mlsanityData to 14 Oct 2026

LexiCan: Lexicographic Canonicalization of Point Clouds for Machine Learning Applications

arXiv 2610.15171 ↗First posted 10 Oct 2026cs.LGcited by 0

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Abstract (arXiv)

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 ~ 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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 17 of its 32 references that are in the map. First posted on arXiv 10 Oct 2026.

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References · 17

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  2. 2021E(n) Equivariant Graph Neural Networkscited by 965
  3. 2020Simple and Deep Graph Convolutional Networkscited by 860
  4. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 746
  5. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 708
  6. 2017SchNet: A continuous-filter convolutional neural network for modeling quantum interactionscited by 571
  7. 2016Steerable CNNscited by 305
  8. 2019Symmetry-adapted generation of 3d point sets for the targeted discovery of moleculescited by 172
  9. 2021Frame Averaging for Invariant and Equivariant Network Designcited by 168
  10. 2022Equivariance with Learned Canonicalization Functionscited by 109
  11. 2023FAENet: Frame Averaging Equivariant GNN for Materials Modelingcited by 73
  12. 2024Equivariant Frames and the Impossibility of Continuous Canonicalizationcited by 43
5 more
  1. 2022Unsupervised Learning of Group Invariant and Equivariant Representationscited by 39
  2. 2022Polynomial-time algorithms for continuous metrics on atomic clouds of unordered pointscited by 8
  3. 2023Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants with no False Negatives and no False Positivescited by 8
  4. 2020Wavelet Networks: Scale-Translation Equivariant Learning From Raw Time-Seriescited by 6
  5. 2023Simplexwise Distance Distributions for finite spaces with metrics and measurescited by 2

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