LexiCan: Lexicographic Canonicalization of Point Clouds for Machine Learning Applications
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 mit...
| Authors | Daniel Sanchez, Djordje Mihajlovic, Federica Valeau et al. |
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| Primary category | cs.LG |
| Published | 10 October 2026 |
| Last updated at source | 10 October 2026 |
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