Decomposition of one-layer neural networks via the infinite sum of reproducing kernel Banach spaces
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Abstract (arXiv)
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.
Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 11 of its 40 references that are in the map. First posted on arXiv 9 Aug 2024.
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11 of 40 references.
References · 11
- 2014Breaking the Curse of Dimensionality with Convex Neural Networkscited by 329
- 2020Representation formulas and pointwise properties for Barron functionscited by 62
- 2021Understanding neural networks with reproducing kernel Banach spacescited by 50
- 2021Characterization of the Variation Spaces Corresponding to Shallow Neural Networkscited by 48
- 2019On Reproducing Kernel Banach Spaces: Generic Definitions and Unified Framework of Constructionscited by 29
- 2018Sparsity of solutions for variational inverse problems with finite-dimensional datacited by 25
- 2018On Representer Theorems and Convex Regularizationcited by 24
- 2019A unifying representer theorem for inverse problems and machine learningcited by 24
- 2022Duality for Neural Networks through Reproducing Kernel Banach Spacescited by 15
- 2021Convex Optimization in Sums of Banach Spacescited by 11
- 2020Reproducing Kernel Hilbert Spaces Cannot Contain all Continuous Functions on a Compact Metric Spacecited by 6
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