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

• URL: http://arxiv.org/abs/2601.01663v1
• Date: Sun, 04 Jan 2026 20:52:07 GMT
• Title: Length-Aware Adversarial Training for Variable-Length Trajectories: Digital Twins for Mall Shopper Paths
• Authors: He Sun, Jiwoong Shin, Ravi Dhar,
• Abstract summary: We study generative modeling of emphvariable-length trajectories -- sequences of visited locations/items with associated timestamps.<n>Standard mini-batch training can be unstable when trajectory lengths are highly heterogeneous.<n>We propose bflength-aware sampling (LAS), a simple strategy that groups trajectories by length and samples batches from a single length bucket.
• Score: 4.841565047500658
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study generative modeling of \emph{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 \emph{distribution matching} for trajectory-derived statistics. We propose \textbf{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 multi-mall 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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