# Improving Out-of-Distribution Generalization of Trajectory Prediction for Autonomous Driving via Polynomial Representations

arXiv: https://arxiv.org/abs/2407.13431 · HTML: https://mlsanity.com/paper/2407.13431/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 30 references that are in the map.
- First posted on arXiv 18 Jul 2024.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Argoverse: 3D Tracking and Forecasting with Rich Maps](https://mlsanity.com/paper/1911.02620/) (2019)
- [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)
- [Learning Lane Graph Representations for Motion Forecasting](https://mlsanity.com/paper/2007.13732/) (2020)
- [A Fourier Perspective on Model Robustness in Computer Vision](https://mlsanity.com/paper/1906.08988/) (2019)
- [MultiPath++: Efficient Information Fusion and Trajectory Aggregation for Behavior Prediction](https://mlsanity.com/paper/2111.14973/) (2021)
- [MTR++: Multi-Agent Motion Prediction with Symmetric Scene Modeling and Guided Intention Querying](https://mlsanity.com/paper/2306.17770/) (2023)
- [Forecast-MAE: Self-supervised Pre-training for Motion Forecasting with Masked Autoencoders](https://mlsanity.com/paper/2308.09882/) (2023)
- [Vehicle trajectory prediction works, but not everywhere](https://mlsanity.com/paper/2112.03909/) (2021)
- [PLOP: Probabilistic poLynomial Objects trajectory Planning for autonomous driving](https://mlsanity.com/paper/2003.08744/) (2020)
- [An Empirical Bayes Analysis of Object Trajectory Representation Models](https://mlsanity.com/paper/2211.01696/) (2022)
- [Temporally-Continuous Probabilistic Prediction using Polynomial Trajectory Parameterization](https://mlsanity.com/paper/2011.00399/) (2020)

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

- [GoIRL: Graph-Oriented Inverse Reinforcement Learning for Multimodal Trajectory Prediction](https://mlsanity.com/paper/2506.21121/) (2025)
- [CHARM3R: Towards Unseen Camera Height Robust Monocular 3D Detector](https://mlsanity.com/paper/2508.11185/) (2025)
- [Uncertainty-Aware Trajectory Prediction via Rule-Regularized Heteroscedastic Deep Classification](https://mlsanity.com/paper/2504.13111/) (2025)
- [Zero-Shot Cross-City Generalization in End-to-End Autonomous Driving: Self-Supervised versus Supervised Representations](https://mlsanity.com/paper/2603.11417/) (2026)
- [Uncertainty Quantification for Physics-Informed Neural Networks with Extended Fiducial Inference](https://mlsanity.com/paper/2505.19136/) (2025)
- [EP-Diffuser: An Efficient Diffusion Model for Traffic Scene Generation and Prediction via Polynomial Representations](https://mlsanity.com/paper/2504.05422/) (2025)
- [Forecasting the Past: Gradient-Based Distribution Shift Detection in Trajectory Prediction](https://mlsanity.com/paper/2604.12425/) (2026)
- [SkyDrive: Learning to Drive in a New City from Aerial Traffic Monitoring](https://mlsanity.com/paper/2608.25142/) (2026)
- [MoCAR: Motion-code Coordinate-aware AutoRegression for Continuous Trajectory Forecasting](https://mlsanity.com/paper/2610.06210/) (2026)

## Abstract (arXiv)

Robustness against Out-of-Distribution (OoD) samples is a key performance indicator of a trajectory prediction model. However, the development and ranking of state-of-the-art (SotA) models are driven by their In-Distribution (ID) performance on individual competition datasets. We present an OoD testing protocol that homogenizes datasets and prediction tasks across two large-scale motion datasets. We introduce a novel prediction algorithm based on polynomial representations for agent trajectory and road geometry on both the input and output sides of the model. With a much smaller model size, training effort, and inference time, we reach near SotA performance for ID testing and significantly improve robustness in OoD testing. Within our OoD testing protocol, we further study two augmentation strategies of SotA models and their effects on model generalization. Highlighting the contrast between ID and OoD performance, we suggest adding OoD testing to the evaluation criteria of trajectory prediction models.