# DRoPE: Directional Rotary Position Embedding for Efficient Agent Interaction Modeling

arXiv: https://arxiv.org/abs/2503.15029 · HTML: https://mlsanity.com/paper/2503.15029/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 24 references that are in the map.
- First posted on arXiv 19 Mar 2025.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Scalability in Perception for Autonomous Driving: Waymo Open Dataset](https://mlsanity.com/paper/1912.04838/) (2019)
- [DriveGPT4: Interpretable End-to-end Autonomous Driving via Large Language Model](https://mlsanity.com/paper/2310.01412/) (2023)
- [Bench2Drive: Towards Multi-Ability Benchmarking of Closed-Loop End-To-End Autonomous Driving](https://mlsanity.com/paper/2406.03877/) (2024)
- [Adan: Adaptive Nesterov Momentum Algorithm for Faster Optimizing Deep Models](https://mlsanity.com/paper/2208.06677/) (2022)
- [DriveTransformer: Unified Transformer for Scalable End-to-End Autonomous Driving](https://mlsanity.com/paper/2503.07656/) (2025)
- [A Survey of End-to-End Driving: Architectures and Training Methods](https://mlsanity.com/paper/2003.06404/) (2020)
- [BehaviorGPT: Smart Agent Simulation for Autonomous Driving with Next-Patch Prediction](https://mlsanity.com/paper/2405.17372/) (2024)
- [Solving Motion Planning Tasks with a Scalable Generative Model](https://mlsanity.com/paper/2407.02797/) (2024)
- [Closed-Loop Supervised Fine-Tuning of Tokenized Traffic Models](https://mlsanity.com/paper/2412.05334/) (2024)
- [MacFormer: Map-Agent Coupled Transformer for Real-time and Robust Trajectory Prediction](https://mlsanity.com/paper/2308.10280/) (2023)
- [QCNeXt: A Next-Generation Framework For Joint Multi-Agent Trajectory Prediction](https://mlsanity.com/paper/2306.10508/) (2023)
- [Multiverse Transformer: 1st Place Solution for Waymo Open Sim Agents Challenge 2023](https://mlsanity.com/paper/2306.11868/) (2023)
- [SMART: Scalable Multi-agent Real-time Motion Generation via Next-token Prediction](https://mlsanity.com/paper/2405.15677/) (2024)
- [KiGRAS: Kinematic-Driven Generative Model for Realistic Agent Simulation](https://mlsanity.com/paper/2407.12940/) (2024)
- [TrafficBots V1.5: Traffic Simulation via Conditional VAEs and Transformers with Relative Pose Encoding](https://mlsanity.com/paper/2406.10898/) (2024)
- [UniMM: A Unified Mixture Model Framework for Multi-Agent Simulation](https://mlsanity.com/paper/2501.17015/) (2025)
- [Context-Aware Timewise VAEs for Real-Time Vehicle Trajectory Prediction](https://mlsanity.com/paper/2302.10873/) (2023)
- [Categorical Traffic Transformer: Interpretable and Diverse Behavior Prediction with Tokenized Latent](https://mlsanity.com/paper/2311.18307/) (2023)
- [Motion Forecasting for Autonomous Vehicles: A Survey](https://mlsanity.com/paper/2502.08664/) (2025)

## Built on by (most cited first, 9 of 9)

- [SPACeR: Self-Play Anchoring with Centralized Reference Models](https://mlsanity.com/paper/2510.18060/) (2025)
- [Deconstructing Positional Information: From Attention Logits to Training Biases](https://mlsanity.com/paper/2505.13027/) (2025)
- [Do LLM Modules Generalize? A Study on Motion Generation for Autonomous Driving](https://mlsanity.com/paper/2509.02754/) (2025)
- [Autoregressive Meta-Actions for Unified Controllable Trajectory Generation](https://mlsanity.com/paper/2505.23612/) (2025)
- [Autoregressive End-to-End Planning with Time-Invariant Spatial Alignment and Multi-Objective Policy Refinement](https://mlsanity.com/paper/2509.20938/) (2025)
- [SoPE: Spherical Coordinate-Based Positional Embedding for Enhancing Spatial Perception of 3D LVLMs](https://mlsanity.com/paper/2602.22716/) (2026)
- [RLFTSim: Realistic and Controllable Multi-Agent Traffic Simulation via Reinforcement Learning Fine-Tuning](https://mlsanity.com/paper/2605.19033/) (2026)
- [Learning Rollout from Sampling:An R1-Style Tokenized Traffic Simulation Model](https://mlsanity.com/paper/2603.24989/) (2026)
- [Efficient Equivariant Transformer for Self-Driving Agent Modeling](https://mlsanity.com/paper/2604.01466/) (2026)

## Abstract (arXiv)

Accurate and efficient modeling of agent interactions is essential for trajectory generation, the core of autonomous driving systems. Existing methods, scene-centric, agent-centric, and query-centric frameworks, each present distinct advantages and drawbacks, creating an impossible triangle among accuracy, computational time, and memory efficiency. To break this limitation, we propose Directional Rotary Position Embedding (DRoPE), a novel adaptation of Rotary Position Embedding (RoPE), originally developed in natural language processing. Unlike traditional relative position embedding (RPE), which introduces significant space complexity, RoPE efficiently encodes relative positions without explicitly increasing complexity but faces inherent limitations in handling angular information due to periodicity. DRoPE overcomes this limitation by introducing a uniform identity scalar into RoPE's 2D rotary transformation, aligning rotation angles with realistic agent headings to naturally encode relative angular information. We theoretically analyze DRoPE's correctness and efficiency, demonstrating its capability to simultaneously optimize trajectory generation accuracy, time complexity, and space complexity. Empirical evaluations compared with various state-of-the-art trajectory generation models, confirm DRoPE's good performance and significantly reduced space complexity, indicating both theoretical soundness and practical effectiveness. The video documentation is available at https://drope-traj.github.io/.