# Test-time Adaptation for Regression by Subspace Alignment arXiv: https://arxiv.org/abs/2410.03263 ยท HTML: https://mlsanity.com/paper/2410.03263/ ## Key facts - Cited by 10 papers in the map (data through 14 Oct 2026). - Builds on 32 of its 62 references that are in the map. - First posted on arXiv 4 Oct 2024. ## Builds on (most cited first, 30 of 32) - [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015) - [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020) - [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019) - [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) - [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) - [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019) - [Efficient Test-Time Model Adaptation without Forgetting](https://mlsanity.com/paper/2204.02610/) (2022) - [Age Progression/Regression by Conditional Adversarial Autoencoder](https://mlsanity.com/paper/1702.08423/) (2017) - [MEMO: Test Time Robustness via Adaptation and Augmentation](https://mlsanity.com/paper/2110.09506/) (2021) - [A Comprehensive Survey on Test-Time Adaptation under Distribution Shifts](https://mlsanity.com/paper/2303.15361/) (2023) - [Domain Adaptation for Visual Applications: A Comprehensive Survey](https://mlsanity.com/paper/1702.05374/) (2017) - [Training BatchNorm and Only BatchNorm: On the Expressive Power of Random Features in CNNs](https://mlsanity.com/paper/2003.00152/) (2020) - [Decorate the Newcomers: Visual Domain Prompt for Continual Test Time Adaptation](https://mlsanity.com/paper/2212.04145/) (2022) - [DELTA: degradation-free fully test-time adaptation](https://mlsanity.com/paper/2301.13018/) (2023) - [Back to the Source: Diffusion-Driven Test-Time Adaptation](https://mlsanity.com/paper/2207.03442/) (2022) - [Revisiting Batch Normalization for Improving Corruption Robustness](https://mlsanity.com/paper/2010.03630/) (2020) - [Source-Free Adaptation to Measurement Shift via Bottom-Up Feature Restoration](https://mlsanity.com/paper/2107.05446/) (2021) - [A Comprehensive Analysis of Deep Regression](https://mlsanity.com/paper/1803.08450/) (2018) - [Improving Deep Regression with Ordinal Entropy](https://mlsanity.com/paper/2301.08915/) (2023) - [KL Guided Domain Adaptation](https://mlsanity.com/paper/2106.07780/) (2021) - [TTTFlow: Unsupervised Test-Time Training with Normalizing Flow](https://mlsanity.com/paper/2210.11389/) (2022) - [DARE-GRAM : Unsupervised Domain Adaptation Regression by Aligning Inverse Gram Matrices](https://mlsanity.com/paper/2303.13325/) (2023) - [Robustifying Vision Transformer without Retraining from Scratch by Test-Time Class-Conditional Feature Alignment](https://mlsanity.com/paper/2206.13951/) (2022) - [Source-free Domain Adaptation via Distributional Alignment by Matching Batch Normalization Statistics](https://mlsanity.com/paper/2101.10842/) (2021) - [CAFA: Class-Aware Feature Alignment for Test-Time Adaptation](https://mlsanity.com/paper/2206.00205/) (2022) - [ClusT3: Information Invariant Test-Time Training](https://mlsanity.com/paper/2310.12345/) (2023) - [Efficient Test-Time Adaptation for Super-Resolution with Second-Order Degradation and Reconstruction](https://mlsanity.com/paper/2310.19011/) (2023) - [Domain-Specificity Inducing Transformers for Source-Free Domain Adaptation](https://mlsanity.com/paper/2308.14023/) (2023) ## Built on by (most cited first, 10 of 10) - [SIMSHIFT: A Benchmark for Adapting Neural Surrogates to Distribution Shifts](https://mlsanity.com/paper/2506.12007/) (2025) - [Structural Alignment Improves Graph Test-Time Adaptation](https://mlsanity.com/paper/2502.18334/) (2025) - [Distill Once, Adapt Life-Long: Exploring Dataset Distillation for Continual Test-Time Adaptation](https://mlsanity.com/paper/2606.20196/) (2026) - [Composable Cross-prompt Essay Scoring by Merging Models](https://mlsanity.com/paper/2505.18548/) (2025) - [DP-TTA: Test-time Adaptation for Transient Electromagnetic Signal Denoising via Dictionary-driven Prior Regularization](https://mlsanity.com/paper/2510.13160/) (2025) - [Stabilizing Test-Time Adaptation of High-Dimensional Simulation Surrogates via D-Optimal Statistics](https://mlsanity.com/paper/2602.15820/) (2026) - [Predictive Spectral Calibration for Source-Free Test-Time Regression](https://mlsanity.com/paper/2603.09338/) (2026) - [Uncertainty-Aware Test-Time Adaptation for Cross-Region Spatio-Temporal Fusion of Land Surface Temperature](https://mlsanity.com/paper/2604.04153/) (2026) - [Test-time adaptation for speech enhancement with an autoregressive speech prior](https://mlsanity.com/paper/2609.03622/) (2026) - [On the Limits of Representation-Based Test-Time Adaptation for Multimodal LLMs](https://mlsanity.com/paper/2610.19892/) (2026) ## Abstract (arXiv) This paper investigates test-time adaptation (TTA) for regression, where a regression model pre-trained in a source domain is adapted to an unknown target distribution with unlabeled target data. Although regression is one of the fundamental tasks in machine learning, most of the existing TTA methods have classification-specific designs, which assume that models output class-categorical predictions, whereas regression models typically output only single scalar values. To enable TTA for regression, we adopt a feature alignment approach, which aligns the feature distributions between the source and target domains to mitigate the domain gap. However, we found that naive feature alignment employed in existing TTA methods for classification is ineffective or even worse for regression because the features are distributed in a small subspace and many of the raw feature dimensions have little significance to the output. For an effective feature alignment in TTA for regression, we propose Significant-subspace Alignment (SSA). SSA consists of two components: subspace detection and dimension weighting. Subspace detection finds the feature subspace that is representative and significant to the output. Then, the feature alignment is performed in the subspace during TTA. Meanwhile, dimension weighting raises the importance of the dimensions of the feature subspace that have greater significance to the output. We experimentally show that SSA outperforms various baselines on real-world datasets.