A recursive subspace based method for errors-in-variables model identification of time-varying systems

What the math gives to ML

The paper offers a constructive online subspace-identification mechanism for time-varying systems with errors in both inputs and outputs. Its transferable asset is a fixed-lag recursive low-rank estimator that jointly tracks latent state subspaces, heteroskedastic measurement noise, system matrices, and changing model order without retaining the full history. The strongest neural-network use is an adaptive latent state-space or world-model layer whose dynamics are periodically re-identified from a recent window, with noise-corrected covariance estimates preventing sensor noise from being mistaken for latent dimensions. The method makes falsifiable predictions: adaptation should track parameter drift with a lag controlled by the forgetting factor, and effective latent rank should change when corrected covariance eigenvalues cross a noise threshold.