R-ODE: Ricci Curvature Tells When You Will be Informed

TL;DR

The paper tackles time-aware personalized information diffusion by introducing R-ODE, a framework that couples graph Ricci curvature with a neural ODE driven by a GNN-based velocity net. It formulates infection-time prediction as a trajectory learning problem in a dynamic representation space, using a recursive graph convolution to update embeddings and a differentiable Ricci-based diffusion signal to guide progression. The method combines a Ricci-based loss $L_{Ricci}$ with a graph ODE loss $L_{ODE}$ to learn realistic diffusion trajectories, showing superior performance on multiple benchmarks and through ablation studies that both the curvature-based diffusion and the GNN velocity component are crucial. This approach provides a principled, geometry-informed mechanism for fine-grained diffusion prediction with potential impact on rumor blocking, influence maximization, and intervention strategies, while offering a framework for time-aware diffusion analysis on graphs. $Ric(m,u_i;t^k)$, $W(p^k_m,p^k_i)$, and the diffusion dynamics are central to the model.$

Abstract

Information diffusion prediction is fundamental to understand the structure and organization of the online social networks, and plays a crucial role to blocking rumor spread, influence maximization, political propaganda, etc. So far, most existing solutions primarily predict the next user who will be informed with historical cascades, but ignore an important factor in the diffusion process - the time. Such limitation motivates us to pose the problem of the time-aware personalized information diffusion prediction for the first time, telling the time when the target user will be informed. In this paper, we address this problem from a fresh geometric perspective of Ricci curvature, and propose a novel Ricci-curvature regulated Ordinary Differential Equation (R-ODE). In the diffusion process, R-ODE considers that the inter-correlated users are organized in a dynamic system in the representation space, and the cascades give the observations sampled from the continuous realm. At each infection time, the message diffuses along the largest Ricci curvature, signifying less transportation effort. In the continuous realm, the message triggers users' movement, whose trajectory in the space is parameterized by an ODE with graph neural network. Consequently, R-ODE predicts the infection time of a target user by the movement trajectory learnt from the observations. Extensive experiments evaluate the personalized time prediction ability of R-ODE, and show R-ODE outperforms the state-of-the-art baselines.

Figures (2)

• Figure 1: Overall Architecture of R-ODE.
• Figure 2: Results of infection time prediction on Android.