# Roto-translated Local Coordinate Frames For Interacting Dynamical Systems

arXiv: https://arxiv.org/abs/2110.14961 · HTML: https://mlsanity.com/paper/2110.14961/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 66 references that are in the map.
- First posted on arXiv 28 Oct 2021.

## Builds on (most cited first, 30 of 47)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Spatial Temporal Graph Convolutional Networks for Skeleton-Based Action Recognition](https://mlsanity.com/paper/1801.07455/) (2018)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Argoverse: 3D Tracking and Forecasting with Rich Maps](https://mlsanity.com/paper/1911.02620/) (2019)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Social-STGCNN: A Social Spatio-Temporal Graph Convolutional Neural Network for Human Trajectory Prediction](https://mlsanity.com/paper/2002.11927/) (2020)
- [Dynamic Filter Networks](https://mlsanity.com/paper/1605.09673/) (2016)

## Built on by (most cited first, 24 of 24)

- [Equivariance with Learned Canonicalization Functions](https://mlsanity.com/paper/2211.06489/) (2022)
- [EqMotion: Equivariant Multi-agent Motion Prediction with Invariant Interaction Reasoning](https://mlsanity.com/paper/2303.10876/) (2023)
- [Geometric Clifford Algebra Networks](https://mlsanity.com/paper/2302.06594/) (2023)
- [Geometry-Complete Diffusion for 3D Molecule Generation and Optimization](https://mlsanity.com/paper/2302.04313/) (2023)
- [Protein Sequence and Structure Co-Design with Equivariant Translation](https://mlsanity.com/paper/2210.08761/) (2022)
- [Functional-Group-Based Diffusion for Pocket-Specific Molecule Generation and Elaboration](https://mlsanity.com/paper/2306.13769/) (2023)
- [Antigen-Specific Antibody Design via Direct Energy-based Preference Optimization](https://mlsanity.com/paper/2403.16576/) (2024)
- [A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications](https://mlsanity.com/paper/2403.00485/) (2024)
- [PPFlow: Target-aware Peptide Design with Torsional Flow Matching](https://mlsanity.com/paper/2405.06642/) (2024)
- [Are High-Degree Representations Really Unnecessary in Equivariant Graph Neural Networks?](https://mlsanity.com/paper/2410.11443/) (2024)
- [Geometry-Complete Perceptron Networks for 3D Molecular Graphs](https://mlsanity.com/paper/2211.02504/) (2022)
- [Graph Neural Network with Local Frame for Molecular Potential Energy Surface](https://mlsanity.com/paper/2208.00716/) (2022)
- [On Robot Grasp Learning Using Equivariant Models](https://mlsanity.com/paper/2306.06489/) (2023)
- [Graph Switching Dynamical Systems](https://mlsanity.com/paper/2306.00370/) (2023)
- [AI-driven inverse design of materials: Past, present and future](https://mlsanity.com/paper/2411.09429/) (2024)
- [Latent Field Discovery In Interacting Dynamical Systems With Neural Fields](https://mlsanity.com/paper/2310.20679/) (2023)
- [PGODE: Towards High-quality System Dynamics Modeling](https://mlsanity.com/paper/2311.06554/) (2023)
- [Variational Inference Failures Under Model Symmetries: Permutation Invariant Posteriors for Bayesian Neural Networks](https://mlsanity.com/paper/2408.05496/) (2024)
- [Pioneering SE(2)-Equivariant Trajectory Planning for Automated Driving](https://mlsanity.com/paper/2403.11304/) (2024)
- [Newton-Cotes Graph Neural Networks: On the Time Evolution of Dynamic Systems](https://mlsanity.com/paper/2305.14642/) (2023)
- [FFINet: Future Feedback Interaction Network for Motion Forecasting](https://mlsanity.com/paper/2311.04512/) (2023)
- [Universally Invariant Learning in Equivariant GNNs](https://mlsanity.com/paper/2510.13169/) (2025)
- [A Circular Argument : Does RoPE need to be Equivariant for Vision?](https://mlsanity.com/paper/2511.08368/) (2025)
- [Temporal Sheaf Neural Networks with Dynamic Orthogonal Transport](https://mlsanity.com/paper/2606.10071/) (2026)

## Abstract (arXiv)

Modelling interactions is critical in learning complex dynamical systems, namely systems of interacting objects with highly non-linear and time-dependent behaviour. A large class of such systems can be formalized as textitgeometric graphs, textiti.e., graphs with nodes positioned in the Euclidean space given an textitarbitrarily chosen global coordinate system, for instance vehicles in a traffic scene. Notwithstanding the arbitrary global coordinate system, the governing dynamics of the respective dynamical systems are invariant to rotations and translations, also known as textitGalilean invariance. As ignoring these invariances leads to worse generalization, in this work we propose local coordinate frames per node-object to induce roto-translation invariance to the geometric graph of the interacting dynamical system. Further, the local coordinate frames allow for a natural definition of anisotropic filtering in graph neural networks. Experiments in traffic scenes, 3D motion capture, and colliding particles demonstrate that the proposed approach comfortably outperforms the recent state-of-the-art.