# Collaborative Uncertainty in Multi-Agent Trajectory Forecasting

arXiv: https://arxiv.org/abs/2110.13947 · HTML: https://mlsanity.com/paper/2110.13947/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 48 references that are in the map.
- First posted on arXiv 26 Oct 2021.

## Builds on (most cited first, 30 of 31)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [nuScenes: A multimodal dataset for autonomous driving](https://mlsanity.com/paper/1903.11027/) (2019)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Mastering Atari with Discrete World Models](https://mlsanity.com/paper/2010.02193/) (2020)
- [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)
- [Learning Lane Graph Representations for Motion Forecasting](https://mlsanity.com/paper/2007.13732/) (2020)
- [TNT: Target-driveN Trajectory Prediction](https://mlsanity.com/paper/2008.08294/) (2020)
- [DESIRE: Distant Future Prediction in Dynamic Scenes with Interacting Agents](https://mlsanity.com/paper/1704.04394/) (2017)
- [Multimodal Trajectory Predictions for Autonomous Driving using Deep Convolutional Networks](https://mlsanity.com/paper/1809.10732/) (2018)
- [Aleatoric uncertainty estimation with test-time augmentation for medical image segmentation with convolutional neural networks](https://mlsanity.com/paper/1807.07356/) (2018)
- [It Is Not the Journey but the Destination: Endpoint Conditioned Trajectory Prediction](https://mlsanity.com/paper/2004.02025/) (2020)
- [Social-BiGAT: Multimodal Trajectory Forecasting using Bicycle-GAN and Graph Attention Networks](https://mlsanity.com/paper/1907.03395/) (2019)
- [Multi-Agent Tensor Fusion for Contextual Trajectory Prediction](https://mlsanity.com/paper/1904.04776/) (2019)
- [HOME: Heatmap Output for future Motion Estimation](https://mlsanity.com/paper/2105.10968/) (2021)
- [Rules of the Road: Predicting Driving Behavior with a Convolutional Model of Semantic Interactions](https://mlsanity.com/paper/1906.08945/) (2019)
- [Peeking into the Future: Predicting Future Person Activities and Locations in Videos](https://mlsanity.com/paper/1902.03748/) (2019)
- [LaneRCNN: Distributed Representations for Graph-Centric Motion Forecasting](https://mlsanity.com/paper/2101.06653/) (2021)
- [Stochastic Segmentation Networks: Modelling Spatially Correlated Aleatoric Uncertainty](https://mlsanity.com/paper/2006.06015/) (2020)
- [Uncertainty Aware Semi-Supervised Learning on Graph Data](https://mlsanity.com/paper/2010.12783/) (2020)
- [TPCN: Temporal Point Cloud Networks for Motion Forecasting](https://mlsanity.com/paper/2103.03067/) (2021)
- [Multi-Head Attention for Multi-Modal Joint Vehicle Motion Forecasting](https://mlsanity.com/paper/1910.03650/) (2019)
- [Towards Safe Autonomous Driving: Capture Uncertainty in the Deep Neural Network For Lidar 3D Vehicle Detection](https://mlsanity.com/paper/1804.05132/) (2018)
- [SDE-Net: Equipping Deep Neural Networks with Uncertainty Estimates](https://mlsanity.com/paper/2008.10546/) (2020)
- [Long-Term On-Board Prediction of People in Traffic Scenes under Uncertainty](https://mlsanity.com/paper/1711.09026/) (2017)
- [Structured Uncertainty Prediction Networks](https://mlsanity.com/paper/1802.07079/) (2018)
- [Discrete Residual Flow for Probabilistic Pedestrian Behavior Prediction](https://mlsanity.com/paper/1910.08041/) (2019)
- [Looking to Relations for Future Trajectory Forecast](https://mlsanity.com/paper/1905.08855/) (2019)

## Built on by (most cited first, 18 of 18)

- [Leapfrog Diffusion Model for Stochastic Trajectory Prediction](https://mlsanity.com/paper/2303.10895/) (2023)
- [GroupNet: Multiscale Hypergraph Neural Networks for Trajectory Prediction with Relational Reasoning](https://mlsanity.com/paper/2204.08770/) (2022)
- [EqMotion: Equivariant Multi-agent Motion Prediction with Invariant Interaction Reasoning](https://mlsanity.com/paper/2303.10876/) (2023)
- [Remember Intentions: Retrospective-Memory-based Trajectory Prediction](https://mlsanity.com/paper/2203.11474/) (2022)
- [Behavioral Intention Prediction in Driving Scenes: A Survey](https://mlsanity.com/paper/2211.00385/) (2022)
- [Dynamic-Group-Aware Networks for Multi-Agent Trajectory Prediction with Relational Reasoning](https://mlsanity.com/paper/2206.13114/) (2022)
- [Collaborative Uncertainty Benefits Multi-Agent Multi-Modal Trajectory Forecasting](https://mlsanity.com/paper/2207.05195/) (2022)
- [IPCC-TP: Utilizing Incremental Pearson Correlation Coefficient for Joint Multi-Agent Trajectory Prediction](https://mlsanity.com/paper/2303.00575/) (2023)
- [Improving Transferability for Cross-domain Trajectory Prediction via Neural Stochastic Differential Equation](https://mlsanity.com/paper/2312.15906/) (2023)
- [Heterogeneous Trajectory Forecasting via Risk and Scene Graph Learning](https://mlsanity.com/paper/2211.00848/) (2022)
- [Multi-Agent Trajectory Prediction with Difficulty-Guided Feature Enhancement Network](https://mlsanity.com/paper/2407.18551/) (2024)
- [CUQDS: Conformal Uncertainty Quantification under Distribution Shift for Trajectory Prediction](https://mlsanity.com/paper/2406.12100/) (2024)
- [Privacy-preserving and Uncertainty-aware Federated Trajectory Prediction for Connected Autonomous Vehicles](https://mlsanity.com/paper/2303.04340/) (2023)
- [DeepFleet: Multi-Agent Foundation Models for Mobile Robots](https://mlsanity.com/paper/2508.08574/) (2025)
- [Discovering Intrinsic Spatial-Temporal Logic Rules to Explain Human Actions](https://mlsanity.com/paper/2306.12244/) (2023)
- [SCT-MOT: Enhancing Air-to-Air Multiple UAVs Tracking with Swarm-Coupled Motion and Trajectory Guidance](https://mlsanity.com/paper/2604.06883/) (2026)
- [SportsNGEN: Sustained Generation of Realistic Multi-player Sports Gameplay](https://mlsanity.com/paper/2403.12977/) (2024)
- [Vision: "What Don't I Know About User's Preferences?" How Uncertainty Estimation Improves Proactive Assistant Alignment](https://mlsanity.com/paper/2610.15948/) (2026)

## Abstract (arXiv)

Uncertainty modeling is critical in trajectory forecasting systems for both interpretation and safety reasons. To better predict the future trajectories of multiple agents, recent works have introduced interaction modules to capture interactions among agents. This approach leads to correlations among the predicted trajectories. However, the uncertainty brought by such correlations is neglected. To fill this gap, we propose a novel concept, collaborative uncertainty(CU), which models the uncertainty resulting from the interaction module. We build a general CU-based framework to make a prediction model to learn the future trajectory and the corresponding uncertainty. The CU-based framework is integrated as a plugin module to current state-of-the-art (SOTA) systems and deployed in two special cases based on multivariate Gaussian and Laplace distributions. In each case, we conduct extensive experiments on two synthetic datasets and two public, large-scale benchmarks of trajectory forecasting. The results are promising: 1) The results of synthetic datasets show that CU-based framework allows the model to appropriately approximate the ground-truth distribution. 2) The results of trajectory forecasting benchmarks demonstrate that the CU-based framework steadily helps SOTA systems improve their performances. Especially, the proposed CU-based framework helps VectorNet improve by 57cm regarding Final Displacement Error on nuScenes dataset. 3) The visualization results of CU illustrate that the value of CU is highly related to the amount of the interactive information among agents.