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

arXiv: https://arxiv.org/abs/2405.17282 · HTML: https://mlsanity.com/paper/2405.17282/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 38 references that are in the map.
- First posted on arXiv 27 May 2024.

## Builds on (most cited first, 22 of 22)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [DeepInf: Social Influence Prediction with Deep Learning](https://mlsanity.com/paper/1807.05560/) (2018)
- [Neural Manifold Ordinary Differential Equations](https://mlsanity.com/paper/2006.10254/) (2020)
- [Learning Continuous System Dynamics from Irregularly-Sampled Partial Observations](https://mlsanity.com/paper/2011.03880/) (2020)
- [Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphs](https://mlsanity.com/paper/2104.02228/) (2021)
- [DeepCas: an End-to-end Predictor of Information Cascades](https://mlsanity.com/paper/1611.05373/) (2016)
- [Neural Dynamics on Complex Networks](https://mlsanity.com/paper/1908.06491/) (2019)
- [Self-Supervised Continual Graph Learning in Adaptive Riemannian Spaces](https://mlsanity.com/paper/2211.17068/) (2022)
- [A Self-supervised Riemannian GNN with Time Varying Curvature for Temporal Graph Learning](https://mlsanity.com/paper/2208.14073/) (2022)
- [Generalizing Graph ODE for Learning Complex System Dynamics across Environments](https://mlsanity.com/paper/2307.04287/) (2023)
- [Motif-aware Riemannian Graph Neural Network with Generative-Contrastive Learning](https://mlsanity.com/paper/2401.01232/) (2024)
- [DTCA: Decision Tree-based Co-Attention Networks for Explainable Claim Verification](https://mlsanity.com/paper/2004.13455/) (2020)
- [DeepRicci: Self-supervised Graph Structure-Feature Co-Refinement for Alleviating Over-squashing](https://mlsanity.com/paper/2401.12780/) (2024)
- [Contrastive Graph Clustering in Curvature Spaces](https://mlsanity.com/paper/2305.03555/) (2023)
- [Inf-VAE: A Variational Autoencoder Framework to Integrate Homophily and Influence in Diffusion Prediction](https://mlsanity.com/paper/2001.00132/) (2020)
- [The Simple Rules of Social Contagion](https://mlsanity.com/paper/1308.5015/) (2013)
- [Learning Hierarchical Review Graph Representations for Recommendation](https://mlsanity.com/paper/2004.11588/) (2020)
- [DyHGCN: A Dynamic Heterogeneous Graph Convolutional Network to Learn Users' Dynamic Preferences for Information Diffusion Prediction](https://mlsanity.com/paper/2006.05169/) (2020)

## Built on by (most cited first, 2 of 2)

- [RiemannGFM: Learning a Graph Foundation Model from Riemannian Geometry](https://mlsanity.com/paper/2502.03251/) (2025)
- [Spiking Graph Neural Network on Riemannian Manifolds](https://mlsanity.com/paper/2410.17941/) (2024)

## Abstract (arXiv)

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.