# Equivariant Map and Agent Geometry for Autonomous Driving Motion Prediction

arXiv: https://arxiv.org/abs/2310.13922 · HTML: https://mlsanity.com/paper/2310.13922/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 33 references that are in the map.
- First posted on arXiv 21 Oct 2023.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [VAD: Vectorized Scene Representation for Efficient Autonomous Driving](https://mlsanity.com/paper/2303.12077/) (2023)
- [VectorNet: Encoding HD Maps and Agent Dynamics from Vectorized Representation](https://mlsanity.com/paper/2005.04259/) (2020)
- [Rotation equivariant vector field networks](https://mlsanity.com/paper/1612.09346/) (2016)
- [EqMotion: Equivariant Multi-agent Motion Prediction with Invariant Interaction Reasoning](https://mlsanity.com/paper/2303.10876/) (2023)
- [Conditional Generative Neural System for Probabilistic Trajectory Prediction](https://mlsanity.com/paper/1905.01631/) (2019)
- [LOKI: Long Term and Key Intentions for Trajectory Prediction](https://mlsanity.com/paper/2108.08236/) (2021)
- [Spectral Temporal Graph Neural Network for Trajectory Prediction](https://mlsanity.com/paper/2106.02930/) (2021)
- [RAIN: Reinforced Hybrid Attention Inference Network for Motion Forecasting](https://mlsanity.com/paper/2108.01316/) (2021)
- [Spatio-Temporal Graph Dual-Attention Network for Multi-Agent Prediction and Tracking](https://mlsanity.com/paper/2102.09117/) (2021)
- [Shared Cross-Modal Trajectory Prediction for Autonomous Driving](https://mlsanity.com/paper/2011.08436/) (2020)
- [Protein Sequence and Structure Co-Design with Equivariant Translation](https://mlsanity.com/paper/2210.08761/) (2022)
- [Point Set Voting for Partial Point Cloud Analysis](https://mlsanity.com/paper/2007.04537/) (2020)
- [Interaction Modeling with Multiplex Attention](https://mlsanity.com/paper/2208.10660/) (2022)

## Built on by (most cited first, 6 of 6)

- [UniOcc: A Unified Benchmark for Occupancy Forecasting and Prediction in Autonomous Driving](https://mlsanity.com/paper/2503.24381/) (2025)
- [CMP: Cooperative Motion Prediction with Multi-Agent Communication](https://mlsanity.com/paper/2403.17916/) (2024)
- [SAFEFLOW: A Principled Protocol for Trustworthy and Transactional Autonomous Agent Systems](https://mlsanity.com/paper/2506.07564/) (2025)
- [EqDrive: Efficient Equivariant Motion Forecasting with Multi-Modality for Autonomous Driving](https://mlsanity.com/paper/2310.17540/) (2023)
- [Novel View Synthesis from a Single RGBD Image for Indoor Scenes](https://mlsanity.com/paper/2311.01065/) (2023)
- [RDD: Retrieval-Based Demonstration Decomposer for Planner Alignment in Long-Horizon Tasks](https://mlsanity.com/paper/2510.14968/) (2025)

## Abstract (arXiv)

In autonomous driving, deep learning enabled motion prediction is a popular topic. A critical gap in traditional motion prediction methodologies lies in ensuring equivariance under Euclidean geometric transformations and maintaining invariant interaction relationships. This research introduces a groundbreaking solution by employing EqMotion, a theoretically geometric equivariant and interaction invariant motion prediction model for particles and humans, plus integrating agent-equivariant high-definition (HD) map features for context aware motion prediction in autonomous driving. The use of EqMotion as backbone marks a significant departure from existing methods by rigorously ensuring motion equivariance and interaction invariance. Equivariance here implies that an output motion must be equally transformed under the same Euclidean transformation as an input motion, while interaction invariance preserves the manner in which agents interact despite transformations. These properties make the network robust to arbitrary Euclidean transformations and contribute to more accurate prediction. In addition, we introduce an equivariant method to process the HD map to enrich the spatial understanding of the network while preserving the overall network equivariance property. By applying these technologies, our model is able to achieve high prediction accuracy while maintain a lightweight design and efficient data utilization.