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arXiv cs.LG
arXiv cs.LG
7/13/2026
LieBN: Batch Normalization over Lie Groups

LieBN: Batch Normalization over Lie Groups

Short summary

LieBN proposes a framework for Riemannian Batch Normalization over Lie groups, leveraging left- and right-invariant metrics with theoretical guarantees for controlling mean and variance. It is instantiated across nine geometries including SPD manifolds, rotation matrices, and full-rank correlation matrices, introducing a novel right-invariant metric for SPD. Experiments across different manifolds validate the framework's effectiveness for manifold-valued deep learning.

  • •Riemannian batch normalization framework generalized to Lie groups
  • •Covers nine geometries: SPD manifolds, rotation matrices, and correlation matrices
  • •Introduces novel right-invariant metric and extends existing Lie group structures

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