Ganesh, Anand and Bose, Babhrubahan and Rajagopalan, Anand (2025) Schauder Bases for C[0, 1] Using ReLU, Softplus and Two Sigmoidal Functions. Transactions on Machine Learning Research.
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Schauder Bases for C[0, 1] Using ReLU, Softplus and Two.pdf - Published Version Download (945kB) |
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| 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, andimproves on the universal approximation property associated with them. We also show an O(1n) 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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| Item Type: | Journal Paper |
| Subjects: | School of Natural and Engineering Sciences School of Natural and Engineering Sciences > Mathematical Modeling School of Natural and Engineering Sciences > Mathematics |
| Divisions: | Schools > Natural Sciences and Engineering |
| Date Deposited: | 27 Apr 2026 11:50 |
| Last Modified: | 27 Apr 2026 11:50 |
| Official URL: | https://arxiv.org/abs/2506.07884 |
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| Funders: | * |
| Projects: | * |
| DOI: | https://doi.org/10.48550/arXiv.2506.07884 |
| URI: | http://eprints.nias.res.in/id/eprint/3319 |
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