一般化传奇变换的根源在于信息几何学
1Sony Computer Science Laboratories, 3-14-13 Higashi Gotanda, Shinagawa Ku, Tokyo 141-0022, Japan.
Entropy (Basel, Switzerland)
|January 28, 2026
概括
这项研究揭示了一般化的莱德变换相当于双相亲变形函数的标准莱德变换. 这些变换来自信息几何学中的双重赫斯结构.
科学领域:
- 凸的分析 凸的分析
- 信息几何学信息几何学
- 功能分析是一种功能分析.
背景情况:
- 列德变换是形分析及其应用中的一个基本工具.
- 阿尔茨泰恩-阿维丹和米尔曼以前将特定的可逆变换描述为莱根德变换的亲属变形.
研究的目的:
- 建立一般化的莱德变换和普通的莱德变换之间的直接对应.
- 为了证明从信息几何学的双重赫斯结构中推导这些通用变换的推导.
主要方法:
- 证明一般化的莱德变换与双相亲变形函数的普通莱德变换的等价性.
- 利用信息几何学固有的双重赫森结构.
主要成果:
- 所有研究的一般化莱德变换都与双相亲变形函数的普通莱德变换相对应.
- 概括凸联被证明是双相亲变形函数的普通凸联.
- 介绍了一种从信息几何学中推导这些通用变换的方法.
结论:
- 这些发现为普遍的莱德变换提供了一个统一的视角.
- 这项工作通过莱根德变换的镜头将凸面分析与信息几何联系起来.
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