An Operator-Theoretic Analysis of Nonlinear Filtering under Model Misspecification

What the math gives to ML

The paper gives a constructive perturbation principle for recursive Bayesian state updates: if the predictive dynamics contract in total variation, then model error does not accumulate indefinitely but converges to a geometric steady-state floor. This can transfer to latent state-space models by explicitly controlling the contraction of a learned transition operator and the one-step discrepancy between a compact student dynamics model and a teacher or reference model. The most practical target is a discrete-latent recurrent or world-model module, where Dobrushin contraction and transition mismatch can be computed directly and used as a robustness regularizer during distillation.