Relaxed Rotational Equivariance via $G$-Biases in Vision

2024-08-22

AI Summary

To address the degradation of group convolution (GConv) performance caused by rotational symmetry breaking (RSB) in real-world images, this paper proposes Relaxed Rotational Equivariant Convolution (RREConv). Its core innovation is the introduction of learnable parametric group biases ($G$-biases), which flexibly relax strict equivariance constraints while preserving the discrete rotational group $mathcal{C}_n$ structure—enabling, for the first time, data-adaptive relaxed equivariance modeling. RREConv integrates seamlessly into standard CNN training pipelines without requiring additional preprocessing or architectural modifications. On natural image classification and 2D object detection benchmarks, RREConv consistently outperforms existing GConv methods. Ablation studies confirm its robustness to rotational perturbations and strong cross-dataset generalization capability.

Technology Category

• Computer Vision: Adversarial Attacks & Robustness
• Machine Learning: Adversarial Learning & Robustness
• Search and Optimization: Non-convex Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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.

Problem

• Image Rotation
• Group Equivariant Convolution (GConv)
• Rotation Symmetry Breaking (RSB)

Innovation

• RREConv
• G-Offset
• Rotation Symmetry Breaking