Finite Sample Identification of Analytic Nonlinear Systems

What the math gives to ML

The paper's key mechanism is that real-analytic feature maps make passive, non-active exploration sufficient for finite-sample identification, whereas merely smooth or piecewise-affine features can remain indistinguishable on the visited region. The transferable asset is an identifiability certificate based on the feature Gram matrix: passive trajectories should eventually produce a nonsingular Gram matrix because a nonzero analytic feature combination cannot vanish on an open set without vanishing globally. For neural state-space models and world models, this suggests using analytic feature bases or analytic adapters together with a Gram-conditioning monitor and an exploration/data-collection schedule that stops only after the smallest Gram eigenvalue crosses a target threshold.