@qi2017pointnet++], local descriptor learning, correspondence, and retrieval [@monti2017geometric; @boscaini2016learning; @masci2015geodesic].

On the other hand, there has been limited progress in representation learning and generation of geometric data (*shape synthesis*). Obtaining descriptive and compact representations of meshes and point clouds is essential for downstream tasks such as classification and 3D reconstruction, when dealing with limited labelled training data. Additionally, geometric data synthesis is pivotal in applications such as 3D printing, computer graphics and animation, virtual reality, and game design, and can heavily assist graphics designers and speed-up production. Furthermore, given the high cost and time of acquiring quality 3D data, geometric generative models can be used as a cheap alternative for producing training data for geometric ML algorithms.

Most of the previous approaches in this direction rely on intermediate representations of 3D shapes, such as point clouds [@achlioptas2017learning], voxels [@wu2016learning] or mappings to a flat domain [@moschoglou20193dfacegan; @ben2018multi] instead of direct surface representations, such as meshes. Despite the success of such techniques, they either suffer from high computational complexity (voxels) or absence of smoothness of the data representation (point clouds), while usually pre- and post-processing steps are needed in order to obtain the output surface model. Learning directly on the mesh 