Which Trajectory Is Safer? Combining Rule and Learning for Safety Evaluation

Xuewen Luo; Linlian Jiang; Bo Yu; Fan Ding; Xinxin Zuo; Yang Wang

cs.ROOct 13, 2026

Which Trajectory Is Safer? Combining Rule and Learning for Safety Evaluation

Authors: Xuewen Luo, Linlian Jiang, Bo Yu, Fan Ding, Xinxin Zuo, Yang Wang

Organizations: Xuewen Luo and Bo Yu are with the University of Utah. · Linlian Jiang, Xinxin Zuo, and Yang Wang are with Concordia University. · Fan Ding is with Monash University.

Abstract

Collision rate remains a dominant metric for evaluating autonomous driving trajectory safety, but its binary nature obscures substantial safety differences among collision-free trajectories. Existing surrogate-safety metrics provide finer-grained assessments, yet often trade off physical interpretability against adaptivity to interaction context. We introduce FutureRisk, a continuous metric that quantifies the latent future risk of a trajectory by how closely and persistently its realized interactions approach unsafe states. At its core, our Context-Adaptive Risk Model (CARM) combines a context-dependent safety-time distribution with an independently supervised critical-event-time distribution. Its safety criterion is bounded around a closed-form physical prior, while a bounded residual provides additional adaptation without abandoning this physical anchor. Experiments on DeepAccident and Bench2Drive show that FutureRisk achieves stronger agreement with native collision labels than existing surrogate-safety measures, discriminates risk among collision-free trajectories, and transfers zero-shot across datasets. Comparisons across four planners further show that FutureRisk reveals safety differences hidden by binary collision outcomes. Together, these results establish FutureRisk as a fine-grained, interpretable, and context-adaptive metric for trajectory safety evaluation. Code is available at https://github.com/Xuewen2025/safety-evaluation.

Figures & tables

Fig. 1: Comparison of trajectory-safety metrics. (A) Rule-based metrics are physically interpretable but rely on fixed criteria. (B) Learning-based metrics adapt to context but lack an explicit physical anchor. (C) FutureRisk combines physical interpretability with bounded, context-adaptive learning.

Fig. 2: Overview of FutureRisk. A shared encoding $\bm{h}^{j}$ feeds a safety-time head bounded around the physics prior $\tau_{\mathrm{phy}}^{j}$ and an independent event-timing head, composed into $\widetilde{R}_{\mathrm{CARM}}^{j}$ . Blue is trained in Stage 1, the red residual in Stage 2 with the rest frozen; noisy-OR gives $R$ .

Rule-based
Method	AUROC $\uparrow$	AUPRC $\uparrow$
$y_{\mathrm{analytic}}$	0.648	0.372
raw 3D-TTC	0.646	0.350
Forward TTC (2-D) [ 19 ]	0.685	0.425
Forward TTC (1-D) [ 19 ]	0.684	0.424
PET [ 15 ]	0.667	0.303

Table I: Instance-level discrimination against the binary collision label, DeepAccident.

Rule-based
	$\rho$ vs. $a(t)$		$\rho$ vs. $m$
Method	in	cross	in	cross
$y_{\mathrm{analytic}}$	0.007	– (const.)	1.000 (circ.)	n/a
raw 3D-TTC	0.006	– (const.)	– (const.)	n/a
Forward TTC (2-D) [ 19 ]	0.274	0.283	– (const.)	n/a
Forward TTC (1-D)	0.265	0.291	– (const.)	n/a

Table II: Fine-grained discrimination on collision-free trajectories. In-domain:

n=6630/286

for

a(t)/m

; cross-domain:

n=3333

zero-shot. Cross-domain

m

is undefined (

m=+\infty

throughout).

Model	(in) $\uparrow$	(in) $\uparrow$	(cross) $\uparrow$	(cross) $\uparrow$	$(R,a_{\max})$ $\uparrow$
	AUROC	AUPRC	AUROC	AUPRC	$\rho$
w/o $\mathcal{L}_{\mathrm{evt}}$	0.821	0.502	0.829	0.357	0.082
Full CARM	0.793	0.490	0.827	0.354	0.276

Table III: Ablation of independent critical-event supervision. The event head is retained when removing

\mathcal{L}_{\mathrm{evt}}

Model	AUROC (in) $\uparrow$	AUPRC (in) $\uparrow$	AUROC (cross) $\uparrow$	AUPRC (cross) $\uparrow$
raw safety-time prior	0.731	0.442	0.799	0.344
$+\,\Delta_{\theta}$ only	0.753	0.483	0.812	0.341
$+\,\sigma_{s}$ only	0.718	0.417	0.802	0.331
Stage-1 only (both, $g_{r}\equiv 0$ )	0.764	0.459	0.818	0.333
Full CARM	0.793	0.490	0.827	0.354

Table IV: Ablation of safety-time and residual terms; the learned critical-event branch is retained throughout.

Method	Anchored $\uparrow$	AUROC (in) $\uparrow$	AUROC (cross) $\uparrow$	$\rho$ vs. $a_{\max}$ $\uparrow$
RSS [ 18 ]	$100\%$	0.529	0.662	0.363
Lu et al. [ 7 ]	$0\%$	0.662	0.990 (circ.)	$-$ 0.001
GSSM [ 8 ]	n/a	0.567	0.817	0.070
FutureRisk (CARM)	$70.1\%$	0.793	0.827	0.276

Table V: Interpretability–adaptivity trade-off. Anchoring is structural for RSS and Lu et al. , empirical for FutureRisk, and undefined for GSSM’s non-decomposable output.

Fig. 3: Per-agent anchored-fraction distributions on DeepAccident and Bench2Drive, grouped by collision and critical-event labels. The dotted line marks the $70.1\%$ in-domain mean; the display is clipped to $[-1,1]$ , while all values remain in the reported statistics.

Fig. 4: Planner ranking by mean $R$ (left) and geometric collision rate (right) over available clips ( $n=13$ for TCP; $n=15$ otherwise); safer planners are plotted higher. Parallel lines (TCP, AD-MLP) indicate agreement; crossing lines (UniAD, VAD) indicate disagreement.

Fig. 5: Mean and median $R$ by quintile of the evasive-severity proxy $a_{\max}$ on pooled native-label collision-free DeepAccident instances ( $n=6630$ ). Both show an overall increasing trend with severity; Spearman $\rho=0.276$ .

Fig. 6: One AccidentTwoWays scenario (Route 1105) under UniAD (red) and VAD (blue). UniAD collides at $t=0.6$ s ( $R=0.962$ ), while VAD avoids overlap within 4 s but closes from $57.8$ m to $3.4$ m at about $4$ m/s ( $R=0.975$ ). (a) Closed-form risk $r(t)$ : nonzero for UniAD but zero for VAD. (b1)/(b2) Bird’s-eye trajectories; light boxes mark $t=0$ and solid boxes the moment of interest. (c) Critical-event hazard $q_{k}$ for the relevant agent.

Fig. 7: Per-frame risk for two DeepAccident instances (rows) under four methods (columns): a near-miss (top; native label $0$ ) and a collision missed by geometric overlap (bottom; native label $1$ , contact at $t=4.0$ s). Path color indicates risk (green low, red high); GSSM is normalized to its own range per row, while the others share one $[0,1]$ scale. Gray dashed: interacting agent; X : contact; o : closest approach.

Fig. 8: $R$ , 3D-TTC score, and PET score as the ego path of one DeepAccident collision instance is shifted laterally by $\delta$ (top: min–max normalized; bottom: raw scores). The rule-based curves change abruptly near their thresholds, while $R$ changes smoothly.

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Accurate and reliable vehicle trajectory prediction is essential for safe autonomous driving. Recent studies have incorporated safety risk into trajectory prediction to quantify dangers posed by surrounding agents. However, most risk-aware approaches use past risk information as a secondary signal to help guide decisions, overlooking its future evolution and uncertainty. In this paper, we propose a risk horizon profiling (RHP) module that incorporates a continuous, learnable potential field model for risk-aware trajectory prediction. The RHP module calculates the spatial-temporal proximity of surrounding objects to profile risk distributions across future horizons, which supports better trajectory prediction by adaptively identifying what human drivers perceive as critical moments. We evaluate our method on two datasets from different driving settings, highD for highway corridors and SHRP2 for urban streets, which cover diverse risk scenarios including safe, near-crash, and crash events. Compared to the baseline methods, our framework achieves a 25.0% reduction in 5s RMSE on the highD dataset and a 29.1% reduction in 5s minFDE on SHRP2. These results indicate strong performance for both short and long horizon prediction and robust generalization across highway and urban scenarios. The proposed method enables more realistic AV path planning and strategic selection, thereby supporting safer autonomous driving and more advanced driver-assistance systems. The source code for this work is available at: https://github.com/bilab-nyu/RHP

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