Simultaneous Approximation of the Score Function and Its Derivatives by Deep Neural Networks
Abstract
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.
Links & Resources
Authors
Cite This Paper
Yakovlev, K., Puchkin, N. (2025). Simultaneous Approximation of the Score Function and Its Derivatives by Deep Neural Networks. arXiv preprint arXiv:2512.23643.
Konstantin Yakovlev and Nikita Puchkin. "Simultaneous Approximation of the Score Function and Its Derivatives by Deep Neural Networks." arXiv preprint arXiv:2512.23643 (2025).