论文标题
卷积网络的谐波分解
Harmonic Decompositions of Convolutional Networks
论文作者
论文摘要
我们使用复制内核Hilbert空间的机制介绍了功能空间和与卷积网络关联的平滑度类别的描述。我们表明，与卷积网络相关的映射将扩展为类似于球形谐波的基本功能的总和。该功能分解可能与非参数统计中的功能方差分析分解有关。在卷积网络的功能表征上，我们获得了统计界，突出了近似误差与估计误差之间的有趣权衡。
We present a description of the function space and the smoothness class associated with a convolutional network using the machinery of reproducing kernel Hilbert spaces. We show that the mapping associated with a convolutional network expands into a sum involving elementary functions akin to spherical harmonics. This functional decomposition can be related to the functional ANOVA decomposition in nonparametric statistics. Building off our functional characterization of convolutional networks, we obtain statistical bounds highlighting an interesting trade-off between the approximation error and the estimation error.
