Li Sun

Li Sun, Zhenhao Huang, Hua Wu et al.

Graph Neural Networks (GNNs) have shown great power for learning and mining on graphs, and Graph Structure Learning (GSL) plays an important role in boosting GNNs with a refined graph. In the literature, most GSL solutions either primarily focus on structure refinement with task-specific supervision (i.e., node classification), or overlook the inherent weakness of GNNs themselves (e.g., over-squashing), resulting in suboptimal performance despite sophisticated designs. In light of these limitations, we propose to study self-supervised graph structure-feature co-refinement for effectively alleviating the issue of over-squashing in typical GNNs. In this paper, we take a fundamentally different perspective of the Ricci curvature in Riemannian geometry, in which we encounter the challenges of modeling, utilizing and computing Ricci curvature. To tackle these challenges, we present a self-supervised Riemannian model, DeepRicci. Specifically, we introduce a latent Riemannian space of heterogeneous curvatures to model various Ricci curvatures, and propose a gyrovector feature mapping to utilize Ricci curvature for typical GNNs. Thereafter, we refine node features by geometric contrastive learning among different geometric views, and simultaneously refine graph structure by backward Ricci flow based on a novel formulation of differentiable Ricci curvature. Finally, extensive experiments on public datasets show the superiority of DeepRicci, and the connection between backward Ricci flow and over-squashing. Codes of our work are given in https://github.com/RiemanGraph/.

Li Sun, Zhenhao Huang, Zixi Wang et al.

Graphs are typical non-Euclidean data of complex structures. In recent years, Riemannian graph representation learning has emerged as an exciting alternative to Euclidean ones. However, Riemannian methods are still in an early stage: most of them present a single curvature (radius) regardless of structural complexity, suffer from numerical instability due to the exponential/logarithmic map, and lack the ability to capture motif regularity. In light of the issues above, we propose the problem of \emph{Motif-aware Riemannian Graph Representation Learning}, seeking a numerically stable encoder to capture motif regularity in a diverse-curvature manifold without labels. To this end, we present a novel Motif-aware Riemannian model with Generative-Contrastive learning (MotifRGC), which conducts a minmax game in Riemannian manifold in a self-supervised manner. First, we propose a new type of Riemannian GCN (D-GCN), in which we construct a diverse-curvature manifold by a product layer with the diversified factor, and replace the exponential/logarithmic map by a stable kernel layer. Second, we introduce a motif-aware Riemannian generative-contrastive learning to capture motif regularity in the constructed manifold and learn motif-aware node representation without external labels. Empirical results show the superiority of MofitRGC.

Li Sun, Zhenhao Huang, Qiqi Wan et al.

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.