将脉冲神经网络引入黎曼流形，提升图学习能效与速度。
Spiking Graph Neural Network on Riemannian Manifolds
- 在黎曼流形上设计新脉冲神经元，避免传统反向传播延迟
- 理论证明其逼近流形常微分方程求解器，性能更优
- 相比传统GNN节能，优于现有脉冲GNN，适合低功耗图学习
图神经网络（GNN）已成为处理非欧几里得结构图数据的主流方法。传统GNN基于人工神经网络（ANN），虽性能出色但计算和能耗高。脉冲GNN因其类脑脉冲神经元具有更高能效，受到关注。然而现有脉冲GNN仅在欧氏空间中建模，忽略图结构几何特性，且依赖基于替代梯度的通过时间反向传播（BPTT），导致延迟高。针对此问题，本文提出黎曼流形上的脉冲图神经网络（MSG）。设计了一种基于微分同胚的黎曼流形上完备测地线神经元，用流形微分替代传统BPTT。理论上，证明了MSG可逼近流形常微分方程求解器。在多个标准图数据集上的实验表明，所提MSG在性能上超越现有脉冲GNN，并实现低于传统GNN的能耗。
原文摘要 · Abstract (English)
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.
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