# Continuous Spiking Graph Neural Networks

arXiv: https://arxiv.org/abs/2404.01897 · HTML: https://mlsanity.com/paper/2404.01897/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 30 references that are in the map.
- First posted on arXiv 2 Apr 2024.

## Builds on (most cited first, 20 of 20)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Residual Gated Graph ConvNets](https://mlsanity.com/paper/1711.07553/) (2017)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [Training Spiking Neural Networks Using Lessons From Deep Learning](https://mlsanity.com/paper/2109.12894/) (2021)
- [SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels](https://mlsanity.com/paper/1711.08920/) (2017)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [Graph-Coupled Oscillator Networks](https://mlsanity.com/paper/2202.02296/) (2022)
- [Continuous Graph Neural Networks](https://mlsanity.com/paper/1912.00967/) (2019)
- [Training High-Performance Low-Latency Spiking Neural Networks by Differentiation on Spike Representation](https://mlsanity.com/paper/2205.00459/) (2022)
- [Spiking Graph Convolutional Networks](https://mlsanity.com/paper/2205.02767/) (2022)
- [Beyond Homophily in Graph Neural Networks: Current Limitations and Effective Designs](https://mlsanity.com/paper/2006.11468/) (2020)
- [Scaling Up Dynamic Graph Representation Learning via Spiking Neural Networks](https://mlsanity.com/paper/2208.10364/) (2022)
- [Exploiting Spiking Dynamics with Spatial-temporal Feature Normalization in Graph Learning](https://mlsanity.com/paper/2107.06865/) (2021)
- [Probabilistic Numeric Convolutional Neural Networks](https://mlsanity.com/paper/2010.10876/) (2020)

## Abstract (arXiv)

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.