# Adapt in the Wild: Test-Time Entropy Minimization with Sharpness and Feature Regularization

arXiv: https://arxiv.org/abs/2509.04977 · HTML: https://mlsanity.com/paper/2509.04977/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 82 of its 98 references that are in the map.
- First posted on arXiv 5 Sep 2025.

## Builds on (most cited first, 30 of 82)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Non-local Neural Networks](https://mlsanity.com/paper/1711.07971/) (2017)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [Unsupervised Representation Learning by Predicting Image Rotations](https://mlsanity.com/paper/1803.07728/) (2018)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [StarGAN: Unified Generative Adversarial Networks for Multi-Domain Image-to-Image Translation](https://mlsanity.com/paper/1711.09020/) (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)
- [Learning to Generalize: Meta-Learning for Domain Generalization](https://mlsanity.com/paper/1710.03463/) (2017)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Maximum Classifier Discrepancy for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1712.02560/) (2017)
- [Continual Test-Time Domain Adaptation](https://mlsanity.com/paper/2203.13591/) (2022)
- [Efficient Test-Time Model Adaptation without Forgetting](https://mlsanity.com/paper/2204.02610/) (2022)
- [Improving robustness against common corruptions by covariate shift adaptation](https://mlsanity.com/paper/2006.16971/) (2020)
- [Towards Stable Test-Time Adaptation in Dynamic Wild World](https://mlsanity.com/paper/2302.12400/) (2023)
- [Domain Generalization via Model-Agnostic Learning of Semantic Features](https://mlsanity.com/paper/1910.13580/) (2019)
- [Understanding Dimensional Collapse in Contrastive Self-supervised Learning](https://mlsanity.com/paper/2110.09348/) (2021)
- [MEMO: Test Time Robustness via Adaptation and Augmentation](https://mlsanity.com/paper/2110.09506/) (2021)

## Built on by (most cited first, 3 of 3)

- [Neural Collapse in Test-Time Adaptation](https://mlsanity.com/paper/2512.10421/) (2025)
- [Decoupling Stability and Plasticity for Multi-Modal Test-Time Adaptation](https://mlsanity.com/paper/2603.00574/) (2026)
- [Ramen: Robust Test-Time Adaptation of Vision-Language Models with Active Sample Selection](https://mlsanity.com/paper/2604.21728/) (2026)

## Abstract (arXiv)

Test-time adaptation (TTA) may fail to improve or even harm the model performance when test data have: 1) mixed distribution shifts, 2) small batch sizes, 3) online imbalanced label distribution shifts. This is often a key obstacle preventing existing TTA methods from being deployed in the real world. In this paper, we investigate the unstable reasons and find that the batch norm layer is a crucial factor hindering TTA stability. Conversely, TTA can perform more stably with batch-agnostic norm layers, i.e., group or layer norm. However, we observe that TTA with group and layer norms does not always succeed and still suffers many failure cases, i.e., the model collapses into trivial solutions by assigning the same class label for all samples. By digging into this, we find that, during the collapse process: 1) the model gradients often undergo an initial explosion followed by rapid degradation, suggesting that certain noisy test samples with large gradients may disrupt adaptation; and 2) the model representations tend to exhibit high correlations and classification bias. To address this, we first propose a sharpness-aware and reliable entropy minimization method, called SAR, for stabilizing TTA from two aspects: 1) remove partial noisy samples with large gradients, 2) encourage model weights to go to a flat minimum so that the model is robust to the remaining noisy samples. Based on SAR, we further introduce SAR^2 to prevent representation collapse with two regularizers: 1) a redundancy regularizer to reduce inter-dimensional correlations among centroid-invariant features; and 2) an inequity regularizer to maximize the prediction entropy of a prototype centroid, thereby penalizing biased representations toward any specific class. Promising results demonstrate that our methods perform more stably over prior methods and are computationally efficient under the above wild test scenarios.