Schauder Bases for $C[0, 1]$ Using ReLU, Softplus and Two Sigmoidal Functions
Anand Ganesh; Babhrubahan Bose; Anand Rajagopalan · 2025 · arXiv
WASTE classifies this as Negative / Null Result Report · AI classification, approximate
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Abstract (excerpt)
We construct four Schauder bases for the space $C[0,1]$, one using ReLU functions, another using Softplus functions, and two more using sigmoidal versions of the ReLU and Softplus functions. This establishes the existence of a basis using these functions for the first time, and improves on the universal approximation property associated with them. We also show an $O(\frac{1}{n})$ approximation bound based on our ReLU basis, and a negative result on constructing multivariate functions using finite combinations of ReLU functions.
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Metadata source: arXiv