LexiCan: Lexicographic Canonicalization of Point Clouds for Machine Learning Applications

Abstract:Canonicalization resolves the rotational and permutation ambiguity of 3D point clouds by selecting a unique orbit representative, maintaining their geometric information while allowing standard architectures, such as Transformers, to operate on them. Existing canonicalizations, however, exhibit discontinuity jumps on molecular configurations and non-trivial invariance errors in popular molecular datasets, which lead to ambiguity in their representation. To bridge this gap, we introduce LexiCan, a canonicalization that is provably invariant under either $O(3)$ or $SO(3)$, empirically invariant to rotations to within $\sim 10^{-6}$ angstroms on the QM9 and QM-sym molecular datasets, and mitigates discontinuity jumps on QM-sym, while running orders of magnitude faster than an existing canonicalization. Finally, non-invariant models perform better on QM9 property prediction and ModelNet40 shape classification with LexiCan than with that canonicalization.

Machine Learning (cs.LG)

arXiv:2610.15171 [cs.LG]

(or arXiv:2610.15171v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.15171 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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