Noisy labels are inevitable in real-world multimedia applications. Due to the strong memorization capacity of deep neural networks, these noisy labels cause significant performance degradation. Existing noise-robust methods have mainly focused on robust loss functions and sample selection strategies, with comparatively limited exploration of dynamic architectural adaptation. In this paper, we rethink the role of classifier connectivity under label noise. Intuitively, performance degradation stems from the backpropagation of noisy gradients. Since the final classifier layer acts as the primary gateway for this error propagation, selectively discarding redundant connections can restrict the backpropagation pathways of noisy gradients. Consequently, to identify redundant connections, we leverage the seminal Optimal Brain Damage (OBD) theory from model compression, which posits that parameters causing negligible loss perturbation can be removed. Guided by this principle, we show that masking low-activation edges limits the estimated loss perturbation to preserve the model's fitting capacity, while tightening a derived upper bound on noise-induced gradient error. To bridge this theoretical insight with practical training, we propose a novel Selective Edge Masking (SEM) mechanism for the fully connected (FC) layer to enhance noise robustness. It can adaptively retain critical edges for information propagation while suppressing gradient errors caused by noisy labels. As a plug-and-play component, SEM can be seamlessly integrated into various noise-robust methods. Additionally, we validate SEM's applicability by applying it to the newly emerged Kolmogorov-Arnold Network (KAN) employed as a classifier. Extensive evaluations on synthetic and real-world benchmarks demonstrate that our approach achieves state-of-the-art performance.

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