In this paper, we propose a novel differentiable activation function for convolutional neural networks. This function is proposed using an orthogonal Legendre polynomial based linear-in-parameter model. First, we present mathematical modeling for max pooling operation in convolutional neural networks and derive the relationship between max pooling and average pooling. The representation of max pooling using signal processing elements is presented. Further, we study approximations of various nonlinearities using the proposed linear-in-parameter model. The proposed activation function can be used as an alternative in place of existing activation functions in convolutional neural networks. Finally, the effectiveness of the proposed activation function is shown with empirical evaluations on benchmark image classification datasets using convolutional neural networks.

在本文中，我们提出了一种用于卷积神经网络的新型微分激活函数。使用基于正交勒让德多项式的线性参数模型提出此功能。首先，我们提出卷积神经网络中最大池运算的数学模型，并推导最大池与平均池之间的关系。给出了使用信号处理元件的最大池化的表示。此外，我们使用提出的参数线性模型研究各种非线性的近似值。所提出的激活函数可以用作卷积神经网络中现有激活函数的替代方法。最后，