# EqDrive: Efficient Equivariant Motion Forecasting with Multi-Modality for Autonomous Driving

arXiv: https://arxiv.org/abs/2310.17540 · HTML: https://mlsanity.com/paper/2310.17540/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 39 references that are in the map.
- First posted on arXiv 26 Oct 2023.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Argoverse: 3D Tracking and Forecasting with Rich Maps](https://mlsanity.com/paper/1911.02620/) (2019)
- [VectorNet: Encoding HD Maps and Agent Dynamics from Vectorized Representation](https://mlsanity.com/paper/2005.04259/) (2020)
- [MultiPath: Multiple Probabilistic Anchor Trajectory Hypotheses for Behavior Prediction](https://mlsanity.com/paper/1910.05449/) (2019)
- [Learning Lane Graph Representations for Motion Forecasting](https://mlsanity.com/paper/2007.13732/) (2020)
- [Invariant and Equivariant Graph Networks](https://mlsanity.com/paper/1812.09902/) (2018)
- [AgentFormer: Agent-Aware Transformers for Socio-Temporal Multi-Agent Forecasting](https://mlsanity.com/paper/2103.14023/) (2021)
- [DenseTNT: End-to-end Trajectory Prediction from Dense Goal Sets](https://mlsanity.com/paper/2108.09640/) (2021)
- [MultiPath++: Efficient Information Fusion and Trajectory Aggregation for Behavior Prediction](https://mlsanity.com/paper/2111.14973/) (2021)
- [Multiple Futures Prediction](https://mlsanity.com/paper/1911.00997/) (2019)
- [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)
- [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)
- [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)
- [Equivariant Map and Agent Geometry for Autonomous Driving Motion Prediction](https://mlsanity.com/paper/2310.13922/) (2023)

## Built on by (most cited first, 7 of 7)

- [OpenEMMA: Open-Source Multimodal Model for End-to-End Autonomous Driving](https://mlsanity.com/paper/2412.15208/) (2024)
- [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)
- [LaneCPP: Continuous 3D Lane Detection using Physical Priors](https://mlsanity.com/paper/2406.08381/) (2024)
- [Pioneering SE(2)-Equivariant Trajectory Planning for Automated Driving](https://mlsanity.com/paper/2403.11304/) (2024)
- [RDD: Retrieval-Based Demonstration Decomposer for Planner Alignment in Long-Horizon Tasks](https://mlsanity.com/paper/2510.14968/) (2025)

## Abstract (arXiv)

Forecasting vehicular motions in autonomous driving requires a deep understanding of agent interactions and the preservation of motion equivariance under Euclidean geometric transformations. Traditional models often lack the sophistication needed to handle the intricate dynamics inherent to autonomous vehicles and the interaction relationships among agents in the scene. As a result, these models have a lower model capacity, which then leads to higher prediction errors and lower training efficiency. In our research, we employ EqMotion, a leading equivariant particle, and human prediction model that also accounts for invariant agent interactions, for the task of multi-agent vehicle motion forecasting. In addition, we use a multi-modal prediction mechanism to account for multiple possible future paths in a probabilistic manner. By leveraging EqMotion, our model achieves state-of-the-art (SOTA) performance with fewer parameters (1.2 million) and a significantly reduced training time (less than 2 hours).