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npx versuz@latest install hiyenwong-ai-collection-collection-skills-geometry-aware-spiking-gnngit clone https://github.com/hiyenwong/ai_collection.gitcp ai_collection/SKILL.MD ~/.claude/skills/hiyenwong-ai-collection-collection-skills-geometry-aware-spiking-gnn/SKILL.md---
name: geometry-aware-spiking-gnn
description: Geometry-Aware Spiking Graph Neural Network combining SNN energy efficiency with Riemannian manifold learning for non-Euclidean graph structures
---
# Geometry-Aware Spiking Graph Neural Network
**Source:** arXiv:2508.06793v2 (August 2025)
**Utility:** 0.89
**Authors:** Bowen Zhang
---
## Description
This skill implements GSG (Geometry-Aware Spiking Graph Neural Network) - a
novel architecture that unifies spike-based neural dynamics with adaptive
representation learning on Riemannian manifolds. Overcomes limitations of
Euclidean spiking GNNs by modeling hierarchies and cycles in curved spaces.
**Core Components:**
1. **Riemannian Embedding Layer** - Projects nodes into constant-curvature manifolds
2. **Manifold Spiking Layer** - Membrane potential evolution in curved spaces
3. **Manifold Learning Objective** - Instance-wise geometry adaptation
---
## Tools Used
- `pytorch` - Deep learning framework
- `torch_geometric` - Graph neural networks
- `spikingjelly` - Spiking neural network toolkit
- `geoopt` - Riemannian optimization
- `networkx` - Graph data structures
---
## Instructions for Agents
1. **Prepare graph data** - Node features and edge structure
2. **Riemannian embedding** - Project to constant-curvature manifolds
3. **Manifold spiking** - Model membrane potential in curved space
4. **Geometry-consistent aggregation** - Neighbor aggregation on manifold
5. **Curvature-based attention** - Adaptive message passing
6. **Joint optimization** - Classification + link prediction losses
7. **Riemannian SGD training** - No backpropagation through time
---
## Examples
### Example 1: Hierarchical Graph Learning
**User:** 如何用 GSG 学习层次图结构?
**Agent:** GSG 方法:
1. **黎曼嵌入** - 将节点投影到负曲率流形(双曲空间)
2. **流形脉冲** - 在弯曲空间建模膜电位演化
3. **几何一致聚合** - 沿测地线聚合邻居信息
4. **曲率注意力** - 自适应曲率的消息传递
**优势:** 捕获层次结构,比欧几里得 GNN 更高效
### Example 2: Energy-Efficient Graph Learning
**User:** 如何实现高能效的图学习?
**Agent:** GSG 能效特性:
| 特性 | 说明 |
|------|------|
| 脉冲计算 | 稀疏、事件驱动 |
| 黎曼优化 | Riemannian SGD,无需 BPTT |
| 几何适应 | 实例级曲率自适应 |
| 能效 | 优于欧几里得 SNN 和流形 GNN |
---
## Activation Keywords
- 几何感知脉冲 GNN、geometry-aware spiking GNN
- 黎曼流形学习、Riemannian manifold learning
- 脉冲图神经网络、spiking graph neural network
- 曲率自适应、curvature-aware
- 测地线距离、geodesic distance
- 常曲率流形、constant-curvature manifold
---
## Key Concepts
### 1. Riemannian Embedding Layer
**Purpose:** Project node features into pool of constant-curvature manifolds
**Manifold types:**
- Hyperbolic (negative curvature) - Hierarchies
- Spherical (positive curvature) - Cycles
- Euclidean (zero curvature) - Standard graphs
### 2. Manifold Spiking Layer
**Mechanism:**
- Membrane potential evolution in curved space
- Geometry-consistent neighbor aggregation
- Curvature-based attention weights
**Formula:**
```
Spiking on manifold: u(t+1) = f(u(t), messages, curvature)
```
### 3. Manifold Learning Objective
**Joint optimization:**
- Classification loss (geodesic-based)
- Link prediction loss (geodesic distance)
- Instance-wise geometry adaptation
### 4. Riemannian SGD
**Advantage:** No backpropagation through time (BPTT)
**Training:** Direct optimization on manifold
---
## Architecture
```
Graph Input → Riemannian Embedding Layer
↓
Manifold Spiking Layer (curved space dynamics)
↓
Geometry-Consistent Aggregation + Curvature Attention
↓
Manifold Learning Objective (classification + link prediction)
↓
Riemannian SGD Optimization
```
---
## Results (Paper)
| Metric | Performance |
|--------|-------------|
| Accuracy | Superior vs Euclidean SNNs ✅ |
| Robustness | Superior vs manifold GNNs ✅ |
| Energy efficiency | Best in class ✅ |
| Hierarchy modeling | Captured via hyperbolic ✅ |
| Cycle modeling | Captured via spherical ✅ |
---
## When to Use
1. **Hierarchical graphs** - Trees, taxonomies, social networks
2. **Cyclic graphs** - Molecular structures, ring patterns
3. **Energy-efficient learning** - Edge deployment
4. **Non-Euclidean structures** - Complex geometries
5. **Graph classification** - Node and edge prediction
---
## Advantages over Prior Methods
| Euclidean SNNs | Manifold GNNs | GSG (This) |
|----------------|---------------|-----------|
| Fixed geometry | No spiking | ✅ Unified approach |
| Limited expressiveness | High energy | ✅ Energy efficient |
| No curvature adaptation | Static manifolds | ✅ Adaptive geometry |
---
## Limitations
1. Computational cost of Riemannian operations
2. Curvature selection requires tuning
3. Limited to constant-curvature manifolds
4. Training stability on complex manifolds
---
## Related Skills
- `spikingjelly-framework` - SNN toolkit
- `geometry-aware-spiking-gnn` - Related architecture
- `hyperbolic-brain-network-neurodegeneration` - Hyperbolic networks
- `graph-laplacian-denoising` - Graph signal processing