# WaveFormer: Frequency-Time Decoupled Vision Modeling with Wave Equation

arXiv: https://arxiv.org/abs/2601.08602 · HTML: https://mlsanity.com/paper/2601.08602/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 45 references that are in the map.
- First posted on arXiv 13 Jan 2026.

## Builds on (most cited first, 26 of 26)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (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)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [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)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [Designing Network Design Spaces](https://mlsanity.com/paper/2003.13678/) (2020)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [CrossViT: Cross-Attention Multi-Scale Vision Transformer for Image Classification](https://mlsanity.com/paper/2103.14899/) (2021)
- [Understanding the Effective Receptive Field in Deep Convolutional Neural Networks](https://mlsanity.com/paper/1701.04128/) (2017)
- [InternImage: Exploring Large-Scale Vision Foundation Models with Deformable Convolutions](https://mlsanity.com/paper/2211.05778/) (2022)
- [BEiT v2: Masked Image Modeling with Vector-Quantized Visual Tokenizers](https://mlsanity.com/paper/2208.06366/) (2022)
- [Focal Self-attention for Local-Global Interactions in Vision Transformers](https://mlsanity.com/paper/2107.00641/) (2021)
- [Deep Learning in Spiking Neural Networks](https://mlsanity.com/paper/1804.08150/) (2018)
- [Training Deep Spiking Neural Networks using Backpropagation](https://mlsanity.com/paper/1608.08782/) (2016)
- [Selective Structured State-Spaces for Long-Form Video Understanding](https://mlsanity.com/paper/2303.14526/) (2023)
- [Building Vision Models upon Heat Conduction](https://mlsanity.com/paper/2405.16555/) (2024)
- [Self-Supervised Learning based on Heat Equation](https://mlsanity.com/paper/2211.13228/) (2022)

## Built on by (most cited first, 5 of 5)

- [CP-WSP: A Declarative CP-SAT Framework for Configurable Multi-Constraint Workforce Scheduling](https://mlsanity.com/paper/2607.05177/) (2026)
- [PS-MOT: Cultivating Instance Awareness from Point Seeds for Multi-Object Tracking](https://mlsanity.com/paper/2606.30476/) (2026)
- [WaveFreqAnchor: Wave-Structural Anchoring and Frequency Correction Diffusion for Training-Free Face Restoration](https://mlsanity.com/paper/2608.06717/) (2026)
- [SpecF2M: A Spectral-Aware Multi-task Network Estimating Axial Length and Refractive Error from Pediatric Fundus Photographs](https://mlsanity.com/paper/2608.09994/) (2026)
- [TailProp: content-adaptive light- and heavy-tailed propagation for vision](https://mlsanity.com/paper/2609.11081/) (2026)

## Abstract (arXiv)

Vision modeling has advanced rapidly with Transformers, whose attention mechanisms capture visual dependencies but lack a principled account of how semantic information propagates spatially. We revisit this problem from a wave-based perspective: feature maps are treated as spatial signals whose evolution over an internal propagation time (aligned with network depth) is governed by an underdamped wave equation. In this formulation, spatial frequency-from low-frequency global layout to high-frequency edges and textures-is modeled explicitly, and its interaction with propagation time is controlled rather than implicitly fixed. We derive a closed-form, frequency-time decoupled solution and implement it as the Wave Propagation Operator (WPO), a lightweight module that models global interactions in O(N log N) time-far lower than attention. Building on WPO, we propose a family of WaveFormer models as drop-in replacements for standard ViTs and CNNs, achieving competitive accuracy across image classification, object detection, and semantic segmentation, while delivering up to 1.6x higher throughput and 30% fewer FLOPs than attention-based alternatives. Furthermore, our results demonstrate that wave propagation introduces a complementary modeling bias to heat-based methods, effectively capturing both global coherence and high-frequency details essential for rich visual semantics. Codes are available at: https://github.com/ZishanShu/WaveFormer.