This paper investigates the usage of kernel functions at the different layers in a convolutional neural network. We carry out extensive studies of their impact on convolutional, pooling and fully-connected layers. We notice that the linear kernel may not be sufficiently effective to fit the input data distributions, whereas high order kernels prone to over-fitting. This leads to conclude that a trade-off between complexity and performance should be reached. We show how one can effectively leverage kernel functions, by introducing a more distortion aware pooling layers which reduces over-fitting while keeping track of the majority of the information fed into subsequent layers. We further propose Kernelized Dense Layers (KDL), which replace fully-connected layers, and capture higher order feature interactions. The experiments on conventional classification datasets i.e. MNIST, FASHION-MNIST and CIFAR-10, show that the proposed techniques improve the performance of the network compared to classical convolution, pooling and fully connected layers. Moreover, experiments on fine-grained classification i.e. facial expression databases, namely RAF-DB, FER2013 and ExpW demonstrate that the discriminative power of the network is boosted, since the proposed techniques improve the awareness to slight visual details and allows the network reaching state-of-the-art results.

翻译：本文研究了卷积神经网络中不同层级上核函数的使用情况。我们对其在卷积层、池化层和全连接层上的影响进行了广泛探究。研究发现，线性核函数可能不足以有效拟合输入数据分布，而高阶核函数则容易出现过拟合现象。由此得出结论：需要在复杂度与性能之间寻求平衡。我们展示了如何通过引入更具形变感知能力的池化层来有效利用核函数——该池化层在减少过拟合的同时，能够保留输入至后续层的大部分信息。进一步地，我们提出了核化密集层（KDL），该结构替代了全连接层，能够捕获高阶特征交互作用。在常规分类数据集（MNIST、FASHION-MNIST、CIFAR-10）上的实验表明，相较于传统卷积层、池化层和全连接层，所提技术提升了网络性能。此外，在细粒度分类任务（即面部表情数据库RAF-DB、FER2013和ExpW）上的实验证明，由于所提技术增强了对细微视觉细节的感知能力，网络判别能力得到显著提升，并达到了当前最优水平。