Before revision: The research community has observed a massive success of convolutional neural networks ( CNN) in visual recognition tasks. Such powerful CNNs , however, do not generalize well to arbitrary-shaped mainfold domains. Thus, still many visual recognition problems  defined on arbitrary manifolds cannot benefit much from the success of CNNs, if at all .
After revision: The research community has observed a massive success of convolutional neural networks ( CNNs) have been shown to possess a promising capability of extracting and codifying features from visual information. However, the application of such capable CNNs has been quite limited to mostly computer vision problems where the visual information is inherently given on a grid-like structure. This, unfortunately, was not the case for the geometry processing community, where many visual recognition problems defined on arbitrary manifolds cannot benefit much from the success of CNNs, if at all .