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.

Graph Neural Networks (GNNs) are exemplary deep models designed for graph data. Message passing mechanism enables GNNs to effectively capture graph topology and push the performance boundaries across various graph tasks. However, the trend of developing such complex machinery for graph representation learning has become unsustainable on large-scale graphs. The computational and time overhead make it imperative to develop more energy-efficient GNNs to cope with the explosive growth of real-world graphs. Spiking Graph Neural Networks (SGNNs), which integrate biologically plausible learning via unique spike-based neurons, have emerged as a promising energy-efficient alternative. Different layers communicate with sparse and binary spikes, which facilitates computation and storage of intermediate graph representations. Despite the proliferation of SGNNs proposed in recent years, there is no systematic benchmark to explore the basic design principles of these brain-inspired networks on the graph data. To bridge this gap, we present SGNNBench to quantify progress in the field of SGNNs. Specifically, SGNNBench conducts an in-depth investigation of SGNNs from multiple perspectives, including effectiveness, energy efficiency, and architectural design. We comprehensively evaluate 9 state-of-the-art SGNNs across 18 datasets. Regarding efficiency, we empirically compare these baselines w.r.t model size, memory usage, and theoretical energy consumption to reveal the often-overlooked energy bottlenecks of SGNNs. Besides, we elaborately investigate the design space of SGNNs to promote the development of a general SGNN paradigm.

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).

The integration of Spiking Neural Networks (SNNs) and Graph Neural Networks (GNNs) is gradually attracting attention due to the low power consumption and high efficiency in processing the non-Euclidean data represented by graphs. However, as a common problem, dynamic graph representation learning faces challenges such as high complexity and large memory overheads. Current work often uses SNNs instead of Recurrent Neural Networks (RNNs) by using binary features instead of continuous ones for efficient training, which would overlooks graph structure information and leads to the loss of details during propagation. Additionally, optimizing dynamic spiking models typically requires propagation of information across time steps, which increases memory requirements. To address these challenges, we present a framework named \underline{Dy}namic \underline{S}p\underline{i}king \underline{G}raph \underline{N}eural Networks (\method{}). To mitigate the information loss problem, \method{} propagates early-layer information directly to the last layer for information compensation. To accommodate the memory requirements, we apply the implicit differentiation on the equilibrium state, which does not rely on the exact reverse of the forward computation. While traditional implicit differentiation methods are usually used for static situations, \method{} extends it to the dynamic graph setting. Extensive experiments on three large-scale real-world dynamic graph datasets validate the effectiveness of \method{} on dynamic node classification tasks with lower computational costs.