# TrajPAC: Towards Robustness Verification of Pedestrian Trajectory Prediction Models

arXiv: https://arxiv.org/abs/2308.05985 · HTML: https://mlsanity.com/paper/2308.05985/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 68 of its 102 references that are in the map.
- First posted on arXiv 11 Aug 2023.

## Builds on (most cited first, 30 of 68)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [Towards Robust Interpretability with Self-Explaining Neural Networks](https://mlsanity.com/paper/1806.07538/) (2018)
- [On Evaluating Adversarial Robustness](https://mlsanity.com/paper/1902.06705/) (2019)
- [MultiPath: Multiple Probabilistic Anchor Trajectory Hypotheses for Behavior Prediction](https://mlsanity.com/paper/1910.05449/) (2019)
- [AgentFormer: Agent-Aware Transformers for Socio-Temporal Multi-Agent Forecasting](https://mlsanity.com/paper/2103.14023/) (2021)
- [Social-STGCNN: A Social Spatio-Temporal Graph Convolutional Neural Network for Human Trajectory Prediction](https://mlsanity.com/paper/2002.11927/) (2020)
- [DESIRE: Distant Future Prediction in Dynamic Scenes with Interacting Agents](https://mlsanity.com/paper/1704.04394/) (2017)
- [SoPhie: An Attentive GAN for Predicting Paths Compliant to Social and Physical Constraints](https://mlsanity.com/paper/1806.01482/) (2018)
- [Adversarial Examples for Semantic Segmentation and Object Detection](https://mlsanity.com/paper/1703.08603/) (2017)
- [CoverNet: Multimodal Behavior Prediction using Trajectory Sets](https://mlsanity.com/paper/1911.10298/) (2019)
- [Generating Adversarial Examples with Adversarial Networks](https://mlsanity.com/paper/1801.02610/) (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)
- [Neural Prototype Trees for Interpretable Fine-grained Image Recognition](https://mlsanity.com/paper/2012.02046/) (2020)
- [Social Attention: Modeling Attention in Human Crowds](https://mlsanity.com/paper/1710.04689/) (2017)
- [Stochastic Trajectory Prediction via Motion Indeterminacy Diffusion](https://mlsanity.com/paper/2203.13777/) (2022)
- [Multiple Futures Prediction](https://mlsanity.com/paper/1911.00997/) (2019)
- [Generating Visual Explanations](https://mlsanity.com/paper/1603.08507/) (2016)
- [Generating 3D Adversarial Point Clouds](https://mlsanity.com/paper/1809.07016/) (2018)
- [Multi-Agent Tensor Fusion for Contextual Trajectory Prediction](https://mlsanity.com/paper/1904.04776/) (2019)
- [NNV: The Neural Network Verification Tool for Deep Neural Networks and Learning-Enabled Cyber-Physical Systems](https://mlsanity.com/paper/2004.05519/) (2020)
- [GroupNet: Multiscale Hypergraph Neural Networks for Trajectory Prediction with Relational Reasoning](https://mlsanity.com/paper/2204.08770/) (2022)
- [SGCN:Sparse Graph Convolution Network for Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2104.01528/) (2021)
- [Universal Physical Camouflage Attacks on Object Detectors](https://mlsanity.com/paper/1909.04326/) (2019)

## Built on by (most cited first, 8 of 8)

- [Enhancing Robust Fairness via Confusional Spectral Regularization](https://mlsanity.com/paper/2501.13273/) (2025)
- [Continuous Locomotive Crowd Behavior Generation](https://mlsanity.com/paper/2504.04756/) (2025)
- [Certified Human Trajectory Prediction](https://mlsanity.com/paper/2403.13778/) (2024)
- [Evaluating Human Trajectory Prediction with Metamorphic Testing](https://mlsanity.com/paper/2407.18756/) (2024)
- [Out-of-Bounding-Box Triggers: A Stealthy Approach to Cheat Object Detectors](https://mlsanity.com/paper/2410.10091/) (2024)
- [RealTraj: Towards Real-World Pedestrian Trajectory Forecasting](https://mlsanity.com/paper/2411.17376/) (2024)
- [Shapley Uncertainty in Natural Language Generation](https://mlsanity.com/paper/2507.21406/) (2025)
- [TrajRS: Towards Certified Robustness in Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2606.28716/) (2026)

## Abstract (arXiv)

Robust pedestrian trajectory forecasting is crucial to developing safe autonomous vehicles. Although previous works have studied adversarial robustness in the context of trajectory forecasting, some significant issues remain unaddressed. In this work, we try to tackle these crucial problems. Firstly, the previous definitions of robustness in trajectory prediction are ambiguous. We thus provide formal definitions for two kinds of robustness, namely label robustness and pure robustness. Secondly, as previous works fail to consider robustness about all points in a disturbance interval, we utilise a probably approximately correct (PAC) framework for robustness verification. Additionally, this framework can not only identify potential counterexamples, but also provides interpretable analyses of the original methods. Our approach is applied using a prototype tool named TrajPAC. With TrajPAC, we evaluate the robustness of four state-of-the-art trajectory prediction models -- Trajectron++, MemoNet, AgentFormer, and MID -- on trajectories from five scenes of the ETH/UCY dataset and scenes of the Stanford Drone Dataset. Using our framework, we also experimentally study various factors that could influence robustness performance.