Testing the rank of the spot covariance matrix of a multidimensional Itô semi-martingale

What the math gives to ML

The paper's transferable asset is a drift-aware method for distinguishing instantaneous stochastic variation from predictable motion before estimating covariance rank. Applied to neural state trajectories, this gives a local intrinsic-dimension diagnostic or regularizer that does not mistake rapidly changing hidden-state means for additional latent factors. The most practical transfer is to estimate covariance from locally re-centred increments, then penalize eigenvalues beyond a desired rank in diffusion and state-space models.