# Spacetime E(n)-Transformer: Equivariant Attention for Spatio-temporal Graphs

arXiv: https://arxiv.org/abs/2408.06039 · HTML: https://mlsanity.com/paper/2408.06039/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 22 references that are in the map.
- First posted on arXiv 12 Aug 2024.

## Builds on (most cited first, 14 of 14)

- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Temporal Graph Networks for Deep Learning on Dynamic Graphs](https://mlsanity.com/paper/2006.10637/) (2020)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [Inductive Representation Learning in Temporal Networks via Causal Anonymous Walks](https://mlsanity.com/paper/2101.05974/) (2021)
- [Towards Better Dynamic Graph Learning: New Architecture and Unified Library](https://mlsanity.com/paper/2303.13047/) (2023)
- [Learning to Reconstruct Missing Data from Spatiotemporal Graphs with Sparse Observations](https://mlsanity.com/paper/2205.13479/) (2022)
- [Can recurrent neural networks warp time?](https://mlsanity.com/paper/1804.11188/) (2018)
- [Incorporating Dynamic Flight Network in SEIR to Model Mobility between Populations](https://mlsanity.com/paper/2010.01408/) (2020)

## Abstract (arXiv)

We introduce an E(n)-equivariant Transformer architecture for spatio-temporal graph data. By imposing rotation, translation, and permutation equivariance inductive biases in both space and time, we show that the Spacetime E(n)-Transformer (SET) outperforms purely spatial and temporal models without symmetry-preserving properties. We benchmark SET against said models on the charged N-body problem, a simple physical system with complex dynamics. While existing spatio-temporal graph neural networks focus on sequential modeling, we empirically demonstrate that leveraging underlying domain symmetries yields considerable improvements for modeling dynamical systems on graphs.