Relaxed Rotational Equivariance via $G$-Biases in Vision

TL;DR

This paper introduces RREConv, a method that relaxes strict rotational equivariance in group convolutions using learnable biases, improving performance on classification and detection tasks with real-world data.

Contribution

It proposes a novel approach using $G$-Biases to relax strict rotational equivariance constraints in GConv, addressing real-world data distribution issues.

Findings

RREConv outperforms existing GConv methods in classification tasks.

RREConv improves 2D object detection accuracy.

Extensive ablation experiments validate the effectiveness of the approach.

Abstract

Group Equivariant Convolution (GConv) can capture rotational equivariance from original data. It assumes uniform and strict rotational equivariance across all features as the transformations under the specific group. However, the presentation or distribution of real-world data rarely conforms to strict rotational equivariance, commonly referred to as Rotational Symmetry-Breaking (RSB) in the system or dataset, making GConv unable to adapt effectively to this phenomenon. Motivated by this, we propose a simple but highly effective method to address this problem, which utilizes a set of learnable biases called $G$-Biases under the group order to break strict group constraints and then achieve a Relaxed Rotational Equivariant Convolution (RREConv). To validate the efficiency of RREConv, we conduct extensive ablation experiments on the discrete rotational group $\mathcal{C}_n$. Experiments demonstrate that the proposed RREConv-based methods achieve excellent performance compared to existing GConv-based methods in both classification and 2D object detection tasks on the natural image datasets.