Characterization of the Variation Spaces Corresponding to Shallow Neural Networks
Characterization of the Variation Spaces Corresponding to Shallow Neural Networks
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DOI：
10.1007/s00365-023-09626-4
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发表时间：
2021-06
影响因子：
2.7
通讯作者：
Jonathan W. Siegel;Jinchao Xu
中科院分区：
文献类型：
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作者：
Jonathan W. Siegel;Jinchao Xu
本文研究了有界区域上函数字典对应的变差空间.具体来说，我们比较的变化空间，这是定义在凸船体与相关概念的基础上积分表示。这使我们能够表明，三个重要的概念有关的近似理论的浅层神经网络，巴伦空间，频谱巴伦空间，和Radon BV空间，实际上是变异空间相对于某些自然字典。
We study the variation space corresponding to a dictionary of functions infor a bounded domain. Specifically, we compare the variation space, which is defined in terms of a convex hull with related notions based on integral representations. This allows us to show that three important notions relating to the approximation theory of shallow neural networks, the Barron space, the spectral Barron space, and the Radon BV space, are actually variation spaces with respect to certain natural dictionaries.