# Future-Interactions-Aware Trajectory Prediction via Braid Theory

arXiv: https://arxiv.org/abs/2603.22035 · HTML: https://mlsanity.com/paper/2603.22035/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 17 references that are in the map.
- First posted on arXiv 23 Mar 2026.

## Builds on (most cited first, 12 of 12)

- [Argoverse 2: Next Generation Datasets for Self-Driving Perception and Forecasting](https://mlsanity.com/paper/2301.00493/) (2023)
- [Large Scale Interactive Motion Forecasting for Autonomous Driving : The Waymo Open Motion Dataset](https://mlsanity.com/paper/2104.10133/) (2021)
- [VectorNet: Encoding HD Maps and Agent Dynamics from Vectorized Representation](https://mlsanity.com/paper/2005.04259/) (2020)
- [INTERACTION Dataset: An INTERnational, Adversarial and Cooperative moTION Dataset in Interactive Driving Scenarios with Semantic Maps](https://mlsanity.com/paper/1910.03088/) (2019)
- [MTR++: Multi-Agent Motion Prediction with Symmetric Scene Modeling and Guided Intention Querying](https://mlsanity.com/paper/2306.17770/) (2023)
- [M2I: From Factored Marginal Trajectory Prediction to Interactive Prediction](https://mlsanity.com/paper/2202.11884/) (2022)
- [FJMP: Factorized Joint Multi-Agent Motion Prediction over Learned Directed Acyclic Interaction Graphs](https://mlsanity.com/paper/2211.16197/) (2022)
- [QCNeXt: A Next-Generation Framework For Joint Multi-Agent Trajectory Prediction](https://mlsanity.com/paper/2306.10508/) (2023)
- [Reasoning Multi-Agent Behavioral Topology for Interactive Autonomous Driving](https://mlsanity.com/paper/2409.18031/) (2024)
- [IMPACT: Behavioral Intention-aware Multimodal Trajectory Prediction with Adaptive Context Trimming](https://mlsanity.com/paper/2504.09103/) (2025)
- [SRefiner: Soft-Braid Attention for Multi-Agent Trajectory Refinement](https://mlsanity.com/paper/2507.04263/) (2025)
- [Analyzing Multiagent Interactions in Traffic Scenes via Topological Braids](https://mlsanity.com/paper/2109.07060/) (2021)

## Abstract (arXiv)

To safely operate, an autonomous vehicle must know the future behavior of a potentially high number of interacting agents around it, a task often posed as multi-agent trajectory prediction. Many previous attempts to model social interactions and solve the joint prediction task either add extensive computational requirements or rely on heuristics to label multi-agent behavior types. Braid theory, in contrast, provides a powerful exact descriptor of multi-agent behavior by projecting future trajectories into braids that express how trajectories cross with each other over time; a braid then corresponds to a specific mode of coordination between the multiple agents in the future. In past work, braids have been used lightly to reason about interacting agents and restrict the attention window of predicted agents. We show that leveraging more fully the expressivity of the braid representation and using it to condition the trajectories themselves leads to even further gains in joint prediction performance, with negligible added complexity either in training or at inference time. We do so by proposing a novel auxiliary task, braid prediction, done in parallel with the trajectory prediction task. By classifying edges between agents into their correct crossing types in the braid representation, the braid prediction task is able to imbue the model with improved social awareness, which is reflected in joint predictions that more closely adhere to the actual multi-agent behavior. This simple auxiliary task allowed us to obtain significant improvements in joint metrics on three separate datasets. We show how the braid prediction task infuses the model with future intention awareness, leading to more accurate joint predictions. Code is available at github.com/caiocj1/traj-pred-braid-theory.