{"ID":2822954,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2601.01663","arxiv_id":"2601.01663","title":"Length-Aware Adversarial Training for Variable-Length Trajectories: Digital Twins for Mall Shopper Paths","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.","short_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 heterogeneo...","url_abs":"https://arxiv.org/abs/2601.01663","url_pdf":"https://arxiv.org/pdf/2601.01663v1","authors":"[\"He Sun\",\"Jiwoong Shin\",\"Ravi Dhar\"]","published":"2026-01-04T20:52:07Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\"]","methods":"[\"Generative Adversarial Network\"]","has_code":false}