The content discusses the introduction of functional input neural networks on possibly infinite dimensional weighted spaces. By utilizing Stone-Weierstrass theorems, the authors prove global universal approximation results for various types of functions. These results have implications in areas like stochastic analysis and mathematical finance.
The examples provided illustrate how different spaces, such as H¨older spaces, p-variation spaces, and Besov spaces, can be considered as weighted spaces with appropriate weight functions. The concept of admissible weight functions is crucial in defining these spaces and ensuring compactness where necessary.
Overall, the content delves into the theoretical framework of weighted function spaces and their applications in universal approximation theory across various mathematical domains.
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by Christa Cuch... às arxiv.org 03-04-2024
https://arxiv.org/pdf/2306.03303.pdfPerguntas Mais Profundas