The ever-growing depth and width of Convolutional Neural Networks (CNNs) drastically increases the number of their parameters and requires more powerful devices to train and deploy. In this paper, we propose a new architecture that outperforms the classical linear convolution function by expanding the latter to a higher degree kernel function without additional weights. We opt for Taylor Series Kernel which maps input data to a higher-dimensional Reproducing Kernel Hilbert Space (RKHS). Mapping features to a higher-order RKHS is performed in both implicit and explicit ways. For the former way, we compute several polynomial kernels of different degrees leveraging the kernel trick. Whereas, the latter way is achieved by concatenating the result of these polynomial kernels. The proposed Taylor Series Kernelized Convolution (TSKC) is able to learn more complex patterns than the linear convolution kernel and thus be more discriminative. The experiments conducted on Facial Expression Recognition (FER) datasets demonstrate that TSKC outperforms the ordinary convolution layer without additional parameters.

卷积神经网络 (CNN) 不断增长的深度和宽度极大地增加了它们的参数数量，并且需要更强大的设备来训练和部署。在本文中，我们提出了一种新的架构，它通过将后者扩展到更高程度的核函数而无需额外的权重，从而优于经典的线性卷积函数。我们选择泰勒系列将输入数据映射到高维再现内核希尔伯特空间 (RKHS) 的内核。将特征映射到高阶 RKHS 以隐式和显式方式执行。对于前一种方式，我们利用核技巧计算了几个不同程度的多项式核。而后一种方式是通过连接这些多项式内核的结果来实现的。提出的泰勒级数核化卷积（TSKC）能够学习比线性卷积核更复杂的模式，因此更具判别力。在面部表情识别 (FER) 数据集上进行的实验表明，TSKC 在没有额外参数的情况下优于普通卷积层。