Neural networks are central to modern artificial intelligence, yet their training remains highly sensitive to data contamination. Standard neural classifiers are trained by minimizing the categorical cross-entropy loss, corresponding to maximum likelihood estimation under a multinomial model. While statistically efficient under ideal conditions, this approach is highly vulnerable to contaminated observations including label noises corrupting supervision in the output space, and adversarial perturbations inducing worst-case deviations in the input space. In this paper, we propose a unified and statistically grounded framework for robust neural classification that addresses both forms of contamination within a single learning objective. We formulate neural network training as a minimum-divergence estimation problem and introduce rSDNet, a robust learning algorithm based on the general class of $S$-divergences. The resulting training objective inherits robustness properties from classical statistical estimation, automatically down-weighting aberrant observations through model probabilities. We establish essential population-level properties of rSDNet, including Fisher consistency, classification calibration implying Bayes optimality, and robustness guarantees under uniform label noise and infinitesimal feature contamination. Experiments on three benchmark image classification datasets show that rSDNet improves robustness to label corruption and adversarial attacks while maintaining competitive accuracy on clean data, Our results highlight minimum-divergence learning as a principled and effective framework for robust neural classification under heterogeneous data contamination.

翻译：神经网络是现代人工智能的核心，但其训练对数据污染高度敏感。标准神经分类器通过最小化分类交叉熵损失进行训练，这对应于多项模型下的最大似然估计。虽然该方式在理想条件下具有统计效率，但极易受到观测污染的影响，包括输出空间中破坏监督信息的标签噪声，以及输入空间中诱发最坏情况偏差的对抗扰动。本文提出了一种统一且基于统计理论的鲁棒神经分类框架，在单一学习目标中同时应对这两种污染形式。我们将神经网络训练表述为最小散度估计问题，并引入rSDNet——一种基于$S$-散度广义类的鲁棒学习算法。该训练目标继承了经典统计估计的鲁棒性特性，通过模型概率自动降低异常观测的权重。我们建立了rSDNet的关键总体层面性质，包括Fisher一致性、蕴含贝叶斯最优性的分类校准，以及在均匀标签噪声和无穷小特征污染下的鲁棒性保证。在三个基准图像分类数据集上的实验表明，rSDNet在保持干净数据上竞争性准确率的同时，提升了对标签污染和对抗攻击的鲁棒性。我们的结果凸显了最小散度学习作为应对异构数据污染的鲁棒神经分类的规范化有效框架。