# Spiking Graph Neural Network on Riemannian Manifolds

arXiv: https://arxiv.org/abs/2410.17941 · HTML: https://mlsanity.com/paper/2410.17941/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 59 references that are in the map.
- First posted on arXiv 23 Oct 2024.

## Builds on (most cited first, 30 of 37)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Spikformer: When Spiking Neural Network Meets Transformer](https://mlsanity.com/paper/2209.15425/) (2022)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Riemannian Adaptive Optimization Methods](https://mlsanity.com/paper/1810.00760/) (2018)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [Cooperative Game Theory Approaches for Network Partitioning](https://mlsanity.com/paper/1707.03587/) (2017)
- [Constant Curvature Graph Convolutional Networks](https://mlsanity.com/paper/1911.05076/) (2019)
- [Fully Hyperbolic Neural Networks](https://mlsanity.com/paper/2105.14686/) (2021)
- [Training High-Performance Low-Latency Spiking Neural Networks by Differentiation on Spike Representation](https://mlsanity.com/paper/2205.00459/) (2022)
- [Neural Manifold Ordinary Differential Equations](https://mlsanity.com/paper/2006.10254/) (2020)
- [Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphs](https://mlsanity.com/paper/2104.02228/) (2021)
- [Gradient Descent for Spiking Neural Networks](https://mlsanity.com/paper/1706.04698/) (2017)
- [A Self-supervised Mixed-curvature Graph Neural Network](https://mlsanity.com/paper/2112.05393/) (2021)
- [Self-Supervised Continual Graph Learning in Adaptive Riemannian Spaces](https://mlsanity.com/paper/2211.17068/) (2022)
- [Pseudo-Riemannian Graph Convolutional Networks](https://mlsanity.com/paper/2106.03134/) (2021)
- [Spiking Graph Convolutional Networks](https://mlsanity.com/paper/2205.02767/) (2022)
- [Scaling Up Dynamic Graph Representation Learning via Spiking Neural Networks](https://mlsanity.com/paper/2208.10364/) (2022)
- [A Self-supervised Riemannian GNN with Time Varying Curvature for Temporal Graph Learning](https://mlsanity.com/paper/2208.14073/) (2022)
- [Motif-aware Riemannian Graph Neural Network with Generative-Contrastive Learning](https://mlsanity.com/paper/2401.01232/) (2024)
- [Exploiting Spiking Dynamics with Spatial-temporal Feature Normalization in Graph Learning](https://mlsanity.com/paper/2107.06865/) (2021)
- [LSEnet: Lorentz Structural Entropy Neural Network for Deep Graph Clustering](https://mlsanity.com/paper/2405.11801/) (2024)
- [Spiking Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2306.17046/) (2023)

## Built on by (most cited first, 16 of 16)

- [RiemannGFM: Learning a Graph Foundation Model from Riemannian Geometry](https://mlsanity.com/paper/2502.03251/) (2025)
- [Deeper with Riemannian Geometry: Overcoming Oversmoothing and Oversquashing for Graph Foundation Models](https://mlsanity.com/paper/2510.17457/) (2025)
- [Multi-Domain Riemannian Graph Gluing for Building Graph Foundation Models](https://mlsanity.com/paper/2603.00618/) (2026)
- [Unsupervised Graph Clustering with Deep Structural Entropy](https://mlsanity.com/paper/2505.14040/) (2025)
- [Edge Intelligence with Spiking Neural Networks](https://mlsanity.com/paper/2507.14069/) (2025)
- [DFNN: A Deep Fr'echet Neural Network Framework for Learning Metric-Space-Valued Responses](https://mlsanity.com/paper/2510.17072/) (2025)
- [Heterophily-Agnostic Hypergraph Neural Networks with Riemannian Local Exchanger](https://mlsanity.com/paper/2603.00599/) (2026)
- [ChronoSpike: An Adaptive Spiking Graph Neural Network for Dynamic Graphs](https://mlsanity.com/paper/2602.01124/) (2026)
- [Towards LLM-Empowered Knowledge Tracing via LLM-Student Hierarchical Behavior Alignment in Hyperbolic Space](https://mlsanity.com/paper/2602.22879/) (2026)
- [Riemannian Geometry Speaks Louder Than Words: From Graph Foundation Model to Next-Generation Graph Intelligence](https://mlsanity.com/paper/2603.21601/) (2026)
- [Geometry-Aware Spiking Graph Neural Network](https://mlsanity.com/paper/2508.06793/) (2025)
- [Neuromorphic Graph Anomaly Detection via Adaptive STDP and Spiking Graph Neural Networks](https://mlsanity.com/paper/2605.13863/) (2026)
- [Are Common Substructures Transferable? Riemannian Graph Foundation Model with Neural Vector Bundles](https://mlsanity.com/paper/2606.03270/) (2026)
- [Analog Quantum Asynchronous Event-Based Graph Neural Network](https://mlsanity.com/paper/2606.11000/) (2026)
- [Unified Complex-valued Neural Network: A Magnitude-Phase Computational Model for Event-Driven Neuromorphic Learning](https://mlsanity.com/paper/2606.29099/) (2026)
- [Riemannian Graph Tokenizer for Structural Knowledge Transfer](https://mlsanity.com/paper/2610.15427/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) have become the dominant solution for learning on graphs, the typical non-Euclidean structures. Conventional GNNs, constructed with the Artificial Neuron Network (ANN), have achieved impressive performance at the cost of high computation and energy consumption. In parallel, spiking GNNs with brain-like spiking neurons are drawing increasing research attention owing to the energy efficiency. So far, existing spiking GNNs consider graphs in Euclidean space, ignoring the structural geometry, and suffer from the high latency issue due to Back-Propagation-Through-Time (BPTT) with the surrogate gradient. In light of the aforementioned issues, we are devoted to exploring spiking GNN on Riemannian manifolds, and present a Manifold-valued Spiking GNN (MSG). In particular, we design a new spiking neuron on geodesically complete manifolds with the diffeomorphism, so that BPTT regarding the spikes is replaced by the proposed differentiation via manifold. Theoretically, we show that MSG approximates a solver of the manifold ordinary differential equation. Extensive experiments on common graphs show the proposed MSG achieves superior performance to previous spiking GNNs and energy efficiency to conventional GNNs.