论文标题
实际订单的总差异，并应用于学习方案中的损失功能
Real order total variation with applications to the loss functions in learning schemes
论文作者
论文摘要
损失功能是现代数据驱动方法的重要组成部分，例如双层培训方案和机器学习。在本文中，我们提出了一个损失功能，该损失功能由$ r $ order（an） - 异位总变量半 - $ TV^r $，$ r \ in \ Mathbb {r}^+$，通过Riemann-Liouville（R-L）分数衍生物定义。我们专注于研究关键的理论特性，例如相对于此类损失功能的衍生$ r $的功能和顺序，较低的半持续性和紧凑性。
Loss function are an essential part in modern data-driven approach, such as bi-level training scheme and machine learnings. In this paper we propose a loss function consisting of a $r$-order (an)-isotropic total variation semi-norms $TV^r$, $r\in \mathbb{R}^+$, defined via the Riemann-Liouville (R-L) fractional derivative. We focus on studying key theoretical properties, such as the lower semi-continuity and compactness with respect to both the function and the order of derivative $r$, of such loss functions.
