Ridge functions are used to describe and study the lower bound of the approximation done by the neural networks which can be written as a linear combination of activation functions. If the activation functions are also ridge functions, these networks are called explainable neural networks. In this brief paper, we first show that quantum neural networks which are based on variational quantum circuits can be written as a linear combination of ridge functions by following matrix notations. Consequently, we show that the interpretability and explainability of such quantum neural networks can be directly considered and studied as an approximation with the linear combination of ridge functions.

翻译：脊函数用于描述和研究神经网络近似下界，该近似可表示为激活函数的线性组合。若激活函数本身亦为脊函数，此类网络称为可解释神经网络。本文首先证明，基于变分量子电路的量子神经网络可通过矩阵表示法转化为脊函数的线性组合形式。由此表明，此类量子神经网络的可解释性可直接视为脊函数线性组合的近似问题进行研究。