# ZOTTA: Test-Time Adaptation with Gradient-Free Zeroth-Order Optimization

arXiv: https://arxiv.org/abs/2603.14254 · HTML: https://mlsanity.com/paper/2603.14254/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 49 references that are in the map.
- First posted on arXiv 15 Mar 2026.

## Builds on (most cited first, 30 of 34)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [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)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Natural Adversarial Examples](https://mlsanity.com/paper/1907.07174/) (2019)
- [Learning Robust Global Representations by Penalizing Local Predictive Power](https://mlsanity.com/paper/1905.13549/) (2019)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [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)
- [MEMO: Test Time Robustness via Adaptation and Augmentation](https://mlsanity.com/paper/2110.09506/) (2021)
- [Fine-Tuning Language Models with Just Forward Passes](https://mlsanity.com/paper/2305.17333/) (2023)
- [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)
- [A Primer on Zeroth-Order Optimization in Signal Processing and Machine Learning](https://mlsanity.com/paper/2006.06224/) (2020)
- [EcoTTA: Memory-Efficient Continual Test-time Adaptation via Self-distilled Regularization](https://mlsanity.com/paper/2303.01904/) (2023)
- [Zeroth-Order Stochastic Variance Reduction for Nonconvex Optimization](https://mlsanity.com/paper/1805.10367/) (2018)
- [Entropy is not Enough for Test-Time Adaptation: From the Perspective of Disentangled Factors](https://mlsanity.com/paper/2403.07366/) (2024)
- [Transfer Learning without Knowing: Reprogramming Black-box Machine Learning Models with Scarce Data and Limited Resources](https://mlsanity.com/paper/2007.08714/) (2020)
- [Test-Time Model Adaptation with Only Forward Passes](https://mlsanity.com/paper/2404.01650/) (2024)
- [SITA: Single Image Test-time Adaptation](https://mlsanity.com/paper/2112.02355/) (2021)
- [Zeroth-Order Regularized Optimization (ZORO): Approximately Sparse Gradients and Adaptive Sampling](https://mlsanity.com/paper/2003.13001/) (2020)
- [A Comprehensive Linear Speedup Analysis for Asynchronous Stochastic Parallel Optimization from Zeroth-Order to First-Order](https://mlsanity.com/paper/1606.00498/) (2016)
- [Model Agnostic Contrastive Explanations for Structured Data](https://mlsanity.com/paper/1906.00117/) (2019)

## Built on by (most cited first, 2 of 2)

- [A Survey on Self-Improving Test-Time Intelligence: Feedback-Driven Adapting, Learning, and Scaling at Inference](https://mlsanity.com/paper/2609.01679/) (2026)
- [Temporal Structure Matters for Efficient Test-Time Adaptation in Wearable Human Activity Recognition](https://mlsanity.com/paper/2605.04617/) (2026)

## Abstract (arXiv)

Test-time adaptation (TTA) aims to improve model robustness under distribution shifts by adapting to unlabeled test data, but most existing methods rely on backpropagation (BP), which is computationally costly and incompatible with non-differentiable models such as quantized models, limiting practical deployment on numerous edge devices. Recent BP-free approaches alleviate overhead but remain either architecture-specific or limited in optimization capacity to handle high-dimensional models. We propose ZOTTA, a fully BP-free TTA framework that performs efficient adaptation using only forward passes via Zeroth-Order Optimization (ZOO). While ZOO is theoretically appealing, naive application leads to slow convergence under high-dimensional parameter spaces and unstable optimization due to the lack of labels. ZOTTA overcomes these challenges through 1) Distribution-Robust Layer Selection, which automatically identifies and freezes layers that already extract distribution-invariant features, updating only domain-sensitive layers to reduce the optimization dimensionality and accelerate convergence; 2) Spatial Feature Aggregation Alignment, which stabilizes ZOO by aligning globally aggregated spatial features between source and target to reduce gradient variance. Together, these components enable architecture-agnostic and stable BP-free adaptation. Extensive experiments on ImageNet-C/R/Sketch/A show that ZOTTA outperforms or matches BP-based methods, e.g., it reduces memory usage by 84% and improves accuracy by 3.9% over SAR on ImageNet-C. Code:https://github.com/Zhang-Ronghao/zotta.