Upper Bounds on the Generalization Error of Deep Learning Models via Local Robustness and Stability
Existing robustness-based generalization error bounds are often excessively loose or even vacuous in practice, failing to reflect the true generalization capability of deep models. This work proposes a locally adaptive approach to constructing generalization bounds by introducing notions of local robustness and stability. The input space is partitioned into subregions, and the robustness term is scaled according to the proportion of stable versus unstable samples within each region, yielding a tighter, data- and model-dependent upper bound. This method is the first to refine global robustness measures into localized forms, substantially mitigating the vacuity commonly observed in traditional bounds. Experiments on ImageNet demonstrate that the proposed bound remains non-vacuous across various robust deep networks and closely tracks their empirical generalization errors, significantly outperforming existing approaches.