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arXiv · 2610.15171

LexiCan: Lexicographic Canonicalization of Point Clouds for Machine Learning Applications

Daniel Sanchez·Djordje Mihajlovic·Federica Valeau·Luka Benić·Raghuwansh Raj·Soutrik Sarangi·Snir Hordan
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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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Daniel Sanchez, Djordje Mihajlovic, Federica Valeau, Luka Benić, Raghuwansh Raj, Soutrik Sarangi, Snir Hordan. 2026-10-10. LexiCan: Lexicographic Canonicalization of Point Clouds for Machine Learning Applications. https://arxiv.org/abs/2610.15171

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