# Energy-Based Test Sample Adaptation for Domain Generalization

arXiv: https://arxiv.org/abs/2302.11215 · HTML: https://mlsanity.com/paper/2302.11215/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 63 of its 91 references that are in the map.
- First posted on arXiv 22 Feb 2023.

## Builds on (most cited first, 30 of 63)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [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)
- [AugMix: A Simple Data Processing Method to Improve Robustness and Uncertainty](https://mlsanity.com/paper/1912.02781/) (2019)
- [Do We Really Need to Access the Source Data? Source Hypothesis Transfer for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2002.08546/) (2020)
- [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)
- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [Domain Generalization with MixStyle](https://mlsanity.com/paper/2104.02008/) (2021)
- [Generalizing to Unseen Domains via Adversarial Data Augmentation](https://mlsanity.com/paper/1805.12018/) (2018)
- [SWAD: Domain Generalization by Seeking Flat Minima](https://mlsanity.com/paper/2102.08604/) (2021)
- [Domain Generalization via Model-Agnostic Learning of Semantic Features](https://mlsanity.com/paper/1910.13580/) (2019)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [Unified Deep Supervised Domain Adaptation and Generalization](https://mlsanity.com/paper/1709.10190/) (2017)
- [Learning to Learn Single Domain Generalization](https://mlsanity.com/paper/2003.13216/) (2020)
- [Learning to Generate Novel Domains for Domain Generalization](https://mlsanity.com/paper/2007.03304/) (2020)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [Generalizing Across Domains via Cross-Gradient Training](https://mlsanity.com/paper/1804.10745/) (2018)
- [Gradient Matching for Domain Generalization](https://mlsanity.com/paper/2104.09937/) (2021)
- [Domain Generalization using Causal Matching](https://mlsanity.com/paper/2006.07500/) (2020)
- [Invariance Principle Meets Information Bottleneck for Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.06607/) (2021)

## Built on by (most cited first, 14 of 14)

- [A Comprehensive Survey on Test-Time Adaptation under Distribution Shifts](https://mlsanity.com/paper/2303.15361/) (2023)
- [DPCore: Dynamic Prompt Coreset for Continual Test-Time Adaptation](https://mlsanity.com/paper/2406.10737/) (2024)
- [TEA: Test-time Energy Adaptation](https://mlsanity.com/paper/2311.14402/) (2023)
- [What, How, and When Should Object Detectors Update in Continually Changing Test Domains?](https://mlsanity.com/paper/2312.08875/) (2023)
- [Robust Fast Adaptation from Adversarially Explicit Task Distribution Generation](https://mlsanity.com/paper/2407.19523/) (2024)
- [A Simple Yet Effective Strategy to Robustify the Meta Learning Paradigm](https://mlsanity.com/paper/2310.00708/) (2023)
- [Shadow Removal Refinement via Material-Consistent Shadow Edges](https://mlsanity.com/paper/2409.06848/) (2024)
- [Probabilistic Test-Time Generalization by Variational Neighbor-Labeling](https://mlsanity.com/paper/2307.04033/) (2023)
- [Gradual Domain Adaptation via Manifold-Constrained Distributionally Robust Optimization](https://mlsanity.com/paper/2410.14061/) (2024)
- [GeneralizeFormer: Layer-Adaptive Model Generation across Test-Time Distribution Shifts](https://mlsanity.com/paper/2502.12195/) (2025)
- [MITA: Bridging the Gap between Model and Data for Test-time Adaptation](https://mlsanity.com/paper/2410.09398/) (2024)
- [LangDAug: Langevin Data Augmentation for Multi-Source Domain Generalization in Medical Image Segmentation](https://mlsanity.com/paper/2505.19659/) (2025)
- [Hierarchical Adaptive networks with Task vectors for Test-Time Adaptation](https://mlsanity.com/paper/2508.09223/) (2025)
- [The Mean is the Mirage: Entropy-Adaptive Model Merging under Heterogeneous Domain Shifts in Medical Imaging](https://mlsanity.com/paper/2602.21372/) (2026)

## Abstract (arXiv)

In this paper, we propose energy-based sample adaptation at test time for domain generalization. Where previous works adapt their models to target domains, we adapt the unseen target samples to source-trained models. To this end, we design a discriminative energy-based model, which is trained on source domains to jointly model the conditional distribution for classification and data distribution for sample adaptation. The model is optimized to simultaneously learn a classifier and an energy function. To adapt target samples to source distributions, we iteratively update the samples by energy minimization with stochastic gradient Langevin dynamics. Moreover, to preserve the categorical information in the sample during adaptation, we introduce a categorical latent variable into the energy-based model. The latent variable is learned from the original sample before adaptation by variational inference and fixed as a condition to guide the sample update. Experiments on six benchmarks for classification of images and microblog threads demonstrate the effectiveness of our proposal.