Foundation models trained on limit order book (LOB) data have become the state of the art for market simulation. Their autoregressive nature allows them to generate realistic sequences of order book events, but the standard pre-training objective may leave a critical weakness unaddressed.
According to the paper's abstract, pre-training with cross-entropy does not penalize the compounding of sampling errors that occurs during autoregressive generation. This means small mistakes can accumulate over time, potentially degrading the quality of long-horizon simulations.
The authors propose adversarial post-training as a remedy. While the abstract does not provide implementation details, the approach is positioned as a way to directly target the compounding error problem that cross-entropy ignores. The source is limited to an abstract, so further specifics on the method or empirical results are not available here.