mlsanityData to 14 Oct 2026

Spiking Graph Neural Network on Riemannian Manifolds

arXiv 2410.17941 ↗First posted 23 Oct 2024cs.LGcited by 16

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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.

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

37 of 59 references.

References · 37

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
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  6. 2018Pitfalls of Graph Neural Network Evaluationcited by 1,007
  7. 2019Surrogate Gradient Learning in Spiking Neural Networkscited by 626
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  9. 2019Hyperbolic Graph Convolutional Neural Networkscited by 402
  10. 2022Spikformer: When Spiking Neural Network Meets Transformercited by 271
  11. 2019Hyperbolic Graph Neural Networkscited by 244
  12. 2018Riemannian Adaptive Optimization Methodscited by 194
25 more
  1. 2019Graph Neural Ordinary Differential Equationscited by 154
  2. 2017Cooperative Game Theory Approaches for Network Partitioningcited by 135
  3. 2019Constant Curvature Graph Convolutional Networkscited by 108
  4. 2021Fully Hyperbolic Neural Networkscited by 108
  5. 2022Training High-Performance Low-Latency Spiking Neural Networks by Differentiation on Spike Representationcited by 89
  6. 2020Neural Manifold Ordinary Differential Equationscited by 81
  7. 2021Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphscited by 50
  8. 2017Gradient Descent for Spiking Neural Networkscited by 48
  9. 2021A Self-supervised Mixed-curvature Graph Neural Networkcited by 33
  10. 2022Self-Supervised Continual Graph Learning in Adaptive Riemannian Spacescited by 32
  11. 2021Pseudo-Riemannian Graph Convolutional Networkscited by 30
  12. 2022Spiking Graph Convolutional Networkscited by 27
  13. 2022Scaling Up Dynamic Graph Representation Learning via Spiking Neural Networkscited by 24
  14. 2022A Self-supervised Riemannian GNN with Time Varying Curvature for Temporal Graph Learningcited by 24
  15. 2024Motif-aware Riemannian Graph Neural Network with Generative-Contrastive Learningcited by 23
  16. 2021Exploiting Spiking Dynamics with Spatial-temporal Feature Normalization in Graph Learningcited by 22
  17. 2024LSEnet: Lorentz Structural Entropy Neural Network for Deep Graph Clusteringcited by 21
  18. 2023Spiking Denoising Diffusion Probabilistic Modelscited by 19
  19. 2024DeepRicci: Self-supervised Graph Structure-Feature Co-Refinement for Alleviating Over-squashingcited by 16
  20. 2021Switch Spaces: Learning Product Spaces with Sparse Gatingcited by 6
  21. 2023A Graph is Worth 1-bit Spikes: When Graph Contrastive Learning Meets Spiking Neural Networkscited by 6
  22. 2022Spiking GATs: Learning Graph Attentions via Spiking Neural Networkcited by 3
  23. 2024SpikeGraphormer: A High-Performance Graph Transformer with Spiking Graph Attentioncited by 3
  24. 2024R-ODE: Ricci Curvature Tells When You Will be Informedcited by 2
  25. 2022Spiking Variational Graph Auto-Encoders for Efficient Graph Representation Learningcited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 6; 2026: 10.

16 papers.

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  1. 2025RiemannGFM: Learning a Graph Foundation Model from Riemannian Geometrycited by 35
  2. 2025Deeper with Riemannian Geometry: Overcoming Oversmoothing and Oversquashing for Graph Foundation Modelscited by 7
  3. 2026Multi-Domain Riemannian Graph Gluing for Building Graph Foundation Modelscited by 5
  4. 2025Unsupervised Graph Clustering with Deep Structural Entropycited by 4
  5. 2025Edge Intelligence with Spiking Neural Networkscited by 2
  6. 2025DFNN: A Deep Fr'echet Neural Network Framework for Learning Metric-Space-Valued Responsescited by 2
  7. 2026Heterophily-Agnostic Hypergraph Neural Networks with Riemannian Local Exchangercited by 2
  8. 2026ChronoSpike: An Adaptive Spiking Graph Neural Network for Dynamic Graphscited by 1
  9. 2026Towards LLM-Empowered Knowledge Tracing via LLM-Student Hierarchical Behavior Alignment in Hyperbolic Spacecited by 1
  10. 2026Riemannian Geometry Speaks Louder Than Words: From Graph Foundation Model to Next-Generation Graph Intelligencecited by 1
  11. 2025Geometry-Aware Spiking Graph Neural Networkcited by 0
  12. 2026Neuromorphic Graph Anomaly Detection via Adaptive STDP and Spiking Graph Neural Networkscited by 0
4 more
  1. 2026Are Common Substructures Transferable? Riemannian Graph Foundation Model with Neural Vector Bundlescited by 0
  2. 2026Analog Quantum Asynchronous Event-Based Graph Neural Networkcited by 0
  3. 2026Unified Complex-valued Neural Network: A Magnitude-Phase Computational Model for Event-Driven Neuromorphic Learningcited by 0
  4. 2026Riemannian Graph Tokenizer for Structural Knowledge Transfercited by 0