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Studying the sensitivity of weight perturbation in neural networks and itsimpacts on model performance, including generalization and robustness, is anactive research topic due to its implications on a wide range of machinelearning tasks such as model compression, generalization gap assessment, andadversarial attacks. In this paper, we provide the first integral study andanalysis for feed-forward neural networks in terms of the robustness inpairwise class margin and its generalization behavior under weightperturbation. We further design a new theory-driven loss function for traininggeneralizable and robust neural networks against weight perturbations.Empirical experiments are conducted to validate our theoretical analysis. Ourresults offer fundamental insights for characterizing the generalization androbustness of neural networks against weight perturbations.

Formalizing Generalization and Robustness of Neural Networks to Weight Perturbations