# Factorised Neural Relational Inference for Multi-Interaction Systems

arXiv: https://arxiv.org/abs/1905.08721 · HTML: https://mlsanity.com/paper/1905.08721/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 May 2019.

## Built on by (most cited first, 15 of 15)

- [Multi-Scale Adaptive Graph Neural Network for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2201.04828/) (2022)
- [Conditional Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/2106.11083/) (2021)
- [Interaction Modeling with Multiplex Attention](https://mlsanity.com/paper/2208.10660/) (2022)
- [Neural Relational Inference with Efficient Message Passing Mechanisms](https://mlsanity.com/paper/2101.09486/) (2021)
- [Inferring Relational Potentials in Interacting Systems](https://mlsanity.com/paper/2310.14466/) (2023)
- [Behavior-Inspired Neural Networks for Relational Inference](https://mlsanity.com/paper/2406.14746/) (2024)
- [Learning Heterogeneous Interaction Strengths by Trajectory Prediction with Graph Neural Network](https://mlsanity.com/paper/2208.13179/) (2022)
- [Flow-based Spatio-Temporal Structured Prediction of Motion Dynamics](https://mlsanity.com/paper/2104.04391/) (2021)
- [PASCL: Supervised Contrastive Learning with Perturbative Augmentation for Particle Decay Reconstruction](https://mlsanity.com/paper/2402.11538/) (2024)
- [SPHINX: Structural Prediction using Hypergraph Inference Network](https://mlsanity.com/paper/2410.03208/) (2024)
- [Neural Interaction Energy for Multi-Agent Trajectory Prediction](https://mlsanity.com/paper/2404.16579/) (2024)
- [Discovering Latent Representations of Relations for Interacting Systems](https://mlsanity.com/paper/2111.05514/) (2021)
- [Flexible Networks for Learning Physical Dynamics of Deformable Objects](https://mlsanity.com/paper/2112.03728/) (2021)
- [Discovering group dynamics in coordinated time series via hierarchical recurrent switching-state models](https://mlsanity.com/paper/2401.14973/) (2024)
- [Interpretable Relational Inference with LLM-Guided Symbolic Dynamics Modeling](https://mlsanity.com/paper/2604.12806/) (2026)

## Abstract (arXiv)

Many complex natural and cultural phenomena are well modelled by systems of simple interactions between particles. A number of architectures have been developed to articulate this kind of structure, both implicitly and explicitly. We consider an unsupervised explicit model, the NRI model, and make a series of representational adaptations and physically motivated changes. Most notably we factorise the inferred latent interaction graph into a multiplex graph, allowing each layer to encode for a different interaction-type. This fNRI model is smaller in size and significantly outperforms the original in both edge and trajectory prediction, establishing a new state-of-the-art. We also present a simplified variant of our model, which demonstrates the NRI's formulation as a variational auto-encoder is not necessary for good performance, and make an adaptation to the NRI's training routine, significantly improving its ability to model complex physical dynamical systems.