Assessing Local Generalization Capability in Deep Models

While it has not yet been proven, empirical evidence suggests that model generalization is related to local properties of the optima, which can be described via the Hessian. We connect model generalization with the local property of a solution under the PAC-Bayes paradigm. In particular, we prove that model generalization ability is related to the Hessian, the higher-order "smoothness" terms characterized by the Lipschitz constant of the Hessian, and the scales of the parameters. Guided by the proof, we propose a metric to score the generalization capability of a model, as well as an algorithm that optimizes the perturbed model accordingly.