Relaxed Rotational Equivariance via $G$-Biases in Vision

• URL: http://arxiv.org/abs/2408.12454v3
• Date: Tue, 14 Jan 2025 15:35:55 GMT
• Title: Relaxed Rotational Equivariance via $G$-Biases in Vision
• Authors: Zhiqiang Wu, Yingjie Liu, Licheng Sun, Jian Yang, Hanlin Dong, Shing-Ho J. Lin, Xuan Tang, Jinpeng Mi, Bo Jin, Xian Wei,
• Abstract summary: Group Equivariant Convolution (GConv) can capture rotational equivariance from original data. However, the presentation or distribution of real-world data rarely conforms to strict rotational equivariance. We propose a simple but highly effective method to address this problem, which utilizes a set of learnable biases called $G$-Biases. 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.
• Score: 19.814324876189772
• License:
• 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.

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