geometry-aware-spiking-gnn

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：

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)

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

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