GPU-Parallel Linearization Error Bounds for Real-Time Robust Optimal Control of Nonlinear and Neural Network Dynamics

What the math gives to ML

The paper develops differentiable, tight bounds on the error made when replacing nonlinear or neural dynamics by a local affine model. The transferable asset is the combination of path-based second-order Taylor bounds, verifier-generated affine relaxations, and local Jacobian corrections: it produces a computable residual set rather than relying on a loose global Lipschitz constant. In a neural classifier or policy, the same residual set can become a certified local robustness loss, an adaptive perturbation radius, or a certificate-guided data augmentation rule. The most practical first transfer is a differentiable margin regularizer that penalizes samples whose affine prediction plus certified residual cannot preserve the correct class or action.