Functional Analytical Methods for Neural Networks and the Infinite-Dimensional Null Space
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- Sonoda Sho
- 理化学研究所革新知能統合研究センター
Bibliographic Information
- Other Title
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- ニューラルネットの関数解析的方法と無限次元零空間
- ニューラルネット ノ カンスウ カイセキテキ ホウホウ ト ムゲンジゲン レイ クウカン
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Abstract
<p>In this paper, we present recent results on the integral representation of neural networks. In the theoretical study of deep learning, using the integral representation to treat neural nets in a functional analytic manner is developing. However, the structure of the domain space <img align="middle" src="./Graphics/abst-50020285_1.gif"/> of the integral representation operator S is mostly unknown. It is less known that there even exists an infinite-dimensional null space ker S. In this paper, we consider several problems related to integral representations and discuss the characterizations of <img align="middle" src="./Graphics/abst-50020285_1.gif"/> and ker S in each context.</p>
Journal
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- Journal of the Japan Statistical Society, Japanese Issue
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Journal of the Japan Statistical Society, Japanese Issue 50 (2), 285-316, 2021-03-05
Japan Statistical Society
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Details 詳細情報について
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- CRID
- 1390005822570120704
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- NII Article ID
- 130007995101
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- NII Book ID
- AA1105098X
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- ISSN
- 21891478
- 03895602
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- NDL BIB ID
- 031362083
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- Text Lang
- ja
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- Data Source
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- JaLC
- NDL
- CiNii Articles
- KAKEN
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- Abstract License Flag
- Disallowed
