mlsanityData to 14 Oct 2026

Roto-translated Local Coordinate Frames For Interacting Dynamical Systems

arXiv 2110.14961 ↗First posted 28 Oct 2021cs.LG stat.MLcited by 24

Not on the map. Why?

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.

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

47 of 66 references.

References · 47

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  3. 2017Graph Attention Networkscited by 8,923
  4. 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 7,005
  5. 2017Inductive Representation Learning on Large Graphscited by 6,320
  6. 2014Neural Machine Translation by Jointly Learning to Align and Translatecited by 4,548
  7. 2014Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translationcited by 4,057
  8. 2017Neural Message Passing for Quantum Chemistrycited by 3,487
  9. 2016Categorical Reparameterization with Gumbel-Softmaxcited by 2,739
  10. 2019Fast Graph Representation Learning with PyTorch Geometriccited by 2,434
  11. 2018Dynamic Graph CNN for Learning on Point Cloudscited by 2,223
  12. 2018Spatial Temporal Graph Convolutional Networks for Skeleton-Based Action Recognitioncited by 1,209
35 more
  1. 2016Group Equivariant Convolutional Networkscited by 1,165
  2. 2016The Concrete Distribution: A Continuous Relaxation of Discrete Random Variablescited by 1,148
  3. 2015Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)cited by 1,070
  4. 2021E(n) Equivariant Graph Neural Networkscited by 965
  5. 2020Learning to Simulate Complex Physics with Graph Networkscited by 880
  6. 2015Gated Graph Sequence Neural Networkscited by 796
  7. 2020Accelerating 3D Deep Learning with PyTorch3Dcited by 784
  8. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 746
  9. 2019Argoverse: 3D Tracking and Forecasting with Rich Mapscited by 732
  10. 2020Benchmarking Graph Neural Networkscited by 680
  11. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 607
  12. 2017SchNet: A continuous-filter convolutional neural network for modeling quantum interactionscited by 571
  13. 2016Interaction Networks for Learning about Objects, Relations and Physicscited by 509
  14. 2016Geometric deep learning on graphs and manifolds using mixture model CNNscited by 468
  15. 2019General E(2)-Equivariant Steerable CNNscited by 446
  16. 2015A Recurrent Latent Variable Model for Sequential Datacited by 362
  17. 2020Social-STGCNN: A Social Spatio-Temporal Graph Convolutional Neural Network for Human Trajectory Predictioncited by 325
  18. 2016Dynamic Filter Networkscited by 319
  19. 2017Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphscited by 310
  20. 2016Steerable CNNscited by 305
  21. 2016Harmonic Networks: Deep Translation and Rotation Equivariancecited by 295
  22. 2019Kornia: an Open Source Differentiable Computer Vision Library for PyTorchcited by 232
  23. 2019Social-BiGAT: Multimodal Trajectory Forecasting using Bicycle-GAN and Graph Attention Networkscited by 229
  24. 2017Social Attention: Modeling Attention in Human Crowdscited by 186
  25. 2015Deep Kalman Filterscited by 166
  26. 2017SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernelscited by 161
  27. 2021Deep Parametric Continuous Convolutional Neural Networkscited by 161
  28. 2018PPF-FoldNet: Unsupervised Learning of Rotation Invariant 3D Local Descriptorscited by 141
  29. 2019The inD Dataset: A Drone Dataset of Naturalistic Road User Trajectories at German Intersectionscited by 137
  30. 2020Human Trajectory Forecasting in Crowds: A Deep Learning Perspectivecited by 129
  31. 2018TrafficPredict: Trajectory Prediction for Heterogeneous Traffic-Agentscited by 111
  32. 2020Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphscited by 92
  33. 2019What the Constant Velocity Model Can Teach Us About Pedestrian Motion Predictioncited by 80
  34. 2021Conditional Neural Relational Inference for Interacting Systemscited by 28
  35. 2020Trajectory Prediction using Equivariant Continuous Convolutioncited by 26

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 4; 2023: 10; 2024: 7; 2025: 2; 2026: 1.

24 papers.

Sort:

By area:

  1. 2022Equivariance with Learned Canonicalization Functionscited by 109
  2. 2023EqMotion: Equivariant Multi-agent Motion Prediction with Invariant Interaction Reasoningcited by 97
  3. 2023Geometric Clifford Algebra Networkscited by 38
  4. 2023Geometry-Complete Diffusion for 3D Molecule Generation and Optimizationcited by 37
  5. 2022Protein Sequence and Structure Co-Design with Equivariant Translationcited by 31
  6. 2023Functional-Group-Based Diffusion for Pocket-Specific Molecule Generation and Elaborationcited by 30
  7. 2024Antigen-Specific Antibody Design via Direct Energy-based Preference Optimizationcited by 30
  8. 2024A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applicationscited by 28
  9. 2024PPFlow: Target-aware Peptide Design with Torsional Flow Matchingcited by 26
  10. 2024Are High-Degree Representations Really Unnecessary in Equivariant Graph Neural Networks?cited by 18
  11. 2022Geometry-Complete Perceptron Networks for 3D Molecular Graphscited by 16
  12. 2022Graph Neural Network with Local Frame for Molecular Potential Energy Surfacecited by 14
12 more
  1. 2023On Robot Grasp Learning Using Equivariant Modelscited by 12
  2. 2023Graph Switching Dynamical Systemscited by 10
  3. 2024AI-driven inverse design of materials: Past, present and futurecited by 10
  4. 2023Latent Field Discovery In Interacting Dynamical Systems With Neural Fieldscited by 7
  5. 2023PGODE: Towards High-quality System Dynamics Modelingcited by 7
  6. 2024Variational Inference Failures Under Model Symmetries: Permutation Invariant Posteriors for Bayesian Neural Networkscited by 6
  7. 2024Pioneering SE(2)-Equivariant Trajectory Planning for Automated Drivingcited by 4
  8. 2023Newton-Cotes Graph Neural Networks: On the Time Evolution of Dynamic Systemscited by 3
  9. 2023FFINet: Future Feedback Interaction Network for Motion Forecastingcited by 3
  10. 2025Universally Invariant Learning in Equivariant GNNscited by 3
  11. 2025A Circular Argument : Does RoPE need to be Equivariant for Vision?cited by 3
  12. 2026Temporal Sheaf Neural Networks with Dynamic Orthogonal Transportcited by 0