Bochner integrals and neural networks
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Abstract (arXiv)
A Bochner integral formula is derived that represents a function in terms of weights and a parametrized family of functions. Comparison is made to pointwise formulations, norm inequalities relating pointwise and Bochner integrals are established, variation-spaces and tensor products are studied, and examples are presented. The paper develops a functional analytic theory of neural networks and shows that variation spaces are Banach spaces.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 0 of its 47 references that are in the map. First posted on arXiv 26 Feb 2023.
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