# Differential invariants for SE(2)-equivariant networks

arXiv: https://arxiv.org/abs/2206.13279 · HTML: https://mlsanity.com/paper/2206.13279/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2022.

## Built on by (most cited first, 6 of 6)

- [Moving Frame Net: SE(3)-Equivariant Network for Volumes](https://mlsanity.com/paper/2211.03420/) (2022)
- [Equivariant Neural Networks for General Linear Symmetries on Lie Algebras](https://mlsanity.com/paper/2510.22984/) (2025)
- [Scale generalisation properties of extended scale-covariant and scale-invariant Gaussian derivative networks on image datasets with spatial scaling variations](https://mlsanity.com/paper/2409.11140/) (2024)
- [Equivariant Eikonal Neural Networks: Grid-Free, Scalable Travel-Time Prediction on Homogeneous Spaces](https://mlsanity.com/paper/2505.16035/) (2025)
- [Scale-invariant Gaussian derivative residual networks](https://mlsanity.com/paper/2603.02843/) (2026)
- [Generalized Reduction to the Isotropy for Flexible Equivariant Neural Fields](https://mlsanity.com/paper/2603.08758/) (2026)

## Abstract (arXiv)

Symmetry is present in many tasks in computer vision, where the same class of objects can appear transformed, e.g. rotated due to different camera orientations, or scaled due to perspective. The knowledge of such symmetries in data coupled with equivariance of neural networks can improve their generalization to new samples. Differential invariants are equivariant operators computed from the partial derivatives of a function. In this paper we use differential invariants to define equivariant operators that form the layers of an equivariant neural network. Specifically, we derive invariants of the Special Euclidean Group SE(2), composed of rotations and translations, and apply them to construct a SE(2)-equivariant network, called SE(2) Differential Invariants Network (SE2DINNet). The network is subsequently tested in classification tasks which require a degree of equivariance or invariance to rotations. The results compare positively with the state-of-the-art, even though the proposed SE2DINNet has far less parameters than the compared models.