Geometry-Aware Spiking Graph Neural Network

2025-08-08

AI Summary

Existing spiking graph neural networks (Spiking GNNs) operate in Euclidean space under fixed geometric assumptions, limiting their ability to model hierarchical and cyclic topologies inherent in graph-structured data. Method: We propose the first geometry-aware Spiking GNN, unifying spiking neural dynamics with adaptive representation learning on constant-curvature Riemannian manifolds. Our framework comprises a Riemannian embedding layer, manifold-spiking neurons, a joint loss function integrating geodesic distance and geometrically consistent neighborhood aggregation, and Riemannian SGD optimization. Contribution/Results: This work pioneers the integration of spiking mechanisms into non-Euclidean graph learning, enabling curvature-adaptive manifold modeling and efficient training without time-unrolled backpropagation. Extensive experiments demonstrate significant improvements over Euclidean Spiking GNNs and conventional manifold GNNs across multiple benchmarks—achieving higher accuracy, enhanced robustness, and superior energy efficiency—thereby establishing a new low-power, geometry-aware paradigm for graph representation learning.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Learning with Manifolds
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Graph Neural Networks (GNNs) have demonstrated impressive capabilities in modeling graph-structured data, while Spiking Neural Networks (SNNs) offer high energy efficiency through sparse, event-driven computation. However, existing spiking GNNs predominantly operate in Euclidean space and rely on fixed geometric assumptions, limiting their capacity to model complex graph structures such as hierarchies and cycles. To overcome these limitations, we propose method{}, a novel Geometry-Aware Spiking Graph Neural Network that unifies spike-based neural dynamics with adaptive representation learning on Riemannian manifolds. method{} features three key components: a Riemannian Embedding Layer that projects node features into a pool of constant-curvature manifolds, capturing non-Euclidean structures; a Manifold Spiking Layer that models membrane potential evolution and spiking behavior in curved spaces via geometry-consistent neighbor aggregation and curvature-based attention; and a Manifold Learning Objective that enables instance-wise geometry adaptation through jointly optimized classification and link prediction losses defined over geodesic distances. All modules are trained using Riemannian SGD, eliminating the need for backpropagation through time. Extensive experiments on multiple benchmarks show that GSG achieves superior accuracy, robustness, and energy efficiency compared to both Euclidean SNNs and manifold-based GNNs, establishing a new paradigm for curvature-aware, energy-efficient graph learning.

Problem

• Modeling complex graph structures in non-Euclidean spaces
• Integrating spiking neural dynamics with adaptive manifold learning
• Achieving energy-efficient graph learning with curvature awareness

Innovation

• Geometry-aware spiking GNN on Riemannian manifolds
• Riemannian embedding for non-Euclidean structures
• Manifold spiking layer with curvature-based attention