# Equivariance by Local Canonicalization: A Matter of Representation

arXiv: https://arxiv.org/abs/2509.26499 · HTML: https://mlsanity.com/paper/2509.26499/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 18 references that are in the map.
- First posted on arXiv 30 Sep 2025.

## Builds on (most cited first, 12 of 12)

- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Deep Learning Scaling is Predictable, Empirically](https://mlsanity.com/paper/1712.00409/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNs](https://mlsanity.com/paper/2302.03655/) (2023)
- [Does equivariance matter at scale?](https://mlsanity.com/paper/2410.23179/) (2024)
- [Beyond Canonicalization: How Tensorial Messages Improve Equivariant Message Passing](https://mlsanity.com/paper/2405.15389/) (2024)
- [Lorentz Local Canonicalization: How to Make Any Network Lorentz-Equivariant](https://mlsanity.com/paper/2505.20280/) (2025)

## Built on by (most cited first, 1 of 1)

- [Rotational Equivariance in Machine Learning: A Comprehensive Tutorial](https://mlsanity.com/paper/2608.31045/) (2026)

## Abstract (arXiv)

Equivariant neural networks offer strong inductive biases for learning from molecular and geometric data but often rely on specialized, computationally expensive tensor operations. We present a framework to transfers existing tensor field networks into the more efficient local canonicalization paradigm, preserving equivariance while significantly improving the runtime. Within this framework, we systematically compare different equivariant representations in terms of theoretical complexity, empirical runtime, and predictive accuracy. We publish the tensor_frames package, a PyTorchGeometric based implementation for local canonicalization, that enables straightforward integration of equivariance into any standard message passing neural network.