  Mesh is a powerful data structure for 3D shapes. Representation learning for
3D meshes is important in many computer vision and graphics applications. The
recent success of convolutional neural networks (CNNs) for structured data
(e.g., images) suggests the value of adapting insight from CNN for 3D shapes.
However, 3D shape data are irregular since each node's neighbors are unordered.
Various graph neural networks for 3D shapes have been developed with isotropic
filters or predefined local coordinate systems to overcome the node
inconsistency on graphs. However, isotropic filters or predefined local
coordinate systems limit the representation power. In this paper, we propose a
local structure-aware anisotropic convolutional operation (LSA-Conv) that
learns adaptive weighting matrices for each node according to the local
neighboring structure and performs shared anisotropic filters. In fact, the
learnable weighting matrix is similar to the attention matrix in the random
synthesizer -- a new Transformer model for natural language processing (NLP).
Comprehensive experiments demonstrate that our model produces significant
improvement in 3D shape reconstruction compared to state-of-the-art methods.
