IMEXnet: A Forward Stable Deep Neural Network.

Deep convolutional neural networks have revolutionized many machine learning and computer vision tasks. Despite their enormous success, remaining key challenges limit their wider use. Pressing challenges include improving the network's robustness to perturbations of the input images and simplifying the design of architectures that generalize. Another problem relates to the limited "field of view" of convolution operators, which means that very deep networks are required to model nonlocal relations in high-resolution image data. We introduce the IMEXnet that addresses these challenges by adapting semi-implicit methods for partial differential equations. Compared to similar explicit networks such as the residual networks (ResNets) our network is more stable. This stability has been recently shown to reduce the sensitivity to small changes in the input features and improve generalization. The implicit step connects all pixels in the images and therefore addresses the field of view problem, while being comparable to standard convolutions in terms of the number of parameters and computational complexity. We also present a new dataset for semantic segmentation and demonstrate the effectiveness of our architecture using the NYU depth dataset.