In this paper, we introduce a novel methodology for characterizing the performance of deep learning networks (ResNets and DenseNet) with respect to training convergence and generalization as a function of mini-batch size and learning rate for image classification. This methodology is based on novel measurements derived from the eigenvalues of the approximate Fisher information matrix, which can be efficiently computed even for high capacity deep models. Our proposed measurements can help practitioners to monitor and control the training process (by actively tuning the mini-batch size and learning rate) to allow for good training convergence and generalization. Furthermore, the proposed measurements also allow us to show that it is possible to optimize the training process with a new dynamic sampling training approach that continuously and automatically change the mini-batch size and learning rate during the training process. Finally, we show that the proposed dynamic sampling training approach has a faster training time and a competitive classification accuracy compared to the current state of the art.