Decomposition of one-layer neural networks via the infinite sum of reproducing kernel Banach spaces
This work offers theoretical insights for researchers in functional analysis and kernel methods, but it appears incremental as it builds on existing RKBS theory without addressing a specific applied problem.
The paper tackles the decomposition of integral reproducing kernel Banach spaces (RKBS) into sums of p-norm RKBSs, establishing compatibility with direct sums of feature spaces and providing applications for structural understanding.
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.