# Curvature-Aware Zeroth-Order Optimization for Memory-Efficient Test-Time Adaptation

arXiv: https://arxiv.org/abs/2608.12279 · HTML: https://mlsanity.com/paper/2608.12279/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 46 of its 64 references that are in the map.
- First posted on arXiv 12 Aug 2026.

## Builds on (most cited first, 30 of 46)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [Learning Robust Global Representations by Penalizing Local Predictive Power](https://mlsanity.com/paper/1905.13549/) (2019)
- [AugMix: A Simple Data Processing Method to Improve Robustness and Uncertainty](https://mlsanity.com/paper/1912.02781/) (2019)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [AdaptFormer: Adapting Vision Transformers for Scalable Visual Recognition](https://mlsanity.com/paper/2205.13535/) (2022)
- [Continual Test-Time Domain Adaptation](https://mlsanity.com/paper/2203.13591/) (2022)
- [Black-box Adversarial Attacks with Limited Queries and Information](https://mlsanity.com/paper/1804.08598/) (2018)
- [Efficient Test-Time Model Adaptation without Forgetting](https://mlsanity.com/paper/2204.02610/) (2022)
- [AdapterHub: A Framework for Adapting Transformers](https://mlsanity.com/paper/2007.07779/) (2020)
- [Towards Stable Test-Time Adaptation in Dynamic Wild World](https://mlsanity.com/paper/2302.12400/) (2023)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [A Comprehensive Survey on Test-Time Adaptation under Distribution Shifts](https://mlsanity.com/paper/2303.15361/) (2023)
- [Fine-Tuning Language Models with Just Forward Passes](https://mlsanity.com/paper/2305.17333/) (2023)
- [Contrastive Test-Time Adaptation](https://mlsanity.com/paper/2204.10377/) (2022)
- [Evaluating Prediction-Time Batch Normalization for Robustness under Covariate Shift](https://mlsanity.com/paper/2006.10963/) (2020)
- [Optimal rates for zero-order convex optimization: the power of two function evaluations](https://mlsanity.com/paper/1312.2139/) (2013)
- [Parameter-free Online Test-time Adaptation](https://mlsanity.com/paper/2201.05718/) (2022)
- [Robust Test-Time Adaptation in Dynamic Scenarios](https://mlsanity.com/paper/2303.13899/) (2023)
- [AutoZOOM: Autoencoder-based Zeroth Order Optimization Method for Attacking Black-box Neural Networks](https://mlsanity.com/paper/1805.11770/) (2018)
- [EcoTTA: Memory-Efficient Continual Test-time Adaptation via Self-distilled Regularization](https://mlsanity.com/paper/2303.01904/) (2023)
- [Entropy is not Enough for Test-Time Adaptation: From the Perspective of Disentangled Factors](https://mlsanity.com/paper/2403.07366/) (2024)
- [TTN: A Domain-Shift Aware Batch Normalization in Test-Time Adaptation](https://mlsanity.com/paper/2302.05155/) (2023)
- [Test-Time Model Adaptation with Only Forward Passes](https://mlsanity.com/paper/2404.01650/) (2024)
- [DELTA: degradation-free fully test-time adaptation](https://mlsanity.com/paper/2301.13018/) (2023)
- [Improving Test-Time Adaptation via Shift-agnostic Weight Regularization and Nearest Source Prototypes](https://mlsanity.com/paper/2207.11707/) (2022)

## Abstract (arXiv)

Test-time adaptation (TTA) aims to enhance the cross-domain performance of pre-trained models by adapting to unlabeled test data. While most existing TTA methods rely on backpropagation (BP) for finetuning, BP-free methods such as zeroth-order (ZO) methods are more desired in practical on-device scenarios. ZO methods rely only on forward computation, which can largely reduce the complexity and memory overhead of on-device deployment. However, ZO methods suffer from much higher variance compared with first-order methods in estimating the gradient. To address this, we propose an improved ZO method to substantially boost the performance of ZO optimization based TTA. First, we provide an observation to reveal the persistent low-rank Hessian structure of the loss during the adaptation process. Based on this insight, we then propose a loss-landscape curvature-aware zeroth-order (CAZO) method, which leverages a sliding-average estimation of the diagonal Hessian to construct a covariance matrix for anisotropic perturbation sampling. CAZO operates by freezing pretrained weights and optimizing minimal adapter parameters via forward-only passes based gradient estimation, which can substantially reduce the memory overhead compared to BP-based methods. Extensive experiments demonstrate that CAZO significantly outperforms existing TTA methods, achieving state-of-the-art performance while maintaining an excellent balance between accuracy and memory efficiency. Code is available at https://github.com/Hollyming/CAZO.