  Deep learning has achieved a remarkable performance breakthrough in several
fields, most notably in speech recognition, natural language processing, and
computer vision. In particular, convolutional neural network (CNN)
architectures currently produce state-of-the-art performance on a variety of
image analysis tasks such as object detection and recognition. Most of deep
learning research has so far focused on dealing with 1D, 2D, or 3D
Euclidean-structured data such as acoustic signals, images, or videos.
Recently, there has been an increasing interest in geometric deep learning,
attempting to generalize deep learning methods to non-Euclidean structured data
such as graphs and manifolds, with a variety of applications from the domains
of network analysis, computational social science, or computer graphics. In
this paper, we propose a unified framework allowing to generalize CNN
architectures to non-Euclidean domains (graphs and manifolds) and learn local,
stationary, and compositional task-specific features. We show that various
non-Euclidean CNN methods previously proposed in the literature can be
considered as particular instances of our framework. We test the proposed
method on standard tasks from the realms of image-, graph- and 3D shape
analysis and show that it consistently outperforms previous approaches.
