On the Universality of Rotation Equivariant Point Cloud Networks.
| dc.contributor.author | Dym, Nadav | |
| dc.contributor.author | Maron, Haggai | |
| dc.date.accessioned | 2020-12-14T19:39:31Z | |
| dc.date.available | 2020-12-14T19:39:31Z | |
| dc.date.issued | 2020 | |
| dc.date.updated | 2020-12-14T19:39:30Z | |
| dc.description.abstract | Learning functions on point clouds has applications in many fields, including computer vision, computer graphics, physics, and chemistry. Recently, there has been a growing interest in neural architectures that are invariant or equivariant to all three shape-preserving transformations of point clouds: translation, rotation, and permutation. In this paper, we present a first study of the approximation power of these architectures. We first derive two sufficient conditions for an equivariant architecture to have the universal approximation property, based on a novel characterization of the space of equivariant polynomials. We then use these conditions to show that two recently suggested models are universal, and for devising two other novel universal architectures. | |
| dc.identifier.uri | ||
| dc.relation.ispartof | CoRR | |
| dc.subject | cs.LG | |
| dc.subject | cs.LG | |
| dc.subject | cs.CG | |
| dc.title | On the Universality of Rotation Equivariant Point Cloud Networks. | |
| dc.type | Journal article | |
| pubs.organisational-group | Trinity College of Arts & Sciences | |
| pubs.organisational-group | Mathematics | |
| pubs.organisational-group | Duke | |
| pubs.volume | abs/2010.02449 |