Length-Aware Adversarial Training for Variable-Length Trajectories: Digital Twins for Mall Shopper Paths

February 09, 2026

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Title: Length-Aware Adversarial Training for Variable-Length Trajectories: Digital Twins for Mall Shopper Paths
ArXiv ID: 2601.01663
Date: 2026-01-04
Authors: He Sun, Jiwoong Shin, Ravi Dhar

📝 Abstract

We study generative modeling of variable-length trajectories-sequences of visited locations/items with associated timestamps-for downstream simulation and counterfactual analysis. A recurring practical issue is that standard mini-batch training can be unstable when trajectory lengths are highly heterogeneous, which in turn degrades distribution matching for trajectoryderived statistics. We propose length-aware sampling (LAS), a simple batching strategy that groups trajectories by length and samples batches from a single length bucket, reducing within-batch length heterogeneity (and making updates more consistent) without changing the model class. We integrate LAS into a conditional trajectory GAN with auxiliary time-alignment losses and provide (i) a distribution-level guarantee for derived variables under mild boundedness assumptions, and (ii) an IPM/Wasserstein mechanism explaining why LAS improves distribution matching by removing length-only shortcut critics and targeting within-bucket discrepancies. Empirically, LAS consistently improves matching of derived-variable distributions on a multimall dataset of shopper trajectories and on diverse public sequence datasets (GPS, education, e-commerce, and movies), outperforming random sampling across dataset-specific metrics.

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Length-Aware Adversarial Training for Variable-Length Trajectories: Digital Twins for Mall Shopper Paths

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