Observability-Aligned Evidential Masked Pretraining for Reliable VRU Motion Prediction

Shang Gao; Franz Götz-Hahn; Konrad Doll; Bernhard Sick

cs.LGOct 29, 2026

Observability-Aligned Evidential Masked Pretraining for Reliable VRU Motion Prediction

Authors: Shang Gao, Franz Götz-Hahn, Konrad Doll, Bernhard Sick

Organizations: Intelligent Embedded Systems, University of Kassel, Germany · Aschaffenburg University of Applied Sciences, Germany

Abstract

Vulnerable road user (VRU) prediction must operate under partial observability and distribution shift, so reliable uncertainty matters alongside accuracy. Masked pretraining is attractive in this setting because it naturally exposes the model to missing content during self-supervision, but existing time-series masked autoencoding methods are typically deterministic and do not constrain how confidence should change with observability. We introduce eCoMAE, an evidential masked pretraining method for multivariate time series that explicitly aligns predictive evidence with what is observed. eCoMAE combines block-wise time-step masking with a Normal-Inverse-Gamma decoder and three observability-aware mechanisms: uncertainty-weighted mean consistency on positions visible in both a masked view and a reference pass, evidence suppression on masked positions, and representation consistency across stochastic masks. On IMPTC benchmark for VRU intention prediction under leave-one-environment-out weather shift, eCoMAE improves the strongest baseline from 0.7971 to 0.8068 in OOD accuracy and from 0.0718 to 0.0648 in OOD AURC. Additional evaluation on pedestrian trajectory forecasting across IMPTC, Waymo, nuScenes, and inD further yields the best fine-tuning MSE on all four datasets. These results show that observability-aligned evidential pretraining improves reliability under shift and remains effective beyond the primary benchmark.

Figures & tables

Figure 1: eCoMAE workflow. For each input sequence, $K$ stochastic masked views and one unmasked reference view are processed by a shared encoder–decoder with an NIG head. Training combines masked fitting, visible-token mean consistency against the reference, masked-token evidence suppression, and cross-view representation consistency.

Figure 2: Mask-rate sensitivity of finetuning accuracy

Capacity scaling at MR=0.80
Capacity	ID finetune		OOD finetune		Cost
Capacity	Acc ${}_{f}\uparrow$	ECE ${}_{f}\downarrow$	Acc ${}_{f}\uparrow$	ECE ${}_{f}\downarrow$	min $\downarrow$
Small	0.8040	0.0384	0.7824	0.0642	40.5
Medium	0.8247	0.0184	0.7941	0.0781	41.4
Large	0.8384	0.0129	0.7971	0.0698	48.7

Table 1: Capacity sweep results and backbone definitions. Small, Medium, and Large set

(d_{model},d_{ff},E,D,H)

to (32, 64, 2, 1, 4), (64, 128, 2, 1, 8), and (128, 256, 3, 2, 8), respectively. Here

d_{model}

is the Transformer hidden size,

d_{ff}

is the width of the feed-forward network inside each Transformer block,

E

is the number of encoder layers,

D

is the number of decoder layers, and

H

is the number of attention heads.

Evidential objective (REP off)
Setting	ID				OOD
Setting	Acc p	ECE p	Acc f	ECE f	Acc p	ECE p	Acc f	ECE f
MAE (no EVI/REP)	0.7987	0.0436	0.8379	0.0226	0.7794	0.0721	0.8000	0.0799
EVI (no REP)	0.7993	0.0434	0.8387	0.0124	0.7765	0.0595	0.8000	0.0658
Representation consistency (EVI on)
$\lambda_{\mathrm{rep}}=0.05$	0.7998	0.0436	0.8394	0.0148	0.7765	0.0557	0.7971	0.0660

Table 2: Main results of 18 variants under ID and OOD. Subscripts

p

and

f

denote probing and finetuning. Higher accuracy and lower ECE are better. Best finetuning values are in bold. In the component ablations, NIG and REP remain enabled; only the

\mu

\alpha

consistency terms vary.

Figure 3: Representative pretraining diagnostic for one sample-feature pair. Shaded regions indicate masked positions. Compared with Evidential MAE, adding representation consistency (eCoMAE) yields lower reconstruction error on masked regions and a clearer increase of predictive variance with reconstruction error, supporting better observability-aligned uncertainty during self-supervised pretraining.

Figure 4: Multi-view scaling design of eCoMAE under different numbers of mask views ( $n_{\mathrm{mask}}$ ) and evidential-consistency views ( $k_{\mathrm{evi}}$ ). Cell text reports finetune accuracy, while color indicates ECE, for both ID and OOD evaluation. Hatched cells denote invalid settings with $k_{\mathrm{evi}}>n_{\mathrm{mask}}$ .

Method	ID				OOD
	Acc ${}_{f}\uparrow$	ECE ${}_{f}\downarrow$	AURC ${}_{f}\downarrow$	UE-corr ${}_{f}\uparrow$	Acc ${}_{f}\uparrow$	ECE ${}_{f}\downarrow$	AURC ${}_{f}\downarrow$	UE-corr ${}_{f}\uparrow$
eCoMAE-S	0.8387	0.0123	0.0388	0.5380	0.8014	0.0701	0.0667	0.4464
eCoMAE-M	0.8389	0.0129	0.0390	0.5388	0.8068	0.0659	0.0672	0.4186
eCoMAE-L	0.8397	0.0144	0.0382	0.5391	0.8066	0.0678	0.0648	0.4323
Transformer (sup.)	0.7838	0.0516	0.0991	0.4145	0.7676	0.0825	0.1497	0.2969
Ti-MAE [ 11 ]	0.8379	0.0226	0.0409	0.5231	0.7971	0.0857	0.0718	0.4255

Table 3: Main comparison. Higher Acc and UE-corr are better. Lower ECE and AURC are better. Best values are shown in bold. All self-supervised methods are evaluated by end-to-end fine-tuning. DAE denotes a denoising autoencoder baseline. Results are averaged over five random seeds.

Method	Finetune MSE $\downarrow$
	IMPTC	Waymo	nuScenes	inD
eCoMAE-L	0.2691	0.2912	0.2514	0.3483
Transformer (sup.)	0.3209	0.4809	0.3279	0.4113
Ti-MAE	0.2997	0.3317	0.2678	0.3753
Gaussian Ti-MAE	0.2977	0.3328	0.2679	0.3752
DAE	0.2857	0.3012	0.3139	0.3756

Table 4: Additional evaluation on pedestrian trajectory forecasting on four datasets. Results report finetune MSE under a shared forecasting protocol, lower is better. Best values are shown in bold. Results are averaged over five random seeds.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Evidential objective (REP off)
Ablation setting	$\lambda_{\mathrm{evi}}$	$\lambda_{\mathrm{reg}}$	$\bar{\Phi}$	$\lambda_{\mu}$	$\lambda_{\alpha}$	$\lambda_{\mathrm{rep}}$
MAE (no EVI/REP)	0.0	0.0	0.0	0.00	0.00	0.00
EVI (no REP)	1.0	$10^{-2}$	2.0	0.05	0.05	0.00
Representation consistency (EVI on)
$\lambda_{\mathrm{rep}}=0.05$	1.0	$10^{-2}$	2.0	0.05	0.05	0.05
eCoMAE ( $\lambda_{\mathrm{rep}}=0.10$ )	1.0	$10^{-2}$	2.0	0.05	0.05	0.10

Appendix

Table 5: Hyperparameters for the 18 experimental variants (same order as Table 2 ). Evidence-cap values (

\bar{\Phi}=2.5

and

6

) follow the main-text ablation study.

Evidential objective (REP off)
Ablation setting	Probe		Finetune
Ablation setting	AURC ${}_{p}\downarrow$	UE-corr ${}_{p}\uparrow$	AURC ${}_{f}\downarrow$	UE-corr ${}_{f}\uparrow$
MAE (no EVI/REP)	0.1807	0.2082	0.0681	0.4397
EVI (no REP)	0.1660	0.2615	0.0666	0.4538
Representation consistency (EVI on)
$\lambda_{\mathrm{rep}}=0.05$	0.1656	0.2616	0.0660	0.4740

Appendix

Table 6: OOD uncertainty quality for the same 18 ablation variants. Lower AURC and higher UE-corr are better; best entries in each column are bold. Subscripts

p

and

f

indicate linear probing and finetuning, respectively.

Uncertainty Quantification

Uncertainty quantification estimates how reliable predictions and scientific inferences are, and how uncertainty propagates into decisions.

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Grounding Predictive Reliability through Masked Observability

Shang Gao, Bernhard Sick, Franz Götz-Hahn

University of Kassel, Germany

Uncertainty Quantification Evidential Deep Learning Representation Learning

Open paper AskPDF arXiv

An uncertainty estimate is meaningful only if its semantics can be tied to observable predictive behavior. Normal-Inverse-Gamma (NIG) evidential regression provides a structured decomposition of predictive variability into data-scale and predictive-mean components, but marginal likelihood does not identify their allocation. We address this semantic ambiguity in masked representation learning. MORSE (Masked Observability for Reliable Structured Encoding) predicts the same hidden target under controlled changes in visible context and uses normalized cross-context variation to ground predictive-mean uncertainty, while a Gaussian objective learns the conditional mean and data scale. The normalized variation plays the role of the NIG factor

1/ν

, which the marginal leaves unidentified; this yields a policy-relative observability variance that measures dependence on visible evidence, distinct from variation induced by resampling the training set. On a Gaussian-process benchmark with a contextual reference built from analytic Bayes conditional means, MORSE has the lowest log-variance error among compared evidential, ensemble, and dropout estimators in all nine tested settings, while the estimator closest to training-set variation perturbs the model rather than its context in every setting, so the two references separate the estimators empirically. MORSE amortizes observability estimation into one forward pass per observation state. On a heteroscedastic pulse benchmark, its predictor's cross-context variance approaches a large-sample reference as training data increase. MORSE also improves low-label transfer on PTB-XL and in-distribution trajectory prediction on IMPTC.

Abstract

Uncertainty Quantification

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