Work

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

Year: 2025

Type: preprint

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. 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2506.07884

Authors: Ganesh, Anand, Bose, Babhrubahan, Rajagopalan, Anand

Institutions: Manipal Academy of Higher Education, National Institute of Advanced Studies, Indian Institute of Science Bangalore

Language: English

Topic: Neural Networks and Applications

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4417136236

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