Fernando Acero's October 14 preprint, What Do Foundation Models for Market Microstructure Learn?, uses synthetic order books for a reason beyond generating cheap data: the researcher knows the hidden process producing the messages.
The experiments move from Poisson order flow through self-exciting arrivals, agent feedback and nonstationary, heavy-tailed conditions. That permits comparisons unavailable in real market data. One family has an exact Bayesian predictive benchmark; the others use an oracle that knows the latent state. Those are importantly different standards.
The strongest result is about training diversity. Once models have enough capacity, exposing them to more regimes matters more than continuing to increase model size or token volume within the tested families. Frozen-model probes also recover some dynamic parameters better than short-window maximum-likelihood fitting or hand-built summaries; simple static parameters provide controls where that advantage disappears.
This is a controlled research result, not an alpha claim. The real-data work uses five tickers from one 2012 NASDAQ day; the fine-tuning comparison evaluates three held-out tickers. Worth reading for the experimental design, particularly if you want to separate learning a process from reproducing its visible surface statistics.