The paper defines robust invertibility for nonlinear dynamics using contraction and bi-Lipschitzness, and constructs biLipREN, a recurrent equilibrium network whose forward and inverse are both contracting and bi-Lipschitz by construction.
Feedback and optimal sensitivity: Model reference trans- formations, multiplicative seminorms, and approximate inverses,
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Robustly Invertible Nonlinear Dynamics and the BiLipREN: Contracting Neural Models with Contracting Inverses
The paper defines robust invertibility for nonlinear dynamics using contraction and bi-Lipschitzness, and constructs biLipREN, a recurrent equilibrium network whose forward and inverse are both contracting and bi-Lipschitz by construction.