On original and latent space connectivity in deep neural networks

We study whether inputs from the same class can be connected by a continuous path, in original or latent representation space, such that all points on the path are mapped by the neural network model to the same class. Understanding how the neural network views its own input space and how the latent spaces are structured has value for explainability and robustness. We show that paths, linear or nonlinear, connecting same-class inputs exist in all cases studied.