用黎曼Zeta函数动态缩放梯度，提升模型泛化与鲁棒性。
ZetA: A Riemann Zeta-Scaled Extension of Adam for Deep Learning
- 基于黎曼Zeta函数设计动态梯度缩放机制
- 在多个数据集上显著优于Adam，最高提升1.8%准确率
- 适合噪声数据或高粒度分类任务的轻量级优化
本文提出ZetA，一种新型深度学习优化器，通过引入基于黎曼Zeta函数的动态缩放机制扩展Adam。据我们所知，ZetA是首个在深度学习优化中应用Zeta函数进行梯度缩放的方法。该方法结合自适应阻尼、余弦相似度驱动动量增强、熵正则化损失以及类似SAM的扰动策略，形成混合更新机制，有效提升模型泛化能力与鲁棒性。在SVHN、CIFAR10、CIFAR100、STL10及带噪CIFAR10上的实验表明，使用轻量全连接网络在混合精度设置下训练5个周期，ZetA在所有测试场景中均超越Adam。结果证明，ZetA是一种计算高效且鲁棒的优化器，尤其适用于噪声或高粒度分类任务。
原文摘要 · Abstract (English)
This work introduces ZetA, a novel deep learning optimizer that extends Adam by incorporating dynamic scaling based on the Riemann zeta function. To the best of our knowledge, ZetA is the first optimizer to apply zeta-based gradient scaling within deep learning optimization. The method improves generalization and robustness through a hybrid update mechanism that integrates adaptive damping, cosine similarity-based momentum boosting, entropy-regularized loss, and Sharpness-Aware Minimization (SAM)-style perturbations. Empirical evaluations on SVHN, CIFAR10, CIFAR100, STL10, and noisy CIFAR10 consistently show test accuracy improvements over Adam. All experiments employ a lightweight fully connected network trained for five epochs under mixed-precision settings. The results demonstrate that ZetA is a computationally efficient and robust alternative to Adam, particularly effective in noisy or high-granularity classification tasks.
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