Chance-Constrained Nonlinear Covariance Control via Robust Linearization Remainder Bounds

What the math gives to ML

The paper provides a constructive method for propagating conservative second-moment tubes through nonlinear stochastic dynamics without discarding Taylor remainders. Its transferable asset is the combination of a uniform nonlinear remainder envelope, Petersen-style robust covariance inequalities, and a Markov trace bound for domain-exit probability. A direct neural-network use is to treat stochastic optimization or recurrent inference as a nonlinear discrete-time dynamical system, propagate an upper covariance bound for parameter or hidden-state perturbations, and use the bound to adapt step sizes or enforce safe operating regions. The key falsifiable signature is a stability boundary shifted by Jacobian uncertainty and the nonlinear remainder envelope, rather than the nominal linearized boundary.