kernels, F-transform, convolution neural networks

In our research, we are focused on a semantic description of feature maps and corresponding to them kernels that are used in Convolutional neural networks (CNN). A CNN is a hierarchically ordered computational tool that uses a training process to learn and extract abstract characteristics (features) of input objects. The extracted features have to approximate the original object sufficiently for a next stage (classification, regression, etc.). The first layer of a CNN extracts features by performing convolution operations with a number of kernels. Therefore, to study the semantic description of feature maps in the first layer, we should be focused on convolutional kernels (otherwise, weight vectors). We make a conjecture that in the first layer, a CNN learns the most typical image processing convolutional kernels, and they appear in subsequent layers as well. To confirm our claim, we have used 5 CNNs~\cite{vgg,inception,resnet,mobilenet,alexnet} trained on the \textit{ImageNet} dataset. In the first layer of selected CNNs, we have identified (after performing clustering) the following kernels: gradient kernels with various rotations, Gaussian kernels and texture extracting kernels (e.g., Gabor filters). Further, we have found kernels sensitive to certain color(s) (combinations) that might be dominant in the ImageNet.To conclude, our hypothesis seems to be correct, and a CNN indeed learns standard image processing convolution kernels. A relationship between kernels in further layers is a subject of the future research.