# Geometry-Aware Spiking Graph Neural Network

arXiv: https://arxiv.org/abs/2508.06793 · HTML: https://mlsanity.com/paper/2508.06793/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 39 references that are in the map.
- First posted on arXiv 9 Aug 2025.

## Builds on (most cited first, 21 of 21)

- [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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Analyzing Learned Molecular Representations for Property Prediction](https://mlsanity.com/paper/1904.01561/) (2019)
- [Deep Learning in Spiking Neural Networks](https://mlsanity.com/paper/1804.08150/) (2018)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Constant Curvature Graph Convolutional Networks](https://mlsanity.com/paper/1911.05076/) (2019)
- [Fully Hyperbolic Neural Networks](https://mlsanity.com/paper/2105.14686/) (2021)
- [Merging Multi-Task Models via Weight-Ensembling Mixture of Experts](https://mlsanity.com/paper/2402.00433/) (2024)
- [How would Stance Detection Techniques Evolve after the Launch of ChatGPT?](https://mlsanity.com/paper/2212.14548/) (2022)
- [A Survey of Graph Neural Networks in Real world: Imbalance, Noise, Privacy and OOD Challenges](https://mlsanity.com/paper/2403.04468/) (2024)
- [Gradient Descent for Spiking Neural Networks](https://mlsanity.com/paper/1706.04698/) (2017)
- [CoCo: A Coupled Contrastive Framework for Unsupervised Domain Adaptive Graph Classification](https://mlsanity.com/paper/2306.04979/) (2023)
- [Exploiting Spiking Dynamics with Spatial-temporal Feature Normalization in Graph Learning](https://mlsanity.com/paper/2107.06865/) (2021)
- [SA-GDA: Spectral Augmentation for Graph Domain Adaptation](https://mlsanity.com/paper/2408.09189/) (2024)
- [Spiking Graph Neural Network on Riemannian Manifolds](https://mlsanity.com/paper/2410.17941/) (2024)
- [Cross-target Stance Detection by Exploiting Target Analytical Perspectives](https://mlsanity.com/paper/2401.01761/) (2024)
- [SpikeGraphormer: A High-Performance Graph Transformer with Spiking Graph Attention](https://mlsanity.com/paper/2403.15480/) (2024)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have demonstrated impressive capabilities in modeling graph-structured data, while Spiking Neural Networks (SNNs) offer high energy efficiency through sparse, event-driven computation. However, existing spiking GNNs predominantly operate in Euclidean space and rely on fixed geometric assumptions, limiting their capacity to model complex graph structures such as hierarchies and cycles. To overcome these limitations, we propose method, a novel Geometry-Aware Spiking Graph Neural Network that unifies spike-based neural dynamics with adaptive representation learning on Riemannian manifolds. method features three key components: a Riemannian Embedding Layer that projects node features into a pool of constant-curvature manifolds, capturing non-Euclidean structures; a Manifold Spiking Layer that models membrane potential evolution and spiking behavior in curved spaces via geometry-consistent neighbor aggregation and curvature-based attention; and a Manifold Learning Objective that enables instance-wise geometry adaptation through jointly optimized classification and link prediction losses defined over geodesic distances. All modules are trained using Riemannian SGD, eliminating the need for backpropagation through time. Extensive experiments on multiple benchmarks show that GSG achieves superior accuracy, robustness, and energy efficiency compared to both Euclidean SNNs and manifold-based GNNs, establishing a new paradigm for curvature-aware, energy-efficient graph learning.