# Spectral State Space Model for Rotation-Invariant Visual Representation Learning

arXiv: https://arxiv.org/abs/2503.06369 · HTML: https://mlsanity.com/paper/2503.06369/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 46 references that are in the map.
- First posted on arXiv 9 Mar 2025.

## Builds on (most cited first, 30 of 36)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Semantic Understanding of Scenes through the ADE20K Dataset](https://mlsanity.com/paper/1608.05442/) (2016)
- [Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Model](https://mlsanity.com/paper/2401.09417/) (2024)
- [VMamba: Visual State Space Model](https://mlsanity.com/paper/2401.10166/) (2024)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [Combining Recurrent, Convolutional, and Continuous-time Models with Linear State-Space Layers](https://mlsanity.com/paper/2110.13985/) (2021)
- [Hungry Hungry Hippos: Towards Language Modeling with State Space Models](https://mlsanity.com/paper/2212.14052/) (2022)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [U-Mamba: Enhancing Long-range Dependency for Biomedical Image Segmentation](https://mlsanity.com/paper/2401.04722/) (2024)
- [XCiT: Cross-Covariance Image Transformers](https://mlsanity.com/paper/2106.09681/) (2021)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Long Range Language Modeling via Gated State Spaces](https://mlsanity.com/paper/2206.13947/) (2022)
- [LocalMamba: Visual State Space Model with Windowed Selective Scan](https://mlsanity.com/paper/2403.09338/) (2024)
- [MambaVision: A Hybrid Mamba-Transformer Vision Backbone](https://mlsanity.com/paper/2407.08083/) (2024)
- [Learning Steerable Filters for Rotation Equivariant CNNs](https://mlsanity.com/paper/1711.07289/) (2017)
- [Frame Averaging for Invariant and Equivariant Network Design](https://mlsanity.com/paper/2110.03336/) (2021)

## Built on by (most cited first, 4 of 4)

- [Purge-Gate: Backpropagation-Free Test-Time Adaptation for Point Clouds Classification via Token Purging](https://mlsanity.com/paper/2509.09785/) (2025)
- [OCTOPUS: Enhancing the Spatial-Awareness of Vision SSMs with Multi-Dimensional Scans and Traversal Selection](https://mlsanity.com/paper/2602.00904/) (2026)
- [Rotation Equivariant Mamba for Vision Tasks](https://mlsanity.com/paper/2603.09138/) (2026)
- [TRUST: Test-Time Refinement using Uncertainty-Guided SSM Traverses](https://mlsanity.com/paper/2509.22813/) (2025)

## Abstract (arXiv)

State Space Models (SSMs) have recently emerged as an alternative to Vision Transformers (ViTs) due to their unique ability of modeling global relationships with linear complexity. SSMs are specifically designed to capture spatially proximate relationships of image patches. However, they fail to identify relationships between conceptually related yet not adjacent patches. This limitation arises from the non-causal nature of image data, which lacks inherent directional relationships. Additionally, current vision-based SSMs are highly sensitive to transformations such as rotation. Their predefined scanning directions depend on the original image orientation, which can cause the model to produce inconsistent patch-processing sequences after rotation. To address these limitations, we introduce Spectral VMamba, a novel approach that effectively captures the global structure within an image by leveraging spectral information derived from the graph Laplacian of image patches. Through spectral decomposition, our approach encodes patch relationships independently of image orientation, achieving rotation invariance with the aid of our Rotational Feature Normalizer (RFN) module. Our experiments on classification tasks show that Spectral VMamba outperforms the leading SSM models in vision, such as VMamba, while maintaining invariance to rotations and a providing a similar runtime efficiency.