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Spiking Graph Neural Network on Riemannian Manifolds
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Proposes MSG, a spiking GNN on Riemannian manifolds (mainly Lorentz hyperbolic space) with a manifold spiking neuron using exponential-map diffeomorphism and a recurrence-free "differentiation via manifold" training rule, shown to approximate a manifold ODE dynamic chart solver.
Problem
Existing spiking GNNs operate in Euclidean space, ignoring graph geometry, and are trained with BPTT plus surrogate gradients, which incurs high latency on long spike trains.
Approach
A manifold spiking neuron couples IF-model spikes with a manifold representation: spike-derived averaged input forms a tangent vector that moves the representation along a geodesic via the exponential map. Gradients are computed by pullback through the manifold forward pass (DvM) rather than through spike time steps, so no surrogate gradient or BPTT is needed.
Key results
- MSG reaches 89.27% node classification accuracy on Computers and 93.11% on Photo, the best among SNN-based models in the paper's table.
- MSG reports 0.026 mJ energy on CS and 0.029 mJ on Physics, the lowest among compared models on those datasets.
- DvM backward time is reported to be significantly lower than BPTT-based surrogate training, with no gradient vanishing or explosion observed in the layer-wise norms.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MSG instead of the strongest listed baseline | Computers node classification · Computers | accuracy (%): 89.20{ $\pm$0.50} -> 89.27{ $\pm$0.19} | No clear effect |
| Use MSG instead of the strongest listed baseline | Computers link prediction · Computers | AUC (%): 96.98{ $\pm$0.05} -> 94.65{ $\pm$0.73} | Hurt |
| Use MSG instead of the strongest listed baseline | Photo node classification · Photo | accuracy (%): 92.90{ $\pm$0.10} -> 93.11{ $\pm$0.11} | Helped |
| Use MSG instead of the strongest listed baseline | Photo link prediction · Photo | AUC (%): 97.70{ $\pm$0.07} -> 96.75{ $\pm$0.18} | Hurt |
| Use MSG instead of the strongest listed baseline | CS node classification · CS | accuracy (%): 92.71{ $\pm$0.73} -> 92.65{ $\pm$0.04} | No clear effect |
| Use MSG instead of the strongest listed baseline | CS link prediction · CS | AUC (%): 95.94{ $\pm$0.43} -> 95.19{ $\pm$0.15} | No clear effect |
| Use MSG instead of the strongest listed baseline | Physics node classification · Physics | accuracy (%): 95.85{ $\pm$0.20} -> 95.93{ $\pm$0.07} | Helped |
| Use MSG instead of the strongest listed baseline | Physics link prediction · Physics | AUC (%): 98.46{ $\pm$0.49} -> 93.43{ $\pm$0.16} | Hurt |
| Use hyperspherical S^32 instead of hyperbolic H^32 (ablation) | MSG · Computers | accuracy (%): 89.27{ $\pm$0.19} -> 87.84{ $\pm$0.77} | Hurt |
| Use Euclidean E^32 instead of hyperbolic H^32 (ablation) | MSG · Computers | accuracy (%): 89.27{ $\pm$0.19} -> 88.94{ $\pm$0.24} | Hurt |
| Use Euclidean E^32 instead of hyperbolic H^32 (ablation) | MSG · CS | accuracy (%): 92.65{ $\pm$0.04} -> 92.82{ $\pm$0.04} | Helped |
| Use product S^16 × S^16 instead of hyperbolic H^32 (ablation) | MSG · Computers | accuracy (%): 89.27{ $\pm$0.19} -> 82.49{ $\pm$1.18} | Hurt |
Surprising findings
- MSG does not beat SpikeNet on Photo energy (SpikeNet 0.040 mJ vs MSG 0.043 mJ), and it trails the best ANN link-prediction baselines on Photo and Physics.
Limitations
- Only undirected, homophilous graphs are considered.
- Evaluated only on four standard static benchmarks (Computers, Photo, CS, Physics).
- Energy numbers are theoretical estimates rather than measured energy.
Experimental setup
Datasets: Computers Photo CS Physics
Benchmarks: Computers Photo CS Physics
Metrics: classification accuracy AUC theoretical energy consumption (mJ) backward time
Baselines: GCN GAT GraphSAGE SGC HGCN HyboNet κ-GCN Q-GCN SpikeNet SpikeGCN SpikeGCL SpikeGT
Builds on: GCN HyboNet HGCN SpikeNet SpikingJelly
Closest papers by meaning
- SGNNBench: A Holistic Evaluation of Spiking Graph Neural Networks on Large-scale Graphs (NeurIPS 2026 · similarity 0.88)
- Exploring the Enigma of Neural Dynamics Through A Scattering-Transform Mixer Landscape for Riemannian Manifold (ICML 2024 · similarity 0.86)
- Hyperbolic-PDE GNN: Spectral Graph Neural Networks in the Perspective of A System of Hyperbolic Partial Differential Equations (ICML 2025 · similarity 0.85)
- Deeper with Riemannian Geometry: Overcoming Oversmoothing and Oversquashing for Graph Foundation Models (NeurIPS 2025 · similarity 0.85)
- Matrix Manifold Neural Networks++ (ICLR 2024 · similarity 0.85)
- Spiking NeRF: Representing the Real-World Geometry by a Discontinuous Representation (AAAI 2024 · similarity 0.85)
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