# Trajectory Entropy: Modeling Game State Stability from Multimodality Trajectory Prediction

arXiv: https://arxiv.org/abs/2506.05810 · HTML: https://mlsanity.com/paper/2506.05810/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 35 references that are in the map.
- First posted on arXiv 6 Jun 2025.

## Builds on (most cited first, 26 of 26)

- [Scalability in Perception for Autonomous Driving: Waymo Open Dataset](https://mlsanity.com/paper/1912.04838/) (2019)
- [Planning-oriented Autonomous Driving](https://mlsanity.com/paper/2212.10156/) (2022)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [NuPlan: A closed-loop ML-based planning benchmark for autonomous vehicles](https://mlsanity.com/paper/2106.11810/) (2021)
- [DenseTNT: End-to-end Trajectory Prediction from Dense Goal Sets](https://mlsanity.com/paper/2108.09640/) (2021)
- [Multimodal Trajectory Predictions for Autonomous Driving using Deep Convolutional Networks](https://mlsanity.com/paper/1809.10732/) (2018)
- [Motion Transformer with Global Intention Localization and Local Movement Refinement](https://mlsanity.com/paper/2209.13508/) (2022)
- [Parting with Misconceptions about Learning-based Vehicle Motion Planning](https://mlsanity.com/paper/2306.07962/) (2023)
- [MP3: A Unified Model to Map, Perceive, Predict and Plan](https://mlsanity.com/paper/2101.06806/) (2021)
- [Scene Transformer: A unified architecture for predicting multiple agent trajectories](https://mlsanity.com/paper/2106.08417/) (2021)
- [GOHOME: Graph-Oriented Heatmap Output for future Motion Estimation](https://mlsanity.com/paper/2109.01827/) (2021)
- [GameFormer: Game-theoretic Modeling and Learning of Transformer-based Interactive Prediction and Planning for Autonomous Driving](https://mlsanity.com/paper/2303.05760/) (2023)
- [Diffusion-Based Planning for Autonomous Driving with Flexible Guidance](https://mlsanity.com/paper/2501.15564/) (2025)
- [HOME: Heatmap Output for future Motion Estimation](https://mlsanity.com/paper/2105.10968/) (2021)
- [Urban Driver: Learning to Drive from Real-world Demonstrations Using Policy Gradients](https://mlsanity.com/paper/2109.13333/) (2021)
- [LookOut: Diverse Multi-Future Prediction and Planning for Self-Driving](https://mlsanity.com/paper/2101.06547/) (2021)
- [PLUTO: Pushing the Limit of Imitation Learning-based Planning for Autonomous Driving](https://mlsanity.com/paper/2404.14327/) (2024)
- [M2I: From Factored Marginal Trajectory Prediction to Interactive Prediction](https://mlsanity.com/paper/2202.11884/) (2022)
- [PiP: Planning-informed Trajectory Prediction for Autonomous Driving](https://mlsanity.com/paper/2003.11476/) (2020)
- [Multi-modal Motion Prediction with Transformer-based Neural Network for Autonomous Driving](https://mlsanity.com/paper/2109.06446/) (2021)
- [Differentiable Integrated Motion Prediction and Planning with Learnable Cost Function for Autonomous Driving](https://mlsanity.com/paper/2207.10422/) (2022)
- [DTPP: Differentiable Joint Conditional Prediction and Cost Evaluation for Tree Policy Planning in Autonomous Driving](https://mlsanity.com/paper/2310.05885/) (2023)
- [From Prediction to Planning With Goal Conditioned Lane Graph Traversals](https://mlsanity.com/paper/2302.07753/) (2023)
- [Conditional Predictive Behavior Planning with Inverse Reinforcement Learning for Human-like Autonomous Driving](https://mlsanity.com/paper/2212.08787/) (2022)
- [Deep Interactive Motion Prediction and Planning: Playing Games with Motion Prediction Models](https://mlsanity.com/paper/2204.02392/) (2022)
- [AIR2 for Interaction Prediction](https://mlsanity.com/paper/2111.08184/) (2021)

## Abstract (arXiv)

Complex interactions among agents present a significant challenge for autonomous driving in real-world scenarios. Recently, a promising approach has emerged, which formulates the interactions of agents as a level-k game framework. It effectively decouples agent policies by hierarchical game levels. However, this framework ignores both the varying driving complexities among agents and the dynamic changes in agent states across game levels, instead treating them uniformly. Consequently, redundant and error-prone computations are introduced into this framework. To tackle the issue, this paper proposes a metric, termed as Trajectory Entropy, to reveal the game status of agents within the level-k game framework. The key insight stems from recognizing the inherit relationship between agent policy uncertainty and the associated driving complexity. Specifically, Trajectory Entropy extracts statistical signals representing uncertainty from the multimodality trajectory prediction results of agents in the game. Then, the signal-to-noise ratio of this signal is utilized to quantify the game status of agents. Based on the proposed Trajectory Entropy, we refine the current level-k game framework through a simple gating mechanism, significantly improving overall accuracy while reducing computational costs. Our method is evaluated on the Waymo and nuPlan datasets, in terms of trajectory prediction, open-loop and closed-loop planning tasks. The results demonstrate the state-of-the-art performance of our method, with precision improved by up to 19.89% for prediction and up to 16.48% for planning.