Deploying deep neural networks in real-world settings requires models that are both compact and robust to common corruptions. However, at deployment-relevant high sparsity, standard pruning pipelines often degrade corruption robustness, and existing sharpness-aware training/pruning approaches provide limited robustness gains. We address this issue by introducing Sparsity-Adaptive Sharpness-Aware Minimization (SA-SAM), which derives a sparsity-dependent SAM/ASAM perturbation radius by keeping the mean absolute perturbation (an $\ell_1$-based proxy) approximately invariant as sparsity increases. As a simple complementary option, we evaluate Magnitude-Weighted Hessian (MWH), derived from a second-order removal-path analysis, yielding an importance proportional to $\mathrm{Diag}(F)_i\,|w_i|$, where $\mathrm{Diag}(F)$ is the diagonal empirical Fisher used as a curvature proxy in our implementation. Across CIFAR-10-C, CIFAR-100-C, and ImageNet-100-C, our approach achieved stronger corruption robustness than the considered pruning baselines at 80--90\% sparsity, while preserving clean accuracy. We additionally quantify the robustness--throughput trade-off by reporting measured inference throughput under sparse execution at deployment-relevant sparsity levels.

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