Research map / Adversarial robustness and security / Certified and empirical robustness
Certified Human Trajectory Prediction
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Applies randomized smoothing (mean and median aggregation) with a diffusion-based denoiser to human trajectory predictors to obtain certified output bounds and new certified metrics.
Problem
Human trajectory predictors lack guaranteed robustness to adversarial and noisy observation inputs, and common metrics ignore input noise.
Approach
Adapts randomized smoothing (mean and median aggregators) to multi-output trajectory regression, adds adaptive clamping to create output bounds, uses an unconditional diffusion denoiser as a pre-processor to limit accuracy loss, and certifies each mode of multi-modal predictors.
Key results
- Smoothed EqMotion with median aggregation keeps FDE near 1.14 vs 1.12 for the original while providing certified bounds (Certified-FDE 2.07).
- Median smoothing yields considerably smaller bounds than mean smoothing across predictors.
- Diffusion denoiser lowers FBD at matched FDE (e.g., 0.78 vs 1.20 at FDE 1.2) relative to no denoiser.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply median smoothing to trajectory predictors | Social-Force, D-Pool, AutoBot, and EqMotion · Trajnet++ | FDE: 1.25 -> 1.26; 1.14 -> 1.23; 1.14 -> 1.17; 1.12 -> 1.14 | Mixed |
| Use median rather than mean aggregation (ablation) | Smoothed trajectory predictors · Trajnet++ | FBD | Helped |
| Add a diffusion-based trajectory denoiser (ablation) | Smoothed EqMotion · Trajnet++ | FBD at FDE 1.2: 1.20 -> 0.78 | Helped |
| Replace the diffusion denoiser with no denoiser (ablation) | Trajectory denoising · Trajnet++ noisy trajectories, noise 0.24 | remaining noise magnitude: 0.14 -> 0.24 | Hurt |
| Use a diffusion denoiser instead of a polynomial denoiser (ablation) | Trajectory denoising · Trajnet++ noisy trajectories, noise 0.24 | remaining noise magnitude: 0.22 -> 0.14 | Helped |
| Use a diffusion denoiser instead of a moving average filter (ablation) | Trajectory denoising · Trajnet++ noisy trajectories, noise 0.24 | remaining noise magnitude: 0.18 -> 0.14 | Helped |
| Use a diffusion denoiser instead of a Wiener filter (ablation) | Trajectory denoising · Trajnet++ noisy trajectories, noise 0.24 | remaining noise magnitude: 0.16 -> 0.14 | Helped |
| Use a multi-modal model rather than a single-modal model (ablation) | Smoothed EqMotion · Trajnet++ | FDE: 1.13 -> 0.39 | Helped |
| Use a multi-modal model rather than a single-modal model (ablation) | Smoothed EqMotion · Trajnet++ | Certified-FDE: 2.07 -> 1.38 | Helped |
| Perturb all agents rather than one agent (ablation) | Smoothed EqMotion · Trajnet++ multi-agent | FBD: 0.99 -> 1.21 | Hurt |
| Add the diffusion denoiser (ablation) | Crowd navigation policy using trajectory predictions · Crowd robot navigation | collision rate: 21.0 -> 15.1 | Helped |
| Add the diffusion denoiser (ablation) | Crowd navigation policy using trajectory predictions · Crowd robot navigation | accumulated reward: 0.230 -> 0.263 | Helped |
Surprising findings
- The most accurate model (EqMotion, lowest FDE) is not the most robust; D-Pool has the lowest Certified-FDE.
- Common metrics like FDE and collision rate greatly overstate robustness compared with certified metrics.
Limitations
- Randomized smoothing multiplies inference cost by the number of Monte-Carlo samples n.
- Mean smoothing requires output bounds estimated by adaptive clamping that are not guaranteed on new data.
- Smoothed predictors incur a modest FDE increase and sigma range was selected experimentally.
Experimental setup
Datasets: ETH UCY WildTrack Trajnet++ nuScenes
Benchmarks: ETH UCY WildTrack Trajnet++
Metrics: ADE FDE FBD ABD Certified-FDE Certified-ADE Collision rate Certified-Col
Baselines: Social-Force D-Pool AutoBot EqMotion Trajpac Wiener filter Moving Average filter polynomial fitting
Builds on: randomized smoothing denoised smoothing median smoothing EqMotion Trajectron-style social pooling
Closest papers by meaning
- C2F-TP: A Coarse-to-Fine Denoising Framework for Uncertainty-Aware Trajectory Prediction (AAAI 2025 · similarity 0.88)
- Improving Transferability for Cross-Domain Trajectory Prediction via Neural Stochastic Differential Equation (AAAI 2024 · similarity 0.85)
- CaDeT: a Causal Disentanglement Approach for Robust Trajectory Prediction in Autonomous Driving (CVPR 2024 · similarity 0.85)
- Enduring, Efficient and Robust Trajectory Prediction Attack in Autonomous Driving via Optimization-Driven Multi-Frame Perturbation Framework (CVPR 2025 · similarity 0.85)
- SingularTrajectory: Universal Trajectory Predictor Using Diffusion Model (CVPR 2024 · similarity 0.85)
- BAT: Behavior-Aware Human-Like Trajectory Prediction for Autonomous Driving (AAAI 2024 · similarity 0.85)
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