# Graph Neural Ordinary Differential Equations-based method for Collaborative Filtering

arXiv: https://arxiv.org/abs/2311.12329 · HTML: https://mlsanity.com/paper/2311.12329/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 32 references that are in the map.
- First posted on arXiv 21 Nov 2023.

## Builds on (most cited first, 23 of 23)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [Neural Graph Collaborative Filtering](https://mlsanity.com/paper/1905.08108/) (2019)
- [Stable Architectures for Deep Neural Networks](https://mlsanity.com/paper/1705.03341/) (2017)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [Revisiting Graph based Collaborative Filtering: A Linear Residual Graph Convolutional Network Approach](https://mlsanity.com/paper/2001.10167/) (2020)
- [Continuous Graph Neural Networks](https://mlsanity.com/paper/1912.00967/) (2019)
- [UltraGCN: Ultra Simplification of Graph Convolutional Networks for Recommendation](https://mlsanity.com/paper/2110.15114/) (2021)
- [GMNN: Graph Markov Neural Networks](https://mlsanity.com/paper/1905.06214/) (2019)
- [Graph Trend Filtering Networks for Recommendations](https://mlsanity.com/paper/2108.05552/) (2021)
- [Collaborative Memory Network for Recommendation Systems](https://mlsanity.com/paper/1804.10862/) (2018)
- [LT-OCF: Learnable-Time ODE-based Collaborative Filtering](https://mlsanity.com/paper/2108.06208/) (2021)
- [Convolutional Neural Networks combined with Runge-Kutta Methods](https://mlsanity.com/paper/1802.08831/) (2018)
- [Graph Collaborative Signals Denoising and Augmentation for Recommendation](https://mlsanity.com/paper/2304.03344/) (2023)
- [Neural Ordinary Differential Equations for Semantic Segmentation of Individual Colon Glands](https://mlsanity.com/paper/1910.10470/) (2019)
- [Layer-refined Graph Convolutional Networks for Recommendation](https://mlsanity.com/paper/2207.11088/) (2022)
- [Graph Neural Networks: a bibliometrics overview](https://mlsanity.com/paper/2201.01188/) (2022)

## Built on by (most cited first, 5 of 5)

- [LLMInit: A Free Lunch from Large Language Models for Selective Initialization of Recommendation](https://mlsanity.com/paper/2503.01814/) (2025)
- [Mixed Supervised Graph Contrastive Learning for Recommendation](https://mlsanity.com/paper/2404.15954/) (2024)
- [Do We Really Need Graph Convolution During Training? Light Post-Training Graph-ODE for Efficient Recommendation](https://mlsanity.com/paper/2407.18910/) (2024)
- [On the Convergence and Size Transferability of Continuous-depth Graph Neural Networks](https://mlsanity.com/paper/2510.03923/) (2025)
- [Toward User Preference Alignment in LLM Recommendation via Explicit Context Feedback](https://mlsanity.com/paper/2605.29141/) (2026)

## Abstract (arXiv)

Graph Convolution Networks (GCNs) are widely considered state-of-the-art for collaborative filtering. Although several GCN-based methods have been proposed and achieved state-of-the-art performance in various tasks, they can be computationally expensive and time-consuming to train if too many layers are created. However, since the linear GCN model can be interpreted as a differential equation, it is possible to transfer it to an ODE problem. This inspired us to address the computational limitations of GCN-based models by designing a simple and efficient NODE-based model that can skip some GCN layers to reach the final state, thus avoiding the need to create many layers. In this work, we propose a Graph Neural Ordinary Differential Equation-based method for Collaborative Filtering (GODE-CF). This method estimates the final embedding by utilizing the information captured by one or two GCN layers. To validate our approach, we conducted experiments on multiple datasets. The results demonstrate that our model outperforms competitive baselines, including GCN-based models and other state-of-the-art CF methods. Notably, our proposed GODE-CF model has several advantages over traditional GCN-based models. It is simple, efficient, and has a fast training time, making it a practical choice for real-world situations.