# Computing Representations for Lie Algebraic Networks

arXiv: https://arxiv.org/abs/2006.00724 · HTML: https://mlsanity.com/paper/2006.00724/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2020.

## Built on by (most cited first, 3 of 3)

- [Clifford-Steerable Convolutional Neural Networks](https://mlsanity.com/paper/2402.14730/) (2024)
- [Orthogonal Low-rank Adaptation in Lie Groups for Continual Learning of Large Language Models](https://mlsanity.com/paper/2509.06100/) (2025)
- [Generalized Tensor-based Parameter-Efficient Fine-Tuning via Lie Group Transformations](https://mlsanity.com/paper/2504.00851/) (2025)

## Abstract (arXiv)

Recent work has constructed neural networks that are equivariant to continuous symmetry groups such as 2D and 3D rotations. This is accomplished using explicit Lie group representations to derive the equivariant kernels and nonlinearities. We present three contributions motivated by frontier applications of equivariance beyond rotations and translations. First, we relax the requirement for explicit Lie group representations with a novel algorithm that finds representations of arbitrary Lie groups given only the structure constants of the associated Lie algebra. Second, we provide a self-contained method and software for building Lie group-equivariant neural networks using these representations. Third, we contribute a novel benchmark dataset for classifying objects from relativistic point clouds, and apply our methods to construct the first object-tracking model equivariant to the Poincar'e group.