Robustness of deep neural networks to input noise remains a critical challenge, as naive noise injection often degrades accuracy on clean (uncorrupted) data. We propose a novel training framework that addresses this trade-off through two complementary objectives. First, we introduce a loss function applied at the penultimate layer that explicitly enforces intra-class compactness and increases the margin to analytically defined decision boundaries. This enhances feature discriminativeness and class separability for clean data. Second, we propose a class-wise feature alignment mechanism that brings noisy data clusters closer to their clean counterparts. Furthermore, we provide a theoretical analysis demonstrating that improving feature stability under additive Gaussian noise implicitly reduces the curvature of the softmax loss landscape in input space, as measured by Hessian eigenvalues.This thus naturally enhances robustness without explicit curvature penalties. Conversely, we also theoretically show that lower curvatures lead to more robust models. We validate the effectiveness of our method on standard benchmarks and our custom dataset. Our approach significantly reinforces model robustness to various perturbations while maintaining high accuracy on clean data, advancing the understanding and practice of noise-robust deep learning.

翻译：深度神经网络对输入噪声的鲁棒性仍然是一个关键挑战，因为简单的噪声注入通常会降低模型在干净（未损坏）数据上的准确性。我们提出了一种新颖的训练框架，通过两个互补的目标来解决这一权衡。首先，我们在倒数第二层引入一个损失函数，该函数明确地强制类内紧凑性，并增大到解析定义的决策边界的间隔。这增强了干净数据的特征判别性和类别可分性。其次，我们提出了一种按类别进行的特征对齐机制，使噪声数据簇更接近其对应的干净数据簇。此外，我们提供了一个理论分析，证明在加性高斯噪声下改善特征稳定性，可以隐式地降低输入空间中softmax损失景观的曲率（以Hessian特征值衡量）。因此，这自然地增强了鲁棒性，而无需显式的曲率惩罚。反之，我们也从理论上证明了较低的曲率会导致更鲁棒的模型。我们在标准基准测试和我们的自定义数据集上验证了该方法的有效性。我们的方法显著增强了模型对各种扰动的鲁棒性，同时保持了在干净数据上的高精度，推进了对噪声鲁棒深度学习的理解和实践。