# Rethinking Multi-domain Generalization with A General Learning Objective

arXiv: https://arxiv.org/abs/2402.18853 · HTML: https://mlsanity.com/paper/2402.18853/

## Key facts

- Cited by 23 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 29 Feb 2024.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [BDD100K: A Diverse Driving Dataset for Heterogeneous Multitask Learning](https://mlsanity.com/paper/1805.04687/) (2018)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [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)
- [Playing for Data: Ground Truth from Computer Games](https://mlsanity.com/paper/1608.02192/) (2016)
- [Generalizing to Unseen Domains: A Survey on Domain Generalization](https://mlsanity.com/paper/2103.03097/) (2021)
- [Domain Generalization: A Survey](https://mlsanity.com/paper/2103.02503/) (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 with MixStyle](https://mlsanity.com/paper/2104.02008/) (2021)
- [SWAD: Domain Generalization by Seeking Flat Minima](https://mlsanity.com/paper/2102.08604/) (2021)
- [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)
- [Gradient Matching for Domain Generalization](https://mlsanity.com/paper/2104.09937/) (2021)
- [RobustNet: Improving Domain Generalization in Urban-Scene Segmentation via Instance Selective Whitening](https://mlsanity.com/paper/2103.15597/) (2021)
- [SelfReg: Self-supervised Contrastive Regularization for Domain Generalization](https://mlsanity.com/paper/2104.09841/) (2021)
- [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)
- [Diverse Weight Averaging for Out-of-Distribution Generalization](https://mlsanity.com/paper/2205.09739/) (2022)
- [Domain Generalization via Conditional Invariant Representation](https://mlsanity.com/paper/1807.08479/) (2018)
- [Domain Generalization by Mutual-Information Regularization with Pre-trained Models](https://mlsanity.com/paper/2203.10789/) (2022)

## Built on by (most cited first, 23 of 23)

- [DGMamba: Domain Generalization via Generalized State Space Model](https://mlsanity.com/paper/2404.07794/) (2024)
- [Handling Out-of-Distribution Data: A Survey](https://mlsanity.com/paper/2507.21160/) (2025)
- [Prompt Disentanglement via Language Guidance and Representation Alignment for Domain Generalization](https://mlsanity.com/paper/2507.02288/) (2025)
- [Hybrid-TTA: Continual Test-time Adaptation via Dynamic Domain Shift Detection](https://mlsanity.com/paper/2409.08566/) (2024)
- [MedMAP: Promoting Incomplete Multi-modal Brain Tumor Segmentation with Alignment](https://mlsanity.com/paper/2408.09465/) (2024)
- [START: A Generalized State Space Model with Saliency-Driven Token-Aware Transformation](https://mlsanity.com/paper/2410.16020/) (2024)
- [Adversarial Domain Prompt Tuning and Generation for Single Domain Generalization](https://mlsanity.com/paper/2606.21736/) (2026)
- [Towards a Universal 3D Medical Multi-modality Generalization via Learning Personalized Invariant Representation](https://mlsanity.com/paper/2411.06106/) (2024)
- [Domain Generalization via Discrete Codebook Learning](https://mlsanity.com/paper/2504.06572/) (2025)
- [Covariance-based Space Regularization for Few-shot Class Incremental Learning](https://mlsanity.com/paper/2411.01172/) (2024)
- [Meta Curvature-Aware Minimization for Domain Generalization](https://mlsanity.com/paper/2412.11542/) (2024)
- [DGFamba: Learning Flow Factorized State Space for Visual Domain Generalization](https://mlsanity.com/paper/2504.08019/) (2025)
- [CPCANet: Deep Unfolding Common Principal Component Analysis for Domain Generalization](https://mlsanity.com/paper/2605.05136/) (2026)
- [Stain-aware Domain Alignment for Imbalance Blood Cell Classification](https://mlsanity.com/paper/2412.02976/) (2024)
- [Generative Classifier for Domain Generalization](https://mlsanity.com/paper/2504.02272/) (2025)
- [FedSDAF: Leveraging Source Domain Awareness for Enhanced Federated Domain Generalization](https://mlsanity.com/paper/2505.02515/) (2025)
- [Should Bias be Eliminated? A General Framework to Use Bias for OOD Generalization](https://mlsanity.com/paper/2507.17001/) (2025)
- [DSP-Reg: Domain-Sensitive Parameter Regularization for Robust Domain Generalization](https://mlsanity.com/paper/2601.19394/) (2026)
- [Robust Domain Generalization under Divergent Marginal and Conditional Distributions](https://mlsanity.com/paper/2602.02015/) (2026)
- [CrossFlowDG: Bridging the Modality Gap with Cross-modal Flow Matching for Domain Generalization](https://mlsanity.com/paper/2604.16892/) (2026)
- [Projection Pursuit CPCANet for Domain Generalization](https://mlsanity.com/paper/2607.22117/) (2026)
- [PatchGen: Learning Soft Intra-Image Predictive Subsets for Visual Generalization](https://mlsanity.com/paper/2608.12766/) (2026)
- [PAPT++: Risk-Aware Adversarial Tuning and Generation for Single Domain Generalization](https://mlsanity.com/paper/2609.04837/) (2026)

## Abstract (arXiv)

Multi-domain generalization (mDG) is universally aimed to minimize the discrepancy between training and testing distributions to enhance marginal-to-label distribution mapping. However, existing mDG literature lacks a general learning objective paradigm and often imposes constraints on static target marginal distributions. In this paper, we propose to leverage a Y-mapping to relax the constraint. We rethink the learning objective for mDG and design a new general learning objective to interpret and analyze most existing mDG wisdom. This general objective is bifurcated into two synergistic amis: learning domain-independent conditional features and maximizing a posterior. Explorations also extend to two effective regularization terms that incorporate prior information and suppress invalid causality, alleviating the issues that come with relaxed constraints. We theoretically contribute an upper bound for the domain alignment of domain-independent conditional features, disclosing that many previous mDG endeavors actually optimize partially the objective and thus lead to limited performance. As such, our study distills a general learning objective into four practical components, providing a general, robust, and flexible mechanism to handle complex domain shifts. Extensive empirical results indicate that the proposed objective with Y-mapping leads to substantially better mDG performance in various downstream tasks, including regression, segmentation, and classification.