Continuous graph neural networks (CGNNs) have garnered significant attention
due to their ability to generalize existing discrete graph neural networks
(GNNs) by introducing continuous dynamics. They typically draw inspiration from
diffusion-based methods to introduce a novel propagation scheme, which is
analyzed using ordinary differential equations (ODE). However, the
implementation of CGNNs requires significant computational power, making them
challenging to deploy on battery-powered devices. Inspired by recent spiking
neural networks (SNNs), which emulate a biological inference process and
provide an energy-efficient neural architecture, we incorporate the SNNs with
CGNNs in a unified framework, named Continuous Spiking Graph Neural Networks
(COS-GNN). We employ SNNs for graph node representation at each time step,
which are further integrated into the ODE process along with time. To enhance
information preservation and mitigate information loss in SNNs, we introduce
the high-order structure of COS-GNN, which utilizes the second-order ODE for
spiking representation and continuous propagation. Moreover, we provide the
theoretical proof that COS-GNN effectively mitigates the issues of exploding
and vanishing gradients, enabling us to capture long-range dependencies between
nodes. Experimental results on graph-based learning tasks demonstrate the
effectiveness of the proposed COS-GNN over competitive baselines.

连续脉冲图神经网络（COS-GNN）是一个统一框架，将脉冲神经网络与连续图神经网络相结合，利用高阶结构和脉冲表示进行连续传播，以增强信息保留并捕捉节点之间的长程依赖。实验结果表明，COS-GNN 在图学习任务中比竞争对手具有更好的效果。