Understanding Neural Network Systems for Image Analysis using Vector Spaces and Inverse Maps
This work provides mathematical tools for researchers to interpret neural networks in image analysis, but it is incremental as it applies existing linear algebra concepts to this domain.
The paper tackled the problem of understanding complex neural networks for image analysis by introducing linear algebra techniques to model layers as maps between signal spaces, enabling visualization of weight spaces and information loss, and studying invertible networks to compute inputs for specific outputs, demonstrated on two invertible networks and ResNet18.
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 study invertible networks using vector spaces for computing input images that yield specific outputs. We demonstrate our approach on two invertible networks and ResNet18.