Differential invariants for SE(2)-equivariant networks

TL;DR

This paper introduces SE(2) differential invariants to build neural networks that are equivariant to rotations and translations, improving classification performance with fewer parameters.

Contribution

It derives SE(2) differential invariants and constructs a novel SE(2)-equivariant network, SE2DINNet, demonstrating improved efficiency and accuracy in rotation-sensitive classification tasks.

Findings

SE2DINNet outperforms state-of-the-art models in classification accuracy.

The proposed network uses fewer parameters than comparable models.

Differential invariants effectively encode SE(2) symmetry in neural networks.

Abstract

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.