# Subspace Optimization for Backpropagation-Free Continual Test-Time Adaptation

arXiv: https://arxiv.org/abs/2603.28678 · HTML: https://mlsanity.com/paper/2603.28678/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 41 references that are in the map.
- First posted on arXiv 30 Mar 2026.

## Builds on (most cited first, 27 of 27)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [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)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (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)
- [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)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [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)
- [Qualitatively characterizing neural network optimization problems](https://mlsanity.com/paper/1412.6544/) (2014)
- [PTQ4ViT: Post-training quantization for vision transformers with twin uniform quantization](https://mlsanity.com/paper/2111.12293/) (2021)
- [NOTE: Robust Continual Test-time Adaptation Against Temporal Correlation](https://mlsanity.com/paper/2208.05117/) (2022)
- [Robust Mean Teacher for Continual and Gradual Test-Time Adaptation](https://mlsanity.com/paper/2211.13081/) (2022)
- [TTN: A Domain-Shift Aware Batch Normalization in Test-Time Adaptation](https://mlsanity.com/paper/2302.05155/) (2023)
- [Fastfood: Approximate Kernel Expansions in Loglinear Time](https://mlsanity.com/paper/1408.3060/) (2014)
- [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)
- [SITA: Single Image Test-time Adaptation](https://mlsanity.com/paper/2112.02355/) (2021)
- [An Efficient Domain-Incremental Learning Approach to Drive in All Weather Conditions](https://mlsanity.com/paper/2204.08817/) (2022)
- [Uncertainty-Calibrated Test-Time Model Adaptation without Forgetting](https://mlsanity.com/paper/2403.11491/) (2024)
- [Persistent Test-time Adaptation in Recurring Testing Scenarios](https://mlsanity.com/paper/2311.18193/) (2023)
- [Test-Time Model Adaptation for Quantized Neural Networks](https://mlsanity.com/paper/2508.02180/) (2025)
- [ReservoirTTA: Prolonged Test-time Adaptation for Evolving and Recurring Domains](https://mlsanity.com/paper/2505.14511/) (2025)
- [Towards Unified and Effective Domain Generalization](https://mlsanity.com/paper/2310.10008/) (2023)

## 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)
- [FORGE: Forward-Only Test-Time Adaptation for Integer-Only Vision Models on Microcontrollers](https://mlsanity.com/paper/2609.01683/) (2026)

## Abstract (arXiv)

We introduce PACE, a backpropagation-free continual test-time adaptation system that directly optimizes the affine parameters of normalization layers. Existing derivative-free approaches struggle to balance runtime efficiency with learning capacity, as they either restrict updates to input prompts or require continuous, resource-intensive adaptation regardless of domain stability. To address these limitations, PACE leverages the Covariance Matrix Adaptation Evolution Strategy with the Fastfood projection to optimize high-dimensional affine parameters within a low-dimensional subspace, leading to superior adaptive performance. Furthermore, we enhance the runtime efficiency by incorporating an adaptation stopping criterion and a domain-specialized vector bank to eliminate redundant computation. Our framework achieves state-of-the-art accuracy across multiple benchmarks under continual distribution shifts, reducing runtime by over 50% compared to existing backpropagation-free methods.