Decomposition of one-layer neural networks via the infinite sum of reproducing kernel Banach spaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916669003137024 |
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| author | Shin, Seungcheol Kang, Myungjoo |
| author_facet | Shin, Seungcheol Kang, Myungjoo |
| contents | In this paper, we define the sum of RKBSs using the characterization theorem of RKBSs and show that the sum of RKBSs is compatible with the direct sum of feature spaces. Moreover, we decompose the integral RKBS into the sum of $p$-norm RKBSs. Finally, we provide applications for the structural understanding of the integral RKBS class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_18132 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Decomposition of one-layer neural networks via the infinite sum of reproducing kernel Banach spaces Shin, Seungcheol Kang, Myungjoo Functional Analysis Artificial Intelligence In this paper, we define the sum of RKBSs using the characterization theorem of RKBSs and show that the sum of RKBSs is compatible with the direct sum of feature spaces. Moreover, we decompose the integral RKBS into the sum of $p$-norm RKBSs. Finally, we provide applications for the structural understanding of the integral RKBS class. |
| title | Decomposition of one-layer neural networks via the infinite sum of reproducing kernel Banach spaces |
| topic | Functional Analysis Artificial Intelligence |
| url | https://arxiv.org/abs/2409.18132 |