Relaxed Rotational Equivariance via $G$-Biases in Vision

• URL: http://arxiv.org/abs/2408.12454v2
• Date: Sun, 25 Aug 2024 05:18:26 GMT
• Title: Relaxed Rotational Equivariance via $G$-Biases in Vision
• Authors: Zhiqiang Wu, Licheng Sun, Yingjie Liu, Jian Yang, Hanlin Dong, Shing-Ho J. Lin, Xuan Tang, Jinpeng Mi, Bo Jin, Xian Wei,
• Abstract summary: Group Equivariant Convolution (GConv) can effectively handle rotational symmetry data. Real-world data rarely conforms to strict rotational symmetry commonly referred to as Rotational Symmetry-Breaking. We propose a simple but highly effective method to address this problem, which utilizes a set of learnable biases called the $G$-Biases.
• Score: 19.814324876189772
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Group Equivariant Convolution (GConv) can effectively handle rotational symmetry data. They assume uniform and strict rotational symmetry across all features, as the transformations under the specific group. However, real-world data rarely conforms to strict rotational symmetry commonly referred to as Rotational Symmetry-Breaking 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 the $G$-Biases under the group order to break strict group constraints and achieve \textbf{R}elaxed \textbf{R}otational \textbf{E}quivarant \textbf{Conv}olution (RREConv). We conduct extensive experiments to validate Relaxed Rotational Equivariance on rotational symmetry groups $\mathcal{C}_n$ (e.g. $\mathcal{C}_2$, $\mathcal{C}_4$, and $\mathcal{C}_6$ groups). Further experiments demonstrate that our proposed RREConv-based methods achieve excellent performance, compared to existing GConv-based methods in classification and detection tasks on natural image datasets.

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