# Vim-F: Visual State Space Model Benefiting from Learning in the Frequency Domain

arXiv: https://arxiv.org/abs/2405.18679 · HTML: https://mlsanity.com/paper/2405.18679/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Vision Mamba backbones, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 38 of its 39 references that are in the map.
- First posted on arXiv 29 May 2024.

## Placed in

- State-space sequence models (S4, Mamba) / [Vision Mamba backbones](https://mlsanity.com/ssm/vision-mamba-backbones/)

## Builds on (most cited first, 30 of 38)

- [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)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [Unified Perceptual Parsing for Scene Understanding](https://mlsanity.com/paper/1807.10221/) (2018)
- [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)
- [Designing Network Design Spaces](https://mlsanity.com/paper/2003.13678/) (2020)
- [PVT v2: Improved Baselines with Pyramid Vision Transformer](https://mlsanity.com/paper/2106.13797/) (2021)
- [MobileViT: Light-weight, General-purpose, and Mobile-friendly Vision Transformer](https://mlsanity.com/paper/2110.02178/) (2021)
- [CoAtNet: Marrying Convolution and Attention for All Data Sizes](https://mlsanity.com/paper/2106.04803/) (2021)
- [Bottleneck Transformers for Visual Recognition](https://mlsanity.com/paper/2101.11605/) (2021)
- [Diagonal State Spaces are as Effective as Structured State Spaces](https://mlsanity.com/paper/2203.14343/) (2022)
- [FNet: Mixing Tokens with Fourier Transforms](https://mlsanity.com/paper/2105.03824/) (2021)
- [VM-UNet: Vision Mamba UNet for Medical Image Segmentation](https://mlsanity.com/paper/2402.02491/) (2024)
- [Long Range Language Modeling via Gated State Spaces](https://mlsanity.com/paper/2206.13947/) (2022)
- [Global Filter Networks for Image Classification](https://mlsanity.com/paper/2107.00645/) (2021)
- [EfficientFormer: Vision Transformers at MobileNet Speed](https://mlsanity.com/paper/2206.01191/) (2022)
- [LocalMamba: Visual State Space Model with Windowed Selective Scan](https://mlsanity.com/paper/2403.09338/) (2024)
- [EfficientVMamba: Atrous Selective Scan for Light Weight Visual Mamba](https://mlsanity.com/paper/2403.09977/) (2024)

## Built on by (most cited first, 8 of 8)

- [Mamba in Vision: A Comprehensive Survey of Techniques and Applications](https://mlsanity.com/paper/2410.03105/) (2024)
- [Vision Mamba in Remote Sensing: A Comprehensive Survey of Techniques, Applications and Outlook](https://mlsanity.com/paper/2505.00630/) (2025)
- [HAMSA: Scanning-Free Vision State Space Models via SpectralPulseNet](https://mlsanity.com/paper/2604.14724/) (2026)
- [UHKD: A Unified Framework for Heterogeneous Knowledge Distillation via Frequency-Domain Representations](https://mlsanity.com/paper/2510.24116/) (2025)
- [Caracal: Causal Architecture via Spectral Mixing](https://mlsanity.com/paper/2605.00292/) (2026)
- [Stochastic Layer-Wise Shuffle for Improving Vision Mamba Training](https://mlsanity.com/paper/2408.17081/) (2024)
- [TCP-SSM: Efficient Vision State Space Models with Token-Conditioned Poles](https://mlsanity.com/paper/2605.11563/) (2026)
- [Can Visual Mamba Improve AI-Generated Image Detection? An In-Depth Investigation](https://mlsanity.com/paper/2605.14799/) (2026)

## Abstract (arXiv)

In recent years, State Space Models (SSMs) with efficient hardware-aware designs, known as the Mamba deep learning models, have made significant progress in modeling long sequences such as language understanding. Therefore, building efficient and general-purpose visual backbones based on SSMs is a promising direction. Compared to traditional convolutional neural networks (CNNs) and Vision Transformers (ViTs), the performance of Vision Mamba (ViM) methods is not yet fully competitive. To enable SSMs to process image data, ViMs typically flatten 2D images into 1D sequences, inevitably ignoring some 2D local dependencies, thereby weakening the model's ability to interpret spatial relationships from a global perspective. We use Fast Fourier Transform (FFT) to obtain the spectrum of the feature map and add it to the original feature map, enabling ViM to model a unified visual representation in both frequency and spatial domains. The introduction of frequency domain information enables ViM to have a global receptive field during scanning. We propose a novel model called Vim-F, which employs pure Mamba encoders and scans in both the frequency and spatial domains. Moreover, we question the necessity of position embedding in ViM and remove it accordingly in Vim-F, which helps to fully utilize the efficient long-sequence modeling capability of ViM. Finally, we redesign a patch embedding for Vim-F, leveraging a convolutional stem to capture more local correlations, further improving the performance of Vim-F. Code is available at: https://github.com/yws-wxs/Vim-F.