相关论文: Scaling Up Graph Propagation Computation on Large …

Unions of graph multiplier operators are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators. The proposed method features…

Chebyshev interpolation polynomials exhibit the exponential approximation property to analytic functions on a cube. Based on the Chebyshev interpolation polynomial approximation, we propose iterative polynomial approximation algorithms to…

The personalized PageRank algorithm is one of the most versatile tools for the analysis of networks. In spite of its ubiquity, maintaining personalized PageRank vectors when the underlying network constantly evolves is still a challenging…

Unions of graph Fourier multipliers are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators to the high-dimensional signals…

Efficient computation of node proximity queries such as transition probabilities, Personalized PageRank, and Katz are of fundamental importance in various graph mining and learning tasks. In particular, several recent works leverage fast…

In the realm of generative models for graphs, extensive research has been conducted. However, most existing methods struggle with large graphs due to the complexity of representing the entire joint distribution across all node pairs and…

Graph neural networks have achieved remarkable success in learning graph representations, especially graph Transformer, which has recently shown superior performance on various graph mining tasks. However, graph Transformer generally treats…

We consider a new semidefinite programming relaxation for directed edge expansion, which is obtained by adding triangle inequalities to the reweighted eigenvalue formulation. Applying the matrix multiplicative weight update method to this…

Graph Neural Networks (GNNs) have achieved great successes in many learning tasks performed on graph structures. Nonetheless, to propagate information GNNs rely on a message passing scheme which can become prohibitively expensive when…

Matrix diagonalization is almost always involved in computing the density matrix needed in quantum chemistry calculations. In the case of modest matrix sizes ($\lesssim$ 5000), performance of traditional dense diagonalization algorithms on…

Graph neural networks (GNNs) have exhibited exceptional efficacy in a diverse array of applications. However, the sheer size of large-scale graphs presents a significant challenge to real-time inference with GNNs. Although existing Scalable…

Efficient computation of graph diffusion equations (GDEs), such as Personalized PageRank, Katz centrality, and the Heat kernel, is crucial for clustering, training neural networks, and many other graph-related problems. Standard iterative…

Recent advancements in Spectral Graph Convolutional Networks (SpecGCNs) have led to state-of-the-art performance in various graph representation learning tasks. To exploit the potential of SpecGCNs, we analyze corresponding graph filters…

Graph neural networks (GNNs) have been widely adopted for semi-supervised learning on graphs. A recent study shows that the graph random neural network (GRAND) model can generate state-of-the-art performance for this problem. However, it is…

Diffusing a graph signal at multiple scales requires computing the action of the exponential of several multiples of the Laplacian matrix. We tighten a bound on the approximation error of truncated Chebyshev polynomial approximations of the…

Designing spectral convolutional networks is a challenging problem in graph learning. ChebNet, one of the early attempts, approximates the spectral graph convolutions using Chebyshev polynomials. GCN simplifies ChebNet by utilizing only the…

The push-sum algorithm is probably the most important distributed averaging approach over directed graphs, which has been applied to various problems including distributed optimization. This paper establishes the explicit absolute…

We prove two generalizations of the Cheeger's inequality. The first generalization relates the second eigenvalue to the edge expansion and the vertex expansion of the graph G, $\lambda_2 = \Omega(\phi^V(G) \phi(G))$, where $\phi^V(G)$…

Graph Neural Networks (GNNs) offer a principled framework for learning over graph-structured data, yet their expressive capacity is often hindered by over-squashing, wherein information from distant nodes is compressed into fixed-size…

Generalized Chebyshev acceleration is a semi-iterative technique applicable to a basic iterative method only when the eigenvalues of the iteration matrix satisfy a highly restrictive inclusion condition. In this work, we relax this…