Partial Observation Amplifies Model Mismatch in MAP Estimation via Information-Curvature Margins

What the math gives to ML

The paper provides a transferable sensitivity mechanism for finite-horizon MAP state estimation under model mismatch: the nominal-to-oracle estimate displacement is controlled by a mismatch injection divided by the weakest posterior-curvature direction. Its key asset is an information-curvature margin, approximately the smallest eigenvalue of the Gauss–Newton posterior Hessian, rather than aggregate Fisher information or trace information. In neural networks, this can become a differentiable robustness objective for latent-state estimators, world models, and partially observed recurrent or state-space architectures. The quantitative prediction is that estimation error under a fixed model perturbation scales approximately as the inverse of this smallest eigenvalue, and that maximizing trace information can fail when one latent direction remains weakly observed.