Title: Towards Scalable Distance-Enhanced Graph Neural Network
Primary area: learning on graphs and other geometries & topologies
Keywords: Graph Neural Networks, Expressive Power, Distance Encoding, Scalability

Abstract: Graph neural networks (GNNs) have demonstrated significant advantages in graph mining tasks, but often suffer from limited expressive power. Among existing expressive GNNs, distance-enhanced GNNs (DE-GNNs) arise as promising ones due to their conceptual simplicity and alignment with the expressive needs of real-world applications. However, scalability remains a key challenge for DE-GNNs, as constructing pairwise distance features requires quadratic complexity. Additionally, while existing work has shown that specialized distance features enable strong expressiveness, the expressive power of simpler distance metrics remains less understood. 
In this paper, we propose a new Scalable Distance-Enhanced Graph Neural Network (termed SDE-GNN) to tackle the above issues. SDE-GNN introduces a distance-aware message-passing framework, where message weights are computed by a learnable distance feature mapping. It first linearly projects the adjacency-power-based distance vector to a scalar, then applies a polynomial expansion. To efficiently scale to large graphs, we reformulate the distance features as the product of two asymmetric node encodings and apply Randomized SVD for dimensionality reduction, lowering the computational complexity from quadratic in the number of nodes to linear in the number of edges. Additionally, we leverage the sparsity of the adjacency matrix to directly compute the first-order term of the distance feature mapping, further mitigating distortion from dimensionality reduction. Theoretically, we show that the adopted adjacency-power-based distance outperforms other commonly used distance features. Empirically, we conduct experiments on 17 datasets and verify the effectiveness, efficiency, and scalability of SDE-GNN.

TL;DR: We propose a scalable distance-enhanced graph neural network which is expressive and can scale to large graphs.