Rotation Equivariant Mamba for Vision Tasks

Rotation equivariance is an important structural prior for a broad range of vision tasks, particularly in domains such as remote sensing and medical imaging where objects have no canonical orientation, yet it remains notably absent from current Mamba-based vision architectures. Despite the success of Mamba in natural language processing and its growing adoption in computer vision, existing visual Mamba models fail to account for rotational symmetry in their design. This omission renders them sensitive to image rotations, thereby constraining their robustness and cross-task generalization. To address this limitation, we incorporate rotation symmetry, an important geometric prior in many visual domains, into Mamba-based architectures. Specifically, we introduce EQ-VMamba, the first rotation equivariant visual Mamba architecture for vision tasks. The core components of EQ-VMamba include a carefully designed rotation equivariant cross-scan strategy and group Mamba blocks. Moreover, we provide a rigorous theoretical analysis of the intrinsic equivariance error, demonstrating that the proposed architecture enforces end-to-end rotation equivariance under the $\mathrm{p}4$ rotation group. Extensive experiments across multiple benchmarks-including high-level image classification, mid-level semantic segmentation, and low-level image super-resolution-demonstrate that EQ-VMamba consistently improves rotation robustness and achieves superior or competitive performance compared to non-equivariant baselines on most evaluated benchmarks, while requiring 40-70% fewer parameters. These results indicate that embedding rotation equivariance not only effectively bolsters the robustness of visual Mamba models against rotation transformations, but also improves accuracy on data exhibiting rotational symmetry, with substantially improved parameter efficiency.