Equivariant Mesh Attention Networks
This work addresses the need for robust mesh processing models that are equivariant to all common symmetries, which is incremental but important for applications in computer graphics and geometry.
The paper tackled the problem of achieving full equivariance to multiple symmetries in mesh processing by introducing an attention-based architecture that uses relative tangential features, resulting in improved performance on FAUST and TOSCA benchmarks and proven robustness to transformations.
Equivariance to symmetries has proven to be a powerful inductive bias in deep learning research. Recent works on mesh processing have concentrated on various kinds of natural symmetries, including translations, rotations, scaling, node permutations, and gauge transformations. To date, no existing architecture is equivariant to all of these transformations. In this paper, we present an attention-based architecture for mesh data that is provably equivariant to all transformations mentioned above. Our pipeline relies on the use of relative tangential features: a simple, effective, equivariance-friendly alternative to raw node positions as inputs. Experiments on the FAUST and TOSCA datasets confirm that our proposed architecture achieves improved performance on these benchmarks and is indeed equivariant, and therefore robust, to a wide variety of local/global transformations.