Real order total variation with applications to the loss functions in learning schemes

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-05-23 DOI:10.1142/s0219199723500165

Pan Liu, Xin Yang Lu, Kunlun He

引用次数: 0

Abstract

Loss functions are an essential part in modern data-driven approaches, such as bi-level training scheme and machine learnings. In this paper, we propose a loss function consisting of a [Formula: see text]-order (an)-isotropic total variation semi-norms [Formula: see text], [Formula: see text], defined via the Riemann–Liouville (RL) 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 [Formula: see text], of such loss functions.

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实阶总变分与学习方案中损失函数的应用

损失函数是现代数据驱动方法的重要组成部分，如双级训练方案和机器学习。在本文中，我们提出了一个由[公式:见文]-阶(an)-各向同性全变分半模[公式:见文]，[公式:见文]组成的损失函数，通过Riemann-Liouville (RL)分数阶导数来定义。我们重点研究了这类损失函数的关键理论性质，如关于函数和导数阶的下半连续性和紧性[公式:见文本]。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.