# LT-OCF: Learnable-Time ODE-based Collaborative Filtering

arXiv: https://arxiv.org/abs/2108.06208 · HTML: https://mlsanity.com/paper/2108.06208/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 54 references that are in the map.
- First posted on arXiv 8 Aug 2021.

## Builds on (most cited first, 30 of 32)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [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)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Neural Graph Collaborative Filtering](https://mlsanity.com/paper/1905.08108/) (2019)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Variational Autoencoders for Collaborative Filtering](https://mlsanity.com/paper/1802.05814/) (2018)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)
- [FractalNet: Ultra-Deep Neural Networks without Residuals](https://mlsanity.com/paper/1605.07648/) (2016)
- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [Dissecting Neural ODEs](https://mlsanity.com/paper/2002.08071/) (2020)
- [Deep Learning based Recommender System: A Survey and New Perspectives](https://mlsanity.com/paper/1707.07435/) (2017)
- [Graph Wavelet Neural Network](https://mlsanity.com/paper/1904.07785/) (2019)
- [Knowledge Graph Convolutional Networks for Recommender Systems](https://mlsanity.com/paper/1904.12575/) (2019)
- [Revisiting Graph based Collaborative Filtering: A Linear Residual Graph Convolutional Network Approach](https://mlsanity.com/paper/2001.10167/) (2020)
- [Large-Scale Learnable Graph Convolutional Networks](https://mlsanity.com/paper/1808.03965/) (2018)
- [Collaborative Deep Learning for Recommender Systems](https://mlsanity.com/paper/1409.2944/) (2014)
- [On Robustness of Neural Ordinary Differential Equations](https://mlsanity.com/paper/1910.05513/) (2019)
- [NAIS: Neural Attentive Item Similarity Model for Recommendation](https://mlsanity.com/paper/1809.07053/) (2018)
- [Collaborative Memory Network for Recommendation Systems](https://mlsanity.com/paper/1804.10862/) (2018)
- [OCT-GAN: Neural ODE-based Conditional Tabular GANs](https://mlsanity.com/paper/2105.14969/) (2021)
- [Convolutional Neural Networks combined with Runge-Kutta Methods](https://mlsanity.com/paper/1802.08831/) (2018)

## Built on by (most cited first, 21 of 21)

- [GREAD: Graph Neural Reaction-Diffusion Networks](https://mlsanity.com/paper/2211.14208/) (2022)
- [Blurring-Sharpening Process Models for Collaborative Filtering](https://mlsanity.com/paper/2211.09324/) (2022)
- [An Attentive Inductive Bias for Sequential Recommendation beyond the Self-Attention](https://mlsanity.com/paper/2312.10325/) (2023)
- [Linear, or Non-Linear, That is the Question!](https://mlsanity.com/paper/2111.07265/) (2021)
- [Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks](https://mlsanity.com/paper/2503.23167/) (2025)
- [PANDA: Expanded Width-Aware Message Passing Beyond Rewiring](https://mlsanity.com/paper/2406.03671/) (2024)
- [LightMove: A Lightweight Next-POI Recommendation for Taxicab Rooftop Advertising](https://mlsanity.com/paper/2108.04993/) (2021)
- [TimeKit: A Time-series Forecasting-based Upgrade Kit for Collaborative Filtering](https://mlsanity.com/paper/2211.04266/) (2022)
- [It's Enough: Relaxing Diagonal Constraints in Linear Autoencoders for Recommendation](https://mlsanity.com/paper/2305.12922/) (2023)
- [Criteria Tell You More than Ratings: Criteria Preference-Aware Light Graph Convolution for Effective Multi-Criteria Recommendation](https://mlsanity.com/paper/2305.18885/) (2023)
- [Graph Neural Ordinary Differential Equations-based method for Collaborative Filtering](https://mlsanity.com/paper/2311.12329/) (2023)
- [SCONE: A Novel Stochastic Sampling to Generate Contrastive Views and Hard Negative Samples for Recommendation](https://mlsanity.com/paper/2405.00287/) (2024)
- [SVD-AE: Simple Autoencoders for Collaborative Filtering](https://mlsanity.com/paper/2405.04746/) (2024)
- [RDGCL: Reaction-Diffusion Graph Contrastive Learning for Recommendation](https://mlsanity.com/paper/2312.16563/) (2023)
- [Do We Really Need Graph Convolution During Training? Light Post-Training Graph-ODE for Efficient Recommendation](https://mlsanity.com/paper/2407.18910/) (2024)
- [Are Graph Transformers Necessary? Efficient Long-Range Message Passing with Fractal Nodes in MPNNs](https://mlsanity.com/paper/2511.13010/) (2025)
- [QoS-Aware Graph Contrastive Learning for Web Service Recommendation](https://mlsanity.com/paper/2401.03162/) (2024)
- [Prediction-based One-shot Dynamic Parking Pricing](https://mlsanity.com/paper/2208.14231/) (2022)
- [Hawkes Process Based on Controlled Differential Equations](https://mlsanity.com/paper/2305.07031/) (2023)
- [Operator-learning-inspired Modeling of Neural Ordinary Differential Equations](https://mlsanity.com/paper/2312.10274/) (2023)
- [TV-Rec: Time-Variant Convolutional Filter for Sequential Recommendation](https://mlsanity.com/paper/2510.25259/) (2025)

## Abstract (arXiv)

Collaborative filtering (CF) is a long-standing problem of recommender systems. Many novel methods have been proposed, ranging from classical matrix factorization to recent graph convolutional network-based approaches. After recent fierce debates, researchers started to focus on linear graph convolutional networks (GCNs) with a layer combination, which show state-of-the-art accuracy in many datasets. In this work, we extend them based on neural ordinary differential equations (NODEs), because the linear GCN concept can be interpreted as a differential equation, and present the method of Learnable-Time ODE-based Collaborative Filtering (LT-OCF). The main novelty in our method is that after redesigning linear GCNs on top of the NODE regime, i) we learn the optimal architecture rather than relying on manually designed ones, ii) we learn smooth ODE solutions that are considered suitable for CF, and iii) we test with various ODE solvers that internally build a diverse set of neural network connections. We also present a novel training method specialized to our method. In our experiments with three benchmark datasets, Gowalla, Yelp2018, and Amazon-Book, our method consistently shows better accuracy than existing methods, e.g., a recall of 0.0411 by LightGCN vs. 0.0442 by LT-OCF and an NDCG of 0.0315 by LightGCN vs. 0.0341 by LT-OCF in Amazon-Book. One more important discovery in our experiments that is worth mentioning is that our best accuracy was achieved by dense connections rather than linear connections.