# An Image Patch is a Wave: Phase-Aware Vision MLP

arXiv: https://arxiv.org/abs/2111.12294 · HTML: https://mlsanity.com/paper/2111.12294/

## Key facts

- Cited by 61 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 53 references that are in the map.
- First posted on arXiv 24 Nov 2021.

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

- [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)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [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)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [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)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [Pyramid Vision Transformer: A Versatile Backbone for Dense Prediction without Convolutions](https://mlsanity.com/paper/2102.12122/) (2021)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Tokens-to-Token ViT: Training Vision Transformers from Scratch on ImageNet](https://mlsanity.com/paper/2101.11986/) (2021)
- [Semantic Understanding of Scenes through the ADE20K Dataset](https://mlsanity.com/paper/1608.05442/) (2016)
- [Designing Network Design Spaces](https://mlsanity.com/paper/2003.13678/) (2020)
- [CrossViT: Cross-Attention Multi-Scale Vision Transformer for Image Classification](https://mlsanity.com/paper/2103.14899/) (2021)
- [Panoptic Feature Pyramid Networks](https://mlsanity.com/paper/1901.02446/) (2019)
- [Transformer in Transformer](https://mlsanity.com/paper/2103.00112/) (2021)
- [Pay Attention to MLPs](https://mlsanity.com/paper/2105.08050/) (2021)
- [Bottleneck Transformers for Visual Recognition](https://mlsanity.com/paper/2101.11605/) (2021)
- [Rethinking Spatial Dimensions of Vision Transformers](https://mlsanity.com/paper/2103.16302/) (2021)
- [ResMLP: Feedforward networks for image classification with data-efficient training](https://mlsanity.com/paper/2105.03404/) (2021)
- [Visual Transformers: Token-based Image Representation and Processing for Computer Vision](https://mlsanity.com/paper/2006.03677/) (2020)
- [CMT: Convolutional Neural Networks Meet Vision Transformers](https://mlsanity.com/paper/2107.06263/) (2021)
- [Global Filter Networks for Image Classification](https://mlsanity.com/paper/2107.00645/) (2021)
- [Rethinking and Improving Relative Position Encoding for Vision Transformer](https://mlsanity.com/paper/2107.14222/) (2021)
- [Patch Slimming for Efficient Vision Transformers](https://mlsanity.com/paper/2106.02852/) (2021)

## Built on by (most cited first, 30 of 61)

- [Focal Modulation Networks](https://mlsanity.com/paper/2203.11926/) (2022)
- [Vision GNN: An Image is Worth Graph of Nodes](https://mlsanity.com/paper/2206.00272/) (2022)
- [TSMixer: Lightweight MLP-Mixer Model for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2306.09364/) (2023)
- [SpectFormer: Frequency and Attention is what you need in a Vision Transformer](https://mlsanity.com/paper/2304.06446/) (2023)
- [A Survey on Transformer Compression](https://mlsanity.com/paper/2402.05964/) (2024)
- [GhostNetV2: Enhance Cheap Operation with Long-Range Attention](https://mlsanity.com/paper/2211.12905/) (2022)
- [BALF: Simple and Efficient Blur Aware Local Feature Detector](https://mlsanity.com/paper/2211.14731/) (2022)
- [Lightweight Vision Transformer with Bidirectional Interaction](https://mlsanity.com/paper/2306.00396/) (2023)
- [PointVector: A Vector Representation In Point Cloud Analysis](https://mlsanity.com/paper/2205.10528/) (2022)
- [BinaryViT: Pushing Binary Vision Transformers Towards Convolutional Models](https://mlsanity.com/paper/2306.16678/) (2023)
- [Scattering Vision Transformer: Spectral Mixing Matters](https://mlsanity.com/paper/2311.01310/) (2023)
- [PanGu-π: Enhancing Language Model Architectures via Nonlinearity Compensation](https://mlsanity.com/paper/2312.17276/) (2023)
- [Brain-inspired Multilayer Perceptron with Spiking Neurons](https://mlsanity.com/paper/2203.14679/) (2022)
- [SPANet: Frequency-balancing Token Mixer using Spectral Pooling Aggregation Modulation](https://mlsanity.com/paper/2308.11568/) (2023)
- [Strip-MLP: Efficient Token Interaction for Vision MLP](https://mlsanity.com/paper/2307.11458/) (2023)
- [Neural Clustering based Visual Representation Learning](https://mlsanity.com/paper/2403.17409/) (2024)
- [Synthetic Thermal and RGB Videos for Automatic Pain Assessment utilizing a Vision-MLP Architecture](https://mlsanity.com/paper/2407.19811/) (2024)
- [Diffusion-Inspired Quantum Noise Mitigation in Parameterized Quantum Circuits](https://mlsanity.com/paper/2406.00843/) (2024)
- [PainFormer: a Vision Foundation Model for Automatic Pain Assessment](https://mlsanity.com/paper/2505.01571/) (2025)
- [ParaFormer: Parallel Attention Transformer for Efficient Feature Matching](https://mlsanity.com/paper/2303.00941/) (2023)
- [C2F-TP: A Coarse-to-Fine Denoising Framework for Uncertainty-Aware Trajectory Prediction](https://mlsanity.com/paper/2412.13231/) (2024)
- [UCIP: A Universal Framework for Compressed Image Super-Resolution using Dynamic Prompt](https://mlsanity.com/paper/2407.13108/) (2024)
- [ParameterNet: Parameters Are All You Need](https://mlsanity.com/paper/2306.14525/) (2023)
- [Quantum-Brain: Quantum-Inspired Neural Network Approach to Vision-Brain Understanding](https://mlsanity.com/paper/2411.13378/) (2024)
- [Mixing and Shifting: Exploiting Global and Local Dependencies in Vision MLPs](https://mlsanity.com/paper/2202.06510/) (2022)
- [Active Token Mixer](https://mlsanity.com/paper/2203.06108/) (2022)
- [Efficiency 360: Efficient Vision Transformers](https://mlsanity.com/paper/2302.08374/) (2023)
- [ClusterViG: Efficient Globally Aware Vision GNNs via Image Partitioning](https://mlsanity.com/paper/2501.10640/) (2025)
- [Heracles: A Hybrid SSM-Transformer Model for High-Resolution Image and Time-Series Analysis](https://mlsanity.com/paper/2403.18063/) (2024)
- [Caterpillar: A Pure-MLP Architecture with Shifted-Pillars-Concatenation](https://mlsanity.com/paper/2305.17644/) (2023)

## Abstract (arXiv)

In the field of computer vision, recent works show that a pure MLP architecture mainly stacked by fully-connected layers can achieve competing performance with CNN and transformer. An input image of vision MLP is usually split into multiple tokens (patches), while the existing MLP models directly aggregate them with fixed weights, neglecting the varying semantic information of tokens from different images. To dynamically aggregate tokens, we propose to represent each token as a wave function with two parts, amplitude and phase. Amplitude is the original feature and the phase term is a complex value changing according to the semantic contents of input images. Introducing the phase term can dynamically modulate the relationship between tokens and fixed weights in MLP. Based on the wave-like token representation, we establish a novel Wave-MLP architecture for vision tasks. Extensive experiments demonstrate that the proposed Wave-MLP is superior to the state-of-the-art MLP architectures on various vision tasks such as image classification, object detection and semantic segmentation. The source code is available at https://github.com/huawei-noah/CV-Backbones/tree/master/wavemlp_pytorch and https://gitee.com/mindspore/models/tree/master/research/cv/wave_mlp.