Relaxed Rotational Equivariance via $G$-Biases in Vision
<|reference_start|>Relaxed Rotational Equivariance via $G$-Biases in Vision: 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.<|reference_end|>
@article{wu2024relaxed,
    title={Relaxed Rotational Equivariance via $G$-Biases in Vision},
    author={Zhiqiang Wu, Licheng Sun, Yingjie Liu, Jian Yang, Hanlin Dong,
  Shing-Ho J. Lin, Xuan Tang, Jinpeng Mi, Bo Jin, Xian Wei},
    journal={arXiv preprint arXiv:2408.12454},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.12454},
    primaryClass={cs.CV cs.AI}
}