# Spectral Neural Graph Sparsification

arXiv: https://arxiv.org/abs/2510.27474 · HTML: https://mlsanity.com/paper/2510.27474/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 51 references that are in the map.
- First posted on arXiv 31 Oct 2025.

## Builds on (most cited first, 23 of 23)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [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)
- [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)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Training robust neural networks using Lipschitz bounds](https://mlsanity.com/paper/2005.02929/) (2020)
- [A Comprehensive Survey on Graph Reduction: Sparsification, Coarsening, and Condensation](https://mlsanity.com/paper/2402.03358/) (2024)
- [Demystifying Graph Sparsification Algorithms in Graph Properties Preservation](https://mlsanity.com/paper/2311.12314/) (2023)
- [On the Ability of Graph Neural Networks to Model Interactions Between Vertices](https://mlsanity.com/paper/2211.16494/) (2022)
- [Network Backboning with Noisy Data](https://mlsanity.com/paper/1701.07336/) (2017)
- [Principle of Relevant Information for Graph Sparsification](https://mlsanity.com/paper/2206.00118/) (2022)
- [Single Pass Spectral Sparsification in Dynamic Streams](https://mlsanity.com/paper/1407.1289/) (2014)
- [Graph Sparsification with Generative Adversarial Network](https://mlsanity.com/paper/2009.11736/) (2020)
- [The Impact of Projection and Backboning on Network Topologies](https://mlsanity.com/paper/1906.09081/) (2019)
- [Weight Thresholding on Complex Networks](https://mlsanity.com/paper/1806.07479/) (2018)

## Built on by (most cited first, 2 of 2)

- [Generative Myopia: Why Diffusion Models Fail at Structure](https://mlsanity.com/paper/2511.18593/) (2025)
- [Scaffold: Support Graph Theory Based Sparsification for Graph Neural Networks](https://mlsanity.com/paper/2609.31466/) (2026)

## Abstract (arXiv)

Graphs are central to modeling complex systems in domains such as social networks, molecular chemistry, and neuroscience. While Graph Neural Networks, particularly Graph Convolutional Networks, have become standard tools for graph learning, they remain constrained by reliance on fixed structures and susceptibility to over-smoothing. We propose the Spectral Preservation Network, a new framework for graph representation learning that generates reduced graphs serving as faithful proxies of the original, enabling downstream tasks such as community detection, influence propagation, and information diffusion at a reduced computational cost. The Spectral Preservation Network introduces two key components: the Joint Graph Evolution layer and the Spectral Concordance loss. The former jointly transforms both the graph topology and the node feature matrix, allowing the structure and attributes to evolve adaptively across layers and overcoming the rigidity of static neighborhood aggregation. The latter regularizes these transformations by enforcing consistency in both the spectral properties of the graph and the feature vectors of the nodes. We evaluate the effectiveness of Spectral Preservation Network on node-level sparsification by analyzing well-established metrics and benchmarking against state-of-the-art methods. The experimental results demonstrate the superior performance and clear advantages of our approach.