用深度网络同时逼近得分函数及其导数，突破维度瓶颈。
Simultaneous Approximation of the Score Function and Its Derivatives by Deep Neural Networks
- 构建神经网络联合逼近得分函数与任意阶导数
- 误差界不随维度增长，支持无界支撑数据
- 适用于低维结构数据，适合高维生成建模研究
本文提出一种理论框架，实现对得分函数及其任意阶导数的联合逼近，能够处理具有低维结构且支撑集无界的概率分布。所获逼近误差界与现有文献相当，但放宽了对支撑集有界的常规假设。关键优势在于误差界不受维度增长影响，避免了维度灾难。此外，该方法可推广至任意指定阶导数的逼近，超越了以往仅关注一阶导数的局限。
原文摘要 · Abstract (English)
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.
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