Geometry-Consistent Bayesian Filtering under Structural Model Uncertainty: A Geometric Projection Particle Filter

What the math gives to ML

The paper offers a nonstandard mechanism for Bayesian state propagation: project the nominal drift onto the subspace compatible with the current measurement geometry, while correcting particle weights through a change of measure so that the posterior is not altered by the proposal construction. Its transferable asset is the decomposition of model mismatch into measurement-visible and measurement-orthogonal components, together with a geometric co-state measuring instantaneous incompatibility. A direct neural implementation is a geometry-consistent latent state-space or world model whose particle proposals are projected using the observation Jacobian, with importance weights retaining exact Bayesian correction.