dorsal/arxiv
View SchemaWaveFormer: Frequency-Time Decoupled Vision Modeling with Wave Equation
| Authors | Zishan Shu, Juntong Wu, Wei Yan, Xudong Liu, Hongyu Zhang, Chang Liu, Youdong Mao, Jie Chen |
|---|---|
| Categories | |
| ArXiv ID | 2601.08602vv1 |
| URL | https://arxiv.org/abs/2601.08602 |
| License | http://creativecommons.org/licenses/by/4.0/ |
Abstract
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.
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"abstract": "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.",
"arxiv_id": "2601.08602",
"authors": [
"Zishan Shu",
"Juntong Wu",
"Wei Yan",
"Xudong Liu",
"Hongyu Zhang",
"Chang Liu",
"Youdong Mao",
"Jie Chen"
],
"categories": [
"cs.CV",
"cs.AI"
],
"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "WaveFormer: Frequency-Time Decoupled Vision Modeling with Wave Equation",
"url": "https://arxiv.org/abs/2601.08602",
"version": "v1"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "b8b6c4f8-546e-4b62-8501-69163c85d886",
"id": "arXiv Dataset",
"type": "Model",
"variant": "snapshot-2026-01-17",
"version": "0.1.0"
},
"user_id": 1000002
}