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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.07884 |
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| _version_ | 1866917134873919488 |
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| author | Ganesh, Anand Bose, Babhrubahan Rajagopalan, Anand |
| author_facet | Ganesh, Anand Bose, Babhrubahan Rajagopalan, Anand |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07884 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Schauder Bases for $C[0, 1]$ Using ReLU, Softplus and Two Sigmoidal Functions Ganesh, Anand Bose, Babhrubahan Rajagopalan, Anand Machine Learning Functional Analysis 46B15 I.2.6 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. |
| title | Schauder Bases for $C[0, 1]$ Using ReLU, Softplus and Two Sigmoidal Functions |
| topic | Machine Learning Functional Analysis 46B15 I.2.6 |
| url | https://arxiv.org/abs/2506.07884 |