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

arXiv: https://arxiv.org/abs/2601.01663 · HTML: https://mlsanity.com/paper/2601.01663/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 26 references that are in the map.
- First posted on arXiv 4 Jan 2026.

## Builds on (most cited first, 13 of 13)

- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Self-Attentive Sequential Recommendation](https://mlsanity.com/paper/1808.09781/) (2018)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [BERT4Rec: Sequential Recommendation with Bidirectional Encoder Representations from Transformer](https://mlsanity.com/paper/1904.06690/) (2019)
- [Session-based Recommendations with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06939/) (2015)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [SeqGAN: Sequence Generative Adversarial Nets with Policy Gradient](https://mlsanity.com/paper/1609.05473/) (2016)
- [Deep Knowledge Tracing](https://mlsanity.com/paper/1506.05908/) (2015)
- [Social-STGCNN: A Social Spatio-Temporal Graph Convolutional Neural Network for Human Trajectory Prediction](https://mlsanity.com/paper/2002.11927/) (2020)
- [Session-based Recommendation with Graph Neural Networks](https://mlsanity.com/paper/1811.00855/) (2018)
- [Shopping in the Multiverse: A Counterfactual Approach to In-Session Attribution](https://mlsanity.com/paper/2007.10087/) (2020)

## Abstract (arXiv)

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 trajectory-derived 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 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.