Exact and Efficient Representation of Totally Anti-Symmetric Functions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866910777286328320 |
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| author | Chen, Ziang Lu, Jianfeng |
| author_facet | Chen, Ziang Lu, Jianfeng |
| contents | This paper concerns the long-standing question of representing (totally) anti-symmetric functions in high dimensions. We propose a new ansatz based on the composition of an odd function with a fixed set of anti-symmetric basis functions. We prove that this ansatz can exactly represent every anti-symmetric and continuous function and the number of basis functions has efficient scaling with respect to dimension (number of particles). The singular locus of the anti-symmetric basis functions is precisely identified. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05064 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Exact and Efficient Representation of Totally Anti-Symmetric Functions Chen, Ziang Lu, Jianfeng Classical Analysis and ODEs Computational Physics Quantum Physics This paper concerns the long-standing question of representing (totally) anti-symmetric functions in high dimensions. We propose a new ansatz based on the composition of an odd function with a fixed set of anti-symmetric basis functions. We prove that this ansatz can exactly represent every anti-symmetric and continuous function and the number of basis functions has efficient scaling with respect to dimension (number of particles). The singular locus of the anti-symmetric basis functions is precisely identified. |
| title | Exact and Efficient Representation of Totally Anti-Symmetric Functions |
| topic | Classical Analysis and ODEs Computational Physics Quantum Physics |
| url | https://arxiv.org/abs/2311.05064 |