ZZ-Net: A Universal Rotation Equivariant Architecture for 2D Point Clouds

Bökman, Georg; Kahl, Fredrik; Flinth, Axel

doi:10.1109/cvpr52688.2022.01070

Cited by 5 publications

(1 citation statement)

References 21 publications

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“…In (Lim et al 2022), universality was proven for Euclidean GNNs with very highorder permutation representations. In the planar case d = 2, universality using low-dimensional features was achieved in (Bökman, Kahl, and Flinth 2022). For d ≥ 3 our construction seems to be the first to achieve universality using low dimensional representations.…”

Section: Related Workmentioning

confidence: 82%

Complete Neural Networks for Complete Euclidean Graphs

Hordan,

Amir,

Gortler

et al. 2024

AAAI

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Neural networks for point clouds, which respect their natural invariance to permutation and rigid motion, have enjoyed recent success in modeling geometric phenomena, from molecular dynamics to recommender systems. Yet, to date, no architecture with polynomial complexity is known to be complete, that is, able to distinguish between any pair of non-isomorphic point clouds. We fill this theoretical gap by showing that point clouds can be completely determined, up to permutation and rigid motion, by applying the 3-WL graph isomorphism test to the point cloud's centralized Gram matrix. Moreover, we formulate an Euclidean variant of the 2-WL test and show that it is also sufficient to achieve completeness. We then show how our complete Euclidean WL tests can be simulated by an Euclidean graph neural network of moderate size and demonstrate their separation capability on highly symmetrical point clouds.

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Section: Related Workmentioning

confidence: 82%