Relaxed Rotational Equivariance via G-Biases in Vision

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 specifc 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 buthighly 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 effciency 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 classifcation and 2D objectdetection tasks on the natural image datasets.

Recommended citation: Z. Wu, Y. Liu, L. Sun, J. Yang, H. Dong, S.-H. J. Lin, X. Tang, J. Mi, B. Jin, and X. Wei, "Relaxed Rotational Equivariance via G-Biases in Vision," in AAAI Conference on Artificial Intelligence, 2025.
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