# FOZO: Forward-Only Zeroth-Order Prompt Optimization for Test-Time Adaptation

arXiv: https://arxiv.org/abs/2603.04733 · HTML: https://mlsanity.com/paper/2603.04733/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 46 references that are in the map.
- First posted on arXiv 5 Mar 2026.

## Builds on (most cited first, 30 of 32)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Rich feature hierarchies for accurate object detection and semantic segmentation](https://mlsanity.com/paper/1311.2524/) (2013)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [Visual Prompt Tuning](https://mlsanity.com/paper/2203.12119/) (2022)
- [Learning Robust Global Representations by Penalizing Local Predictive Power](https://mlsanity.com/paper/1905.13549/) (2019)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [RobustBench: a standardized adversarial robustness benchmark](https://mlsanity.com/paper/2010.09670/) (2020)
- [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)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [Fine-Tuning Language Models with Just Forward Passes](https://mlsanity.com/paper/2305.17333/) (2023)
- [Revisiting Batch Normalization For Practical Domain Adaptation](https://mlsanity.com/paper/1603.04779/) (2016)
- [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)
- [Parameter-free Online Test-time Adaptation](https://mlsanity.com/paper/2201.05718/) (2022)
- [PTQ4ViT: Post-training quantization for vision transformers with twin uniform quantization](https://mlsanity.com/paper/2111.12293/) (2021)
- [Self-Supervised Policy Adaptation during Deployment](https://mlsanity.com/paper/2007.04309/) (2020)
- [Entropy is not Enough for Test-Time Adaptation: From the Perspective of Disentangled Factors](https://mlsanity.com/paper/2403.07366/) (2024)
- [Test-Time Model Adaptation with Only Forward Passes](https://mlsanity.com/paper/2404.01650/) (2024)
- [On Pitfalls of Test-Time Adaptation](https://mlsanity.com/paper/2306.03536/) (2023)
- [Stochastic Zeroth-order Optimization in High Dimensions](https://mlsanity.com/paper/1710.10551/) (2017)
- [Zeroth-Order Regularized Optimization (ZORO): Approximately Sparse Gradients and Adaptive Sampling](https://mlsanity.com/paper/2003.13001/) (2020)
- [ActMAD: Activation Matching to Align Distributions for Test-Time-Training](https://mlsanity.com/paper/2211.12870/) (2022)
- [Zeroth-order Nonconvex Stochastic Optimization: Handling Constraints, High-Dimensionality and Saddle-Points](https://mlsanity.com/paper/1809.06474/) (2018)
- [Test-Time Training on Video Streams](https://mlsanity.com/paper/2307.05014/) (2023)
- [Inference Stage Optimization for Cross-scenario 3D Human Pose Estimation](https://mlsanity.com/paper/2007.02054/) (2020)
- [One-Shot Unsupervised Cross-Domain Detection](https://mlsanity.com/paper/2005.11610/) (2020)

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

- [EVA-0: Test-Time Model Evolution with Only Two Forward Passes per Sample](https://mlsanity.com/paper/2605.18867/) (2026)
- [Cross-device Collaborative Test-time Adaptation with Zeroth-order Optimization and Model Merging](https://mlsanity.com/paper/2607.02988/) (2026)
- [Test-Time Adaptation of Quantized ViTs via Single-Pass Quantizer-Aligned Recalibration](https://mlsanity.com/paper/2610.08358/) (2026)

## Abstract (arXiv)

Test-Time Adaptation (TTA) is essential for enabling deep learning models to handle real-world data distribution shifts. However, current approaches face significant limitations: backpropagation-based methods are not suitable for low-end deployment devices, due to their high computation and memory requirements, as well as their tendency to modify model weights during adaptation; while traditional backpropagation-free techniques exhibit constrained adaptation capabilities. In this work, we propose Forward-Only Zeroth-Order Optimization (FOZO), a novel and practical backpropagation-free paradigm for TTA. FOZO leverages a memory-efficient zeroth-order prompt optimization, which is led by objectives optimizing both intermediate feature statistics and prediction entropy. To ensure efficient and stable adaptation over the out-of-distribution data stream, we introduce a dynamically decaying perturbation scale during zeroth-order gradient estimation and theoretically prove its convergence under the TTA data stream assumption. Extensive continual adaptation experiments on ImageNet-C, ImageNet-R, and ImageNet-Sketch demonstrate FOZO's superior performance, achieving 59.52% Top-1 accuracy on ImageNet-C (5K, level 5) and outperforming main gradient-based methods and SOTA forward-only FOA (58.13%). Furthermore, FOZO exhibits strong generalization on quantized (INT8) models. These findings demonstrate that FOZO is a highly competitive solution for TTA deployment in resource-limited scenarios.