/2505.18289/) (2025)
- [Learning from Heterophilic Graphs: A Spectral Theory Perspective on the Impact of Self-Loops and Parallel Edges](https://mlsanity.com/paper/2509.13139/) (2025)
- [Rethinking Graph Domain Adaptation: A Spectral Contrastive Perspective](https://mlsanity.com/paper/2510.13254/) (2025)
- [How Do Graph Signals Affect Recommendation: Unveiling the Mystery of Low and High-Frequency Graph Signals](https://mlsanity.com/paper/2512.15744/) (2025)
- [Multi-Head Spectral-Adaptive Graph Anomaly Detection](https://mlsanity.com/paper/2512.22291/) (2025)
- [Graph Learning Should Move Beyond Restrictive Views of Spectral and Message-Passing GNNs](https://mlsanity.com/paper/2602.10031/) (2026)
- [AdvSynGNN: Structure-Adaptive Graph Neural Nets via Adversarial Synthesis and Self-Corrective Propagation](https://mlsanity.com/paper/2602.17071/) (2026)
- [Delving into Non-Exchangeability for Conformal Prediction in Graph-Structured Multivariate Time Series](https://mlsanity.com/paper/2605.04957/) (2026)
- [PANDA: Prior-guided Attentional Dual-path Architecture](https://mlsanity.com/paper/2610.13635/) (2026)

## Abstract (arXiv)

Deep learning's performance has been extensively recognized recently. Graph neural networks (GNNs) are designed to deal with graph-structural data that classical deep learning does not easily manage. Since most GNNs were created using distinct theories, direct comparisons are impossible. Prior research has primarily concentrated on categorizing existing models, with little attention paid to their intrinsic connections. The purpose of this study is to establish a unified framework that integrates GNNs based on spectral graph and approximation theory. The framework incorporates a strong integration between spatial- and spectral-based GNNs while tightly associating approaches that exist within each respective domain.