LexiCan: Lexicographic Canonicalization of Point Clouds for Machine Learning Applications

arXiv:2610.15171v1 Announce Type: new 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.

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Source: arXiv cs.LG | 2026-10-14