Schauder Bases for $C[0, 1]$ Using ReLU, Softplus and Two Sigmoidal Functions

TMLR Paper5132 Authors

Abstract: 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.

Submission Length: Regular submission (no more than 12 pages of main content)

Changes Since Last Submission: Not applicable.

Assigned Action Editor: ~Surbhi_Goel1

Submission Number: 5132