# Matching High-Dimensional Geometric Quantiles for Test-Time Adaptation of Transformers and Convolutional Networks Alike

arXiv: https://arxiv.org/abs/2601.11022 · HTML: https://mlsanity.com/paper/2601.11022/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 17 references that are in the map.
- First posted on arXiv 16 Jan 2026.

## Builds on (most cited first, 12 of 12)

- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [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)
- [Towards Stable Test-Time Adaptation in Dynamic Wild World](https://mlsanity.com/paper/2302.12400/) (2023)
- [Escaping the Big Data Paradigm with Compact Transformers](https://mlsanity.com/paper/2104.05704/) (2021)
- [Evaluating Prediction-Time Batch Normalization for Robustness under Covariate Shift](https://mlsanity.com/paper/2006.10963/) (2020)
- [Robust Test-Time Adaptation in Dynamic Scenarios](https://mlsanity.com/paper/2303.13899/) (2023)
- [Stochastic Gradient Descent on Separable Data: Exact Convergence with a Fixed Learning Rate](https://mlsanity.com/paper/1806.01796/) (2018)
- [SoTTA: Robust Test-Time Adaptation on Noisy Data Streams](https://mlsanity.com/paper/2310.10074/) (2023)
- [A Probabilistic Framework for Lifelong Test-Time Adaptation](https://mlsanity.com/paper/2212.09713/) (2022)
- [MedBN: Robust Test-Time Adaptation against Malicious Test Samples](https://mlsanity.com/paper/2403.19326/) (2024)

## Abstract (arXiv)

Test-time adaptation (TTA) refers to adapting a classifier for the test data when the probability distribution of the test data slightly differs from that of the training data of the model. To the best of our knowledge, most of the existing TTA approaches modify the weights of the classifier relying heavily on the architecture. It is unclear as to how these approaches are extendable to generic architectures. In this article, we propose an architecture-agnostic approach to TTA by adding an adapter network pre-processing the input images suitable to the classifier. This adapter is trained using the proposed quantile loss. Unlike existing approaches, we correct for the distribution shift by matching high-dimensional geometric quantiles. We prove theoretically that under suitable conditions minimizing quantile loss can learn the optimal adapter. We validate our approach on CIFAR10-C, CIFAR100-C and TinyImageNet-C by training both classic convolutional and transformer networks on CIFAR10, CIFAR100 and TinyImageNet datasets.