Sharp Wasserstein Convergence Rates for Empirical Path Laws of Itô Processes

What the math gives to ML

The paper provides a constructive adaptive representation of continuous stochastic paths: recursively split a dyadic time interval only when its within-interval excursion exceeds a threshold. The transferable asset is the resulting data-dependent multiresolution partition, which concentrates computation around high-variation portions of a trajectory while retaining a uniform approximation guarantee. This can become an event-driven tokenizer or adaptive temporal attention scheme for trajectory transformers, diffusion models, and neural operators, with a maximum-depth fallback for deterministic implementation.