Relaxed Rotational Equivariance via G-Biases in Vision

2024/08/22 by Zhiqiang Wu, Yingjie Liu, Wu, Zhiqiang +17 · 1 citation
Physics and Astronomy · #Artificial Intelligence (cs.AI) #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Historical Astronomy and Related Studies #History and Developments in Astronomy

paper · pdf · doi:10.48550/arxiv.2408.12454

openalex publication_date 2024/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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 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.

Cited by

• Achieving Approximate Symmetry Is Exponentially Easier than Exact Symmetry

Related

• R2Det: Exploring Relaxed Rotation Equivariance in 2D object detection
• Deformation Robust Roto-Scale-Translation Equivariant CNNs
• Learning Partial Equivariances from Data
• RotDCF: Decomposition of Convolutional Filters for Rotation-Equivariant Deep Networks
• Exploiting Cyclic Symmetry in Convolutional Neural Networks