Robust deep learning under heavy-tailed and impulsive noise remains challenging because conventional losses such as mean squared error (MSE) exhibit unbounded sensitivity to outliers. Although correntropy-based objectives improve robustness, existing formulations rely on fixed kernel parameters that must be empirically tuned and remain static during training. To address these limitations, we propose an Adaptive Log-Correntropy Loss (ALCL), a heavy-tailed loss formulation that adaptively learns its robustness geometry during optimization. ALCL introduces a logarithmic residual model whose shape and scale parameters are learned jointly with network weights through differentiable reparameterization. This yields a principled maximum likelihood formulation whose influence function is formally bounded and redescending, allowing the loss geometry to adapt dynamically to evolving residual statistics while suppressing extreme outliers. Comparative experiments on four widely used benchmark datasets spanning grayscale and red-green-blue (RGB) image data under mixed heavy-tailed and impulsive noise demonstrate that ALCL consistently outperforms MSE and optimally tuned generalized correntropy losses in both reconstruction fidelity and downstream classification accuracy. While performance differences remain small under low-noise conditions, under high-noise regimes ALCL improves median accuracy by up to 4.75% on grayscale benchmarks and 4.51% on RGB datasets, with reduced variance across runs. These results demonstrate that adaptive robustness through joint learning of loss parameters provides a computationally efficient alternative to static correntropy-based losses for deep learning in non-Gaussian environments.

翻译：在重尾和脉冲噪声下的鲁棒深度学习仍具挑战性，因为均方误差（MSE）等传统损失函数对异常值具有无界敏感性。尽管基于相关熵的目标函数改善了鲁棒性，但现有公式依赖于固定的核参数，这些参数需经验性调整且在训练期间保持不变。针对这些局限，我们提出了一种自适应对数相关熵损失（ALCL），这是一种在优化过程中自适应学习其鲁棒几何形态的重尾损失函数。ALCL引入一个对数残差模型，其形状和尺度参数通过可微分重参数化与网络权重联合学习。这产生了一个具有原则性的最大似然公式，其影响函数具有形式上界且呈再下降特性，使得损失几何能动态适应不断变化的残差统计特性，同时抑制极端异常值。在涵盖混合重尾和脉冲噪声下的灰度与红绿蓝（RGB）图像数据的四个广泛使用的基准数据集上进行的对比实验表明，ALCL在重建保真度和下游分类精度上均一致优于MSE和最优调整的广义相关熵损失。尽管在低噪声条件下性能差异较小，但在高噪声环境下，ALCL在灰度基准上中位数精度提升高达4.75%，在RGB数据集上提升4.51%，且运行间方差更低。这些结果表明，通过联合学习损失参数实现的自适应鲁棒性，为非高斯环境下深度学习提供了一种计算高效的替代静态相关熵损失的方法。