Understanding Neural Network Systems for Image Analysis using Vector Spaces and Inverse Maps

There is strong interest in developing mathematical methods that can be used to understand complex neural networks used in image analysis. In this paper, we introduce techniques from Linear Algebra to model neural network layers as maps between signal spaces. First, we demonstrate how signal spaces can be used to visualize weight spaces and convolutional layer kernels. We also demonstrate how residual vector spaces can be used to further visualize information lost at each layer. Second, we introduce the concept …

algebra analysis cs.cv cs.lg image linear linear algebra maps network networks neural network neural networks paper signal spaces systems understanding vector