# Domain Adaptation with Cauchy-Schwarz Divergence

arXiv: https://arxiv.org/abs/2405.19978 · HTML: https://mlsanity.com/paper/2405.19978/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 72 references that are in the map.
- First posted on arXiv 30 May 2024.

## Builds on (most cited first, 30 of 34)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Learning Transferable Features with Deep Adaptation Networks](https://mlsanity.com/paper/1502.02791/) (2015)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [Do We Really Need to Access the Source Data? Source Hypothesis Transfer for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2002.08546/) (2020)
- [Maximum Classifier Discrepancy for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1712.02560/) (2017)
- [Deep Transfer Learning with Joint Adaptation Networks](https://mlsanity.com/paper/1605.06636/) (2016)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [VisDA: The Visual Domain Adaptation Challenge](https://mlsanity.com/paper/1710.06924/) (2017)
- [Bridging Theory and Algorithm for Domain Adaptation](https://mlsanity.com/paper/1904.05801/) (2019)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [Generate To Adapt: Aligning Domains using Generative Adversarial Networks](https://mlsanity.com/paper/1704.01705/) (2017)
- [Unbalanced minibatch Optimal Transport; applications to Domain Adaptation](https://mlsanity.com/paper/2103.03606/) (2021)
- [Visual Domain Adaptation with Manifold Embedded Distribution Alignment](https://mlsanity.com/paper/1807.07258/) (2018)
- [Cross-Domain Gradient Discrepancy Minimization for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2106.04151/) (2021)
- [Implicit Class-Conditioned Domain Alignment for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2006.04996/) (2020)
- [Domain Invariant Representation Learning with Domain Density Transformations](https://mlsanity.com/paper/2102.05082/) (2021)
- [f-Domain-Adversarial Learning: Theory and Algorithms](https://mlsanity.com/paper/2106.11344/) (2021)
- [Robust Learning with the Hilbert-Schmidt Independence Criterion](https://mlsanity.com/paper/1910.00270/) (2019)
- [KL Guided Domain Adaptation](https://mlsanity.com/paper/2106.07780/) (2021)
- [Conditional Bures Metric for Domain Adaptation](https://mlsanity.com/paper/2108.00302/) (2021)
- [Conditional Generative Moment-Matching Networks](https://mlsanity.com/paper/1606.04218/) (2016)
- [Prior Knowledge Guided Unsupervised Domain Adaptation](https://mlsanity.com/paper/2207.08877/) (2022)
- [Discriminative Joint Probability Maximum Mean Discrepancy (DJP-MMD) for Domain Adaptation](https://mlsanity.com/paper/1912.00320/) (2019)

## Built on by (most cited first, 6 of 6)

- [Distributional Vision-Language Alignment by Cauchy-Schwarz Divergence](https://mlsanity.com/paper/2502.17028/) (2025)
- [DreamCS: Geometry-Aware Text-to-3D Generation with Unpaired 3D Reward Supervision](https://mlsanity.com/paper/2506.09814/) (2025)
- [Dual-branch Graph Domain Adaptation for Cross-scenario Multi-modal Emotion Recognition](https://mlsanity.com/paper/2603.26840/) (2026)
- [Rethinking Cross-Modal Fine-Tuning: Optimizing the Interaction Between Feature Alignment and Target Fitting](https://mlsanity.com/paper/2601.18231/) (2026)
- [Brain foundation model-guided source-selective domain adaptation for cross-subject EEG decoding](https://mlsanity.com/paper/2507.21037/) (2025)
- [Cross-Modal Retrieval with Cauchy-Schwarz Divergence](https://mlsanity.com/paper/2509.21339/) (2025)

## Abstract (arXiv)

Domain adaptation aims to use training data from one or multiple source domains to learn a hypothesis that can be generalized to a different, but related, target domain. As such, having a reliable measure for evaluating the discrepancy of both marginal and conditional distributions is crucial. We introduce Cauchy-Schwarz (CS) divergence to the problem of unsupervised domain adaptation (UDA). The CS divergence offers a theoretically tighter generalization error bound than the popular Kullback-Leibler divergence. This holds for the general case of supervised learning, including multi-class classification and regression. Furthermore, we illustrate that the CS divergence enables a simple estimator on the discrepancy of both marginal and conditional distributions between source and target domains in the representation space, without requiring any distributional assumptions. We provide multiple examples to illustrate how the CS divergence can be conveniently used in both distance metric- or adversarial training-based UDA frameworks, resulting in compelling performance.