A Language Model for Stadium Crowds, Trained Only on Aggregate Counts

A new preprint fine-tunes a language model to reproduce where stadium crowds go after a game, using only aggregate cell counts from two baseball games. No individual trajectories go in or come out.

A new arXiv preprint tackles a narrow but thorny problem: if you only know how many phones were in each zone before and after a stadium event, can a model still reproduce where the crowd actually went? The authors fine-tune a language model, the same family of neural networks that power chatbots and code assistants, to act as a sequential decision-maker for individual movement, where each "decision" is the next cell on a person's path. The training input is only aggregate origin-destination flow between zones: no device IDs, no trajectories, no per-person sequence. The reported payoff is destination-share error dropping by roughly 25% compared with a baseline policy, with the model running without any inference-time correction step.

The testbed is two baseball games, which sets the upper bound on what the result can tell us. Post-event crowd movement is one specific kind of distribution, and baseball cases have characteristic structure: entry and exit chokepoints, transit hubs, parking lots. The aggregate input is what mobile carriers see in aggregate, specifically zone-level device counts and the volume of phones that moved from one zone to another. The model never sees a single path, so there is nothing to de-anonymize at inference.

The mechanism runs in three steps. The authors start from a language model whose default destination probabilities come from text-prediction training, not from any spatial reasoning. That profile does not match the post-game reality of a baseball crowd. So they read the origin-destination flow and run an iterative proportional fitting (IPF) step, a classical rebalancing technique where row and column totals of a count table are nudged toward a target, to compute a target destination composition. That target then drives a resampling of training trajectories. The fine-tune itself is a low-rank adapter, a small parameter-efficient patch on top of the base model, fit on the resampled paths. Once trained, the model produces destination shares that match the target without needing any runtime correction.

Destination-share error is one axis; spatial fidelity at the grid-cell level is another. The fine-tuned model improves the first, but "grid correlation remains similar across policies." The model gets where the crowd is going, but not how individuals move through the city to get there. The method is aggregate in, aggregate-out, and it inherits the limits of aggregate in.

Some caveats before anyone treats this as a deployable tool: it is an arXiv preprint, not peer-reviewed. The 25% figure is reported against a baseline that the abstract does not name; the full paper would need to be read to identify the exact comparison. Mobile network counts carry known coverage and demographic biases that aggregate-only framing cannot remove. And the test is two baseball games, which is a thin empirical base for generalizing to other event types, cities, or transport modes.

The paper offers, fairly, a privacy-by-construction baseline for a category that usually requires the opposite. Crowd-simulation work that does model individual behavior typically needs trajectory data, which is expensive and politically loaded. A method that, by design, cannot leak individual paths because it never sees them is a different kind of artifact. Whether it can be extended to grid-fidelity, not just destination fidelity, is the open question the paper itself flags. The next round of evaluations on other event types and other cities will need to answer it.