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.

使用再生核 Hilbert 空间的机器，描述卷积网络的函数空间和光滑性，研究了卷积网络的函数分解和统计界限，并突出显示了逼近误差和估计误差之间的有趣权衡。

卷积神经网络的谐分解

Harmonic Decompositions of Convolutional Networks

Post-hoc model-agnostic interpretation methods such as partial dependence
plots can be employed to interpret complex machine learning models. While these
interpretation methods can be applied regardless of model complexity, they can
produce misleading and verbose results if the model is too complex, especially
w.r.t. feature interactions. To quantify the complexity of arbitrary machine
learning models, we propose model-agnostic complexity measures based on
functional decomposition: number of features used, interaction strength and
main effect complexity. We show that post-hoc interpretation of models that
minimize the three measures is more reliable and compact. Furthermore, we
demonstrate the application of these measures in a multi-objective optimization
approach which simultaneously minimizes loss and complexity.

提出了基于功能分解的模型不可知复杂度量度来量化任意机器学习模型的复杂度，并展示了在同时最小化损失和复杂度的多目标优化中应用这些量度的方法。