Rotation Equivariant Mamba for Vision Tasks

Zhongchen Zhao; Qi Xie; Keyu Huang; Lei Zhang; Deyu Meng; Zongben Xu

cs.CVMar 10, 2026

Rotation Equivariant Mamba for Vision Tasks

Authors: Zhongchen Zhao, Qi Xie, Keyu Huang, Lei Zhang, Deyu Meng, Zongben Xu

Organizations: School of Mathematics and Statistics, Xi’an Jiaotong University, Shaanxi, P.R. China · Department of Computing, the Hong Kong Polytechnic University, Hong Kong, P.R. China

Abstract

Rotation equivariance constitutes one of the most general and crucial structural priors for visual data, 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 inherently sensitive to image rotations, thereby constraining their robustness and cross-task generalization. To address this limitation, we incorporate rotation symmetry, a universal and fundamental geometric prior in images, 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 throughout the network. 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, while requiring approximately 50% fewer parameters. These results indicate that embedding rotation equivariance not only effectively bolsters the robustness of visual Mamba models against rotation transformations, but also enhances overall performance with significantly improved parameter efficiency. Code is available at https://github.com/zhongchenzhao/EQ-VMamba.

Figures & tables

Fig. 1: (a)-(b) Visualization of output feature maps for an input image and its rotated version using VMamba and our proposed EQ-VMamba, respectively. (c) Performance comparison between VMamba and EQ-VMamba on the rotated ImageNet-100 dataset.

Fig. 2: Illustration of the group dimension (indexed by colors), and three fundamental transformation operators utilized in our equivariant framework. (a)-(c) illustrate $\pi^{\scriptscriptstyle{\mathcal{R}}}_{\scriptscriptstyle G}(\cdot)$ , $\pi^{\scriptscriptstyle{\mathcal{R}S}}_{\scriptscriptstyle G}(\cdot)$ , and $\pi^{\scriptscriptstyle{\mathcal{S}}}_{\scriptscriptstyle G}(\cdot)$ , respectively.

Fig. 3: Overall architecture of the proposed end-to-end rotation equivariant visual Mamba (EQ-VMamba). The framework mainly comprises: (a) an EQ-patch embedding module that tokenizes the input image into group-structured feature maps, and (b) a stack of EQ-VSS blocks for hierarchical feature extraction. Each EQ-VSS block integrates an EQ-cross-scan operation for image-to-sequence flattening, group Mamba blocks for sequence modeling, and an EQ-cross-merge operation for sequence-to-image reconstruction.

Fig. 4: Illustration of the rotation equivariant patch embedding. A spatial rotation applied to the input image induces a joint transformation on the output feature map, i.e., $\mathrm{PE}_{eq}\left({{\pi}}^{\scriptscriptstyle{\mathcal{R}}}_{\scriptscriptstyle G}\left({\bm{I}}\right)\right)={{\pi}}^{\scriptscriptstyle{\mathcal{RS}}}_{\scriptscriptstyle G}\left(\mathrm{PE}_{eq}\left({\bm{I}}\right)\right)$ .

Fig. 5: Comparison between the non-equivariant cross-scan and the proposed equivariant EQ-cross-scan. (a) Under a 90 ∘ rotation of the input image, the standard cross-scan in VMamba fails to maintain sequence consistency. (b) In contrast, EQ-cross-scan preserves the ordering of tokens within each 1D sequence, ensuring rigorous structural correspondence between the rotated and unrotated representations.

Fig. 6: Upper : Architectural pipeline of the proposed equivariant Visual State-Space (EQ-VSS) block. (1) The block first employs EQ-Linear layers to generate input-dependent Mamba parameters ${\bm{A}}$ , ${\bm{B}}$ , and ${\bm{C}}$ . (2) These parameters, along with the input feature map, are partitioned along the group dimension and flattened into four 1D sequences via EQ-cross-scan. (3) Each feature sequence is processed in parallel by the group Mamba block using its corresponding group-wise parameters. (4) Finally, the output feature map is restored through the EQ-cross-merge operation. Bottom : Illustration of the proposed theoretical results, which show the correspondence between each theorem and its respective network module.

Model	Arch.	#Param.	FLOPs	Top-1 (%)	Top-5 (%)
ConvNeXt-T [ 6 ]	CNN	29M	4.5G	87.06	96.70
DeiT-S [ 64 ]	Trans.	22M	4.6G	78.88	93.64
Swin-T [ 9 ]	Trans.	29M	4.5G	87.42	97.20
XCiT-S24 [ 65 ]	Trans.	26M	9.2G	87.14	96.98
Vim-T [ 13 ]	SSM	7M	1.5G	82.20	95.60
MSVMamba-M [ 42 ]	SSM	12M	1.5G	87.56	97.76

TABLE I: Quantitative comparison of image classification performance on the ImageNet-100 validation set.

Fig. 7: Robustness comparison of VMamba-T, Spectral VMamba-T, and EQ-VMamba-T on the rotated ImageNet-100 dataset.

Backbone	#Param.	Natural Image				Remote Sensing Image
Backbone	#Param.	ADE20K	VOC 2012	Cityscapes	COCO-Stuff	LoveDA	ISPRS Potsdam
ConvNeXt-T [ 6 ]	48M	35.59	53.99	76.33	32.81	38.52	50.61
DeiT-S [ 64 ]	52M	23.13	24.17	24.29	54.23	38.74	48.63
Swin-T [ 9 ]	48M	27.05	35.73	70.05	25.83	40.78	53.78
XCiT-S24 [ 65 ]	76M	36.21	58.08	73.02	35.11	36.29	49.01
Vim-T [ 13 ]	13M	24.31	32.20	60.04	23.64	36.12	44.01

TABLE II: Quantitative comparison of semantic segmentation performance on natural/remote sensing image datasets (mIoU: %).

Backbone	#Param.	Natural Image				Remote Sensing Image
Backbone	#Param.	ADE20K	VOC 2012	Cityscapes	COCO-Stuff	LoveDA	ISPRS Potsdam
VMamba-T [ 14 ]	62M	15.98 (24.17 $\downarrow$ )	40.42 (23.28 $\downarrow$ )	32.70 (45.72 $\downarrow$ )	24.26 (14.41 $\downarrow$ )	41.68 (0.94 $\downarrow$ )	53.15 (0.09 $\downarrow$ )
EQ-VMamba-T	18M	39.59 ( 0.08 $\uparrow$ )	63.19 ( 1.27 $\downarrow$ )	78.01 ( 0.00 )	37.80 ( 0.50 $\downarrow$ )	45.69 ( 0.00 )	59.54 ( 0.00 )
VMamba-S [ 14 ]	82M	19.60 (22.08 $\downarrow$ )	47.54 (18.60 $\downarrow$ )	39.42 (39.61 $\downarrow$ )	26.51 (10.92 $\downarrow$ )	39.19 (1.71 $\downarrow$ )	53.08 (2.98 $\downarrow$ )
EQ-VMamba-S	25M	39.87 ( 0.03 $\downarrow$ )	65.64 ( 0.93 $\downarrow$ )	80.36 ( 0.00 )	37.76 ( 0.54 $\downarrow$ )	44.04 ( 0.00 )	62.00 ( 0.00 )

TABLE III: Quantitative comparison of semantic segmentation performance on rotated natural/remote sensing datasets (mIoU: %) (The values inside the parentheses indicate the increase/decrease in performance on rotated inputs compared with unrotated inputs).

Fig. 8: Visual comparison of segmentation results between VMamba and EQ-VMamba on the PASCAL VOC 2012 natural image dataset (top row) and the ISPRS Potsdam remote sensing dataset (bottom row).

Fig. 9: Robustness comparison of VMamba and EQ-VMamba on the rotated semantic segmentation datasets. Input image rotations lead to a substantial performance degradation in VMamba, while EQ-VMamba preserves performance under 90-degree rotations.

Model	Scale	#Param.	Set5		Set14		BSD100		Urban100		Manga109
Model	Scale	#Param.	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM
EDSR [ 77 ]	$\times 2$	42.6M	38.11	0.9602	33.92	0.9195	32.32	0.9013	32.93	0.9351	39.10	0.9773
RCAN [ 78 ]	$\times 2$	15.4M	38.27	0.9614	34.12	0.9216	32.41	0.9027	33.34	0.9384	39.44	0.9786
SAN [ 79 ]	$\times 2$	15.7M	38.31	0.9620	34.07	0.9213	32.42	0.9028	33.10	0.9370	39.32	0.9792
HAN [ 80 ]	$\times 2$	15.9M	38.27	0.9614	34.16	0.9217	32.41	0.9027	33.35	0.9385	39.46	0.9785
IPT [ 81 ]	$\times 2$	115M	38.37	-	34.43	-	32.48	-	33.76	-	-	-

TABLE IV: Quantitative comparison of different methods on the classic image super-resolution benchmark.

Model	Scale	#Param.	Set5		Set14		BSD100		Urban100		Manga109
Model	Scale	#Param.	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM
CARN [ 89 ]	$\times 2$	1,592K	37.76	0.9590	33.52	0.9166	32.09	0.8978	31.92	0.9256	38.36	0.9765
IMDN [ 90 ]	$\times 2$	694K	38.00	0.9605	33.63	0.9177	32.19	0.8996	32.17	0.9283	38.88	0.9774
LAPAR-A [ 91 ]	$\times 2$	548K	38.01	0.9605	33.62	0.9183	32.19	0.8999	32.10	0.9283	38.67	0.9772
LatticeNet [ 92 ]	$\times 2$	756K	38.13	0.9610	33.78	0.9193	32.25	0.9005	32.43	0.9302	-	-
SwinIR-light [ 53 ]	$\times 2$	910K	38.14	0.9611	33.86	0.9206	32.31	0.9012	32.76	0.9340	39.12	0.9783

TABLE V: Quantitative comparison of different methods on the lightweight image super-resolution benchmark.

Fig. 10: Visual comparison of image super-resolution results between MambaIR and EQ-MambaIR on Urban100 and Manga109 datasets.

Model	Image Classification		Semantic Segmentation
Model	Untrained	Trained	Untrained	Trained
VMamba-T [ 14 ]	0.1721	0.4404	0.3547	0.1958
EQ-VMamba-T	0.0003	0.0003	0.0004	0.0002
VMamba-S [ 14 ]	0.2017	0.1497	0.3617	0.1809
EQ-VMamba-S	0.0003	0.0003	0.0004	0.0002

TABLE VI: Average equivariance error of different models on

\mathrm{p}4

rotation group (NMSE

\downarrow

EQ-cross scan	EQ-VSS block	Scale	#Param.	Top-1 (%)	Top-5 (%)
✗	✗	Tiny	30M	87.80	97.70
✓	✗	Tiny	30M	87.88	97.54
✓	✓	Tiny	10M	88.58	98.14
✗	✗	Small	50M	88.32	97.82
✓	✗	Small	50M	87.76	97.70
✓	✓	Small	17M	88.70	98.22

TABLE VII: Ablation study on EQ-cross-scan and EQ-VSS block.

Mamba block type	Scale	#Param.	Top-1 (%)	Top-5 (%)
Independent Mamba block	Tiny	9M	87.98	97.96
Group Mamba block	Tiny	10M	88.58	98.14
Independent Mamba block	Small	15M	88.04	97.98
Group Mamba block	Small	17M	88.70	98.22

TABLE VIII: Ablation study on the group Mamba block.

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