# Rethinking SO(3)-equivariance with Bilinear Tensor Networks

arXiv: https://arxiv.org/abs/2303.11288 · HTML: https://mlsanity.com/paper/2303.11288/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 27 references that are in the map.
- First posted on arXiv 20 Mar 2023.

## Builds on (most cited first, 9 of 9)

- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups](https://mlsanity.com/paper/2104.09459/) (2021)
- [Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network](https://mlsanity.com/paper/1806.09231/) (2018)
- [Particle Transformer for Jet Tagging](https://mlsanity.com/paper/2202.03772/) (2022)
- [Energy Flow Networks: Deep Sets for Particle Jets](https://mlsanity.com/paper/1810.05165/) (2018)
- [Decorrelated Jet Substructure Tagging using Adversarial Neural Networks](https://mlsanity.com/paper/1703.03507/) (2017)
- [Particle Convolution for High Energy Physics](https://mlsanity.com/paper/2107.02908/) (2021)

## Abstract (arXiv)

Many datasets in scientific and engineering applications are comprised of objects which have specific geometric structure. A common example is data which inhabits a representation of the group SO(3) of 3D rotations: scalars, vectors, tensors, textitetc. One way for a neural network to exploit prior knowledge of this structure is to enforce SO(3)-equivariance throughout its layers, and several such architectures have been proposed. While general methods for handling arbitrary SO(3) representations exist, they computationally intensive and complicated to implement. We show that by judicious symmetry breaking, we can efficiently increase the expressiveness of a network operating only on vector and order-2 tensor representations of SO(2). We demonstrate the method on an important problem from High Energy Physics known as textitb-tagging, where particle jets originating from b-meson decays must be discriminated from an overwhelming QCD background. In this task, we find that augmenting a standard architecture with our method results in a ensuremath2.3× improvement in rejection score.