Generalization as a robust performance property of learning-enabled dynamical systems

What the math gives to ML

The paper provides a transferable robust-control interpretation of algorithmic stability: replacing one training sample is treated as an exogenous disturbance entering a sensitivity system, while the incremental behavior of the data-dependent operator is represented by an integral quadratic constraint (IQC). A dissipativity certificate then separates the one-sample perturbation magnitude from the dynamical gain of the learning algorithm, yielding a matrix-inequality bound on cumulative sensitivity and hence generalization. The most direct neural-network transfer is to use this certificate to constrain or monitor recurrent optimizers, learned update rules, and feedback-controlled training modules, with the certified gain serving as a principled stability and generalization regularizer.