The Inference-Compute Frontier and a Latency-Efficient Architecture for Limit Order Book Prediction

Modeling the dynamics of financial Limit Order Books (LOB) at the message level is challenging due to irregular event timing, rapid regime shifts, and the reactions of high-frequency traders to visible order flow. Previous LOB models require cumbersome data representations and lack adaptability outside their original tasks, leading us to introduce LOBERT, a general-purpose encoder-only foundation model for LOB data suitable for downstream fine-tuning. LOBERT adapts the original BERT architecture for LOB data by using a novel tokenization scheme that treats complete multi-dimensional messages as single tokens while retaining continuous representations of price, volume, and time. With these methods, LOBERT achieves leading performance in tasks such as predicting mid-price movements and next messages, while reducing the required context length compared to previous methods.

Generative models of limit orderbook (LOB) data have advanced rapidly, but their evaluation often focuses on stylised facts and selected market statistics. These measures provide useful diagnostics but may not capture the joint temporal and cross-level structure of order-book trajectories. We introduce LOB-ID, an embedding-based framework that adapts the Fréchet Inception Distance (FID) and Monge Inception Distance (MIND) to LOB data. To obtain domain-specific embeddings, we train the DeepLOB architecture on four months of Level-2 order-book data for five equities. We show that LOB-ID is stable across time, instruments, and embedding checkpoints, and rises monotonically under controlled distortions. We then construct a moment-matching attack against FID and a deep-book perturbation that evades statistic-based evaluation. MIND remains substantially more sensitive to both distortions. Finally, we score five generative LOB models, spanning stochastic baselines and deep learning approaches, and find that LOB-ID ranks them in line with the joint temporal and cross-level structure each captures by construction.

Limit order books can transition rapidly from stable to stressed conditions, yet standard early-warning signals such as order flow imbalance and short-term volatility are inherently reactive. We formalise this limitation via a three-regime causal data-generating process (stable $\to$ latent build-up $\to$ stress) in which a latent deterioration phase creates a prediction window prior to observable stress. Under mild assumptions on temporal drift and regime persistence, we establish identifiability of the latent build-up regime and derive guarantees for strictly positive expected lead-time and non-trivial probability of early detection. We propose a trigger-based detector combining MAX aggregation of complementary signal channels, a rising-edge condition, and adaptive thresholding. Across 200 simulations, the method achieves mean lead-time $+18.6 \pm 3.2$ timesteps with perfect precision and moderate coverage, outperforming classical change-point and microstructure baselines. A preliminary application to one week of BTC/USDT order book data shows consistent positive lead-times while baselines remain reactive. Results degrade in low signal-to-noise and short build-up regimes, consistent with theory.