# Decompose, Adjust, Compose: Effective Normalization by Playing with Frequency for Domain Generalization

arXiv: https://arxiv.org/abs/2303.02328 · HTML: https://mlsanity.com/paper/2303.02328/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 57 references that are in the map.
- First posted on arXiv 4 Mar 2023.

## Builds on (most cited first, 30 of 40)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Arbitrary Style Transfer in Real-time with Adaptive Instance Normalization](https://mlsanity.com/paper/1703.06868/) (2017)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [Generalizing to Unseen Domains: A Survey on Domain Generalization](https://mlsanity.com/paper/2103.03097/) (2021)
- [Learning to Generalize: Meta-Learning for Domain Generalization](https://mlsanity.com/paper/1710.03463/) (2017)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Recognition in Terra Incognita](https://mlsanity.com/paper/1807.04975/) (2018)
- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [Domain Generalization with MixStyle](https://mlsanity.com/paper/2104.02008/) (2021)
- [FDA: Fourier Domain Adaptation for Semantic Segmentation](https://mlsanity.com/paper/2004.05498/) (2020)
- [Self-Challenging Improves Cross-Domain Generalization](https://mlsanity.com/paper/2007.02454/) (2020)
- [Two at Once: Enhancing Learning and Generalization Capacities via IBN-Net](https://mlsanity.com/paper/1807.09441/) (2018)
- [High Frequency Component Helps Explain the Generalization of Convolutional Neural Networks](https://mlsanity.com/paper/1905.13545/) (2019)
- [A Fourier-based Framework for Domain Generalization](https://mlsanity.com/paper/2105.11120/) (2021)
- [SelfReg: Self-supervised Contrastive Regularization for Domain Generalization](https://mlsanity.com/paper/2104.09841/) (2021)
- [Fishr: Invariant Gradient Variances for Out-of-Distribution Generalization](https://mlsanity.com/paper/2109.02934/) (2021)
- [Improve Unsupervised Domain Adaptation with Mixup Training](https://mlsanity.com/paper/2001.00677/) (2020)
- [Adaptive Risk Minimization: Learning to Adapt to Domain Shift](https://mlsanity.com/paper/2007.02931/) (2020)
- [Domain Generalization by Marginal Transfer Learning](https://mlsanity.com/paper/1711.07910/) (2017)
- [Domain Generalization Using a Mixture of Multiple Latent Domains](https://mlsanity.com/paper/1911.07661/) (2019)
- [Style Normalization and Restitution for Generalizable Person Re-identification](https://mlsanity.com/paper/2005.11037/) (2020)

## Built on by (most cited first, 26 of 26)

- [Learning Spectral-Decomposed Tokens for Domain Generalized Semantic Segmentation](https://mlsanity.com/paper/2407.18568/) (2024)
- [DomainDrop: Suppressing Domain-Sensitive Channels for Domain Generalization](https://mlsanity.com/paper/2308.10285/) (2023)
- [Diversifying Spatial-Temporal Perception for Video Domain Generalization](https://mlsanity.com/paper/2310.17942/) (2023)
- [Lightweight Frequency Masker for Cross-Domain Few-Shot Semantic Segmentation](https://mlsanity.com/paper/2410.22135/) (2024)
- [PracticalDG: Perturbation Distillation on Vision-Language Models for Hybrid Domain Generalization](https://mlsanity.com/paper/2404.09011/) (2024)
- [CLIP-Powered Domain Generalization and Domain Adaptation: A Comprehensive Survey](https://mlsanity.com/paper/2504.14280/) (2025)
- [Causality-inspired Discriminative Feature Learning in Triple Domains for Gait Recognition](https://mlsanity.com/paper/2407.12519/) (2024)
- [Generalization Boosted Adapter for Open-Vocabulary Segmentation](https://mlsanity.com/paper/2409.08468/) (2024)
- [Direct Distillation between Different Domains](https://mlsanity.com/paper/2401.06826/) (2024)
- [Learning Generalizable Models via Disentangling Spurious and Enhancing Potential Correlations](https://mlsanity.com/paper/2401.05752/) (2024)
- [INSURE: An Information Theory Inspired Disentanglement and Purification Model for Domain Generalization](https://mlsanity.com/paper/2309.04063/) (2023)
- [Domain-invariant Progressive Knowledge Distillation for UAV-based Object Detection](https://mlsanity.com/paper/2408.11407/) (2024)
- [Frequency Domain Modality-invariant Feature Learning for Visible-infrared Person Re-Identification](https://mlsanity.com/paper/2401.01839/) (2024)
- [SETA: Semantic-Aware Token Augmentation for Domain Generalization](https://mlsanity.com/paper/2403.11792/) (2024)
- [Divide, Conquer and Unite: Hierarchical Style-Recalibrated Prototype Alignment for Federated Medical Segmentation](https://mlsanity.com/paper/2511.10945/) (2025)
- [ED-SAM: An Efficient Diffusion Sampling Approach to Domain Generalization in Vision-Language Foundation Models](https://mlsanity.com/paper/2406.01432/) (2024)
- [PAD: Phase-Amplitude Decoupling Fusion for Multi-Modal Land Cover Classification](https://mlsanity.com/paper/2504.19136/) (2025)
- [PAID: Pairwise Angular-Invariant Decomposition for Continual Test-Time Adaptation](https://mlsanity.com/paper/2506.02453/) (2025)
- [FSG-Net: Frequency-Spatial Synergistic Gated Network for High-Resolution Remote Sensing Change Detection](https://mlsanity.com/paper/2509.06482/) (2025)
- [Multi-Granularity Feature Calibration via VFM for Domain Generalized Semantic Segmentation](https://mlsanity.com/paper/2508.03007/) (2025)
- [Towards Principled Dataset Distillation: A Spectral Distribution Perspective](https://mlsanity.com/paper/2603.01698/) (2026)
- [Dual Feature Decoupling for Fine-Grained OOD Detection](https://mlsanity.com/paper/2606.05536/) (2026)
- [A Sliced-Wasserstein Framework on Correlation Matrices for EEG Decoding](https://mlsanity.com/paper/2606.06104/) (2026)
- [Cross-Species Animal Re-Identification with Semantic Consistency Learning](https://mlsanity.com/paper/2609.09705/) (2026)
- [PhaseAT: Fourier Phase Adversarial Training for Medical Image Domain Generalization](https://mlsanity.com/paper/2610.01807/) (2026)
- [Decouple, Purify and Unite: Semantic-Structural Prototype Learning for Federated Medical Segmentation](https://mlsanity.com/paper/2610.04700/) (2026)

## Abstract (arXiv)

Domain generalization (DG) is a principal task to evaluate the robustness of computer vision models. Many previous studies have used normalization for DG. In normalization, statistics and normalized features are regarded as style and content, respectively. However, it has a content variation problem when removing style because the boundary between content and style is unclear. This study addresses this problem from the frequency domain perspective, where amplitude and phase are considered as style and content, respectively. First, we verify the quantitative phase variation of normalization through the mathematical derivation of the Fourier transform formula. Then, based on this, we propose a novel normalization method, PCNorm, which eliminates style only as the preserving content through spectral decomposition. Furthermore, we propose advanced PCNorm variants, CCNorm and SCNorm, which adjust the degrees of variations in content and style, respectively. Thus, they can learn domain-agnostic representations for DG. With the normalization methods, we propose ResNet-variant models, DAC-P and DAC-SC, which are robust to the domain gap. The proposed models outperform other recent DG methods. The DAC-SC achieves an average state-of-the-art performance of 65.6% on five datasets: PACS, VLCS, Office-Home, DomainNet, and TerraIncognita.