Given the inevitability of domain shifts during inference in real-world applications, test-time adaptation (TTA) is essential for model adaptation after deployment. However, the real-world scenario of continuously changing target distributions presents challenges including catastrophic forgetting and error accumulation. Existing TTA methods for non-stationary domain shifts, while effective, incur excessive computational load, making them impractical for on-device settings. In this paper, we introduce a layer-wise auto-weighting algorithm for continual and gradual TTA that autonomously identifies layers for preservation or concentrated adaptation. By leveraging the Fisher Information Matrix (FIM), we first design the learning weight to selectively focus on layers associated with log-likelihood changes while preserving unrelated ones. Then, we further propose an exponential min-max scaler to make certain layers nearly frozen while mitigating outliers. This minimizes forgetting and error accumulation, leading to efficient adaptation to non-stationary target distribution. Experiments on CIFAR-10C, CIFAR-100C, and ImageNet-C show our method outperforms conventional continual and gradual TTA approaches while significantly reducing computational load, highlighting the importance of FIM-based learning weight in adapting to continuously or gradually shifting target domains.

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