An Invertible Graph Diffusion Neural Network for Source Localization

Localizing the source of graph diffusion phenomena, such as misinformation propagation, is an important yet extremely challenging task in the real world. Existing source localization models typically are heavily dependent on the hand-crafted rules and only tailored for certain domain-specific applications. Unfortunately, a large portion of the graph diffusion process for many applications is still unknown to human beings so it is important to have expressive models for learning such underlying rules automatically. Recently, there is a surge of research body on expressive models such as Graph Neural Networks (GNNs) for automatically learning the underlying graph diffusion. However, source localization is instead the inverse of graph diffusion, which is a typical inverse problem in graphs that is well-known to be ill-posed because there can be multiple solutions and hence different from the traditional (semi-)supervised learning settings. This paper aims to establish a generic framework of invertible graph diffusion models for source localization on graphs, namely Invertible Validity-aware Graph Diffusion (IVGD), to handle major challenges including 1) Difficulty to leverage knowledge in graph diffusion models for modeling their inverse processes in an end-to-end fashion, 2) Difficulty to ensure the validity of the inferred sources, and 3) Efficiency and scalability in source inference. Specifically, first, to inversely infer sources of graph diffusion, we propose a graph residual scenario to make existing graph diffusion models invertible with theoretical guarantees; second, we develop a novel error compensation mechanism that learns to offset the errors of the inferred sources. Finally, to ensure the validity of the inferred sources, a new set of validity-aware layers have been devised to project inferred sources to feasible regions by flexibly encoding constraints with unrolled optimization techniques. A linearization technique is proposed to strengthen the efficiency of our proposed layers. The convergence of the proposed IVGD is proven theoretically. Extensive experiments on nine real-world datasets demonstrate that our proposed IVGD outperforms state-of-the-art comparison methods significantly. We have released our code at https://github.com/xianggebenben/IVGD .