Low-Discrepancy Set Post-Processing via Gradient Descent
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914156882427904 |
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| author | Clément, François Huang, Linhang Lee, Woorim Smidt, Cole Sodt, Braeden Zhang, Xuan |
| author_facet | Clément, François Huang, Linhang Lee, Woorim Smidt, Cole Sodt, Braeden Zhang, Xuan |
| contents | The construction of low-discrepancy sets, used for uniform sampling and numerical integration, has recently seen great improvements based on optimization and machine learning techniques. However, these methods are computationally expensive, often requiring days of computation or access to GPU clusters. We show that simple gradient descent-based techniques allow for comparable results when starting with a reasonably uniform point set. Not only is this method much more efficient and accessible, but it can be applied as post-processing to any low-discrepancy set generation method for a variety of standard discrepancy measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10496 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Low-Discrepancy Set Post-Processing via Gradient Descent Clément, François Huang, Linhang Lee, Woorim Smidt, Cole Sodt, Braeden Zhang, Xuan Optimization and Control Numerical Analysis The construction of low-discrepancy sets, used for uniform sampling and numerical integration, has recently seen great improvements based on optimization and machine learning techniques. However, these methods are computationally expensive, often requiring days of computation or access to GPU clusters. We show that simple gradient descent-based techniques allow for comparable results when starting with a reasonably uniform point set. Not only is this method much more efficient and accessible, but it can be applied as post-processing to any low-discrepancy set generation method for a variety of standard discrepancy measures. |
| title | Low-Discrepancy Set Post-Processing via Gradient Descent |
| topic | Optimization and Control Numerical Analysis |
| url | https://arxiv.org/abs/2511.10496 |