Simultaneous Approximation of the Score Function and Its Derivatives by Deep Neural Networks
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912794339704832 |
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| author | Yakovlev, Konstantin Puchkin, Nikita |
| author_facet | Yakovlev, Konstantin Puchkin, Nikita |
| contents | We present a theory for simultaneous approximation of the score function and its derivatives, enabling the handling of data distributions with low-dimensional structure and unbounded support. Our approximation error bounds match those in the literature while relying on assumptions that relax the usual bounded support requirement. Crucially, our bounds are free from the curse of dimensionality. Moreover, we establish approximation guarantees for derivatives of any prescribed order, extending beyond the commonly considered first-order setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23643 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simultaneous Approximation of the Score Function and Its Derivatives by Deep Neural Networks Yakovlev, Konstantin Puchkin, Nikita Numerical Analysis Machine Learning Statistics Theory We present a theory for simultaneous approximation of the score function and its derivatives, enabling the handling of data distributions with low-dimensional structure and unbounded support. Our approximation error bounds match those in the literature while relying on assumptions that relax the usual bounded support requirement. Crucially, our bounds are free from the curse of dimensionality. Moreover, we establish approximation guarantees for derivatives of any prescribed order, extending beyond the commonly considered first-order setting. |
| title | Simultaneous Approximation of the Score Function and Its Derivatives by Deep Neural Networks |
| topic | Numerical Analysis Machine Learning Statistics Theory |
| url | https://arxiv.org/abs/2512.23643 |