Spiking Graph Neural Network on Riemannian Manifolds

TL;DR

This paper introduces a novel spiking graph neural network operating on Riemannian manifolds, improving energy efficiency and performance by leveraging manifold geometry and a new differentiation method, addressing limitations of Euclidean-based spiking GNNs.

Contribution

The paper proposes a Manifold-valued Spiking GNN with a new neuron design on Riemannian manifolds, replacing BPTT with manifold differentiation for improved efficiency and accuracy.

Findings

Achieves superior performance over previous spiking GNNs

Demonstrates energy efficiency compared to conventional GNNs

Approximates a solver of the manifold ordinary differential equation

Abstract

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.