Test-time adaptation (TTA) addresses the machine learning challenge of adapting models to unlabeled test data from shifting distributions in dynamic environments. A key issue in this online setting arises from using unsupervised learning techniques, which introduce explicit gradient noise that degrades model weights. To invest in weight degradation, we propose a Bayesian weight enhancement framework, which generalizes existing weight-based TTA methods that effectively mitigate the issue. Our framework enables robust adaptation to distribution shifts by accounting for diverse weights by modeling weight distributions.Building on our framework, we identify a key limitation in existing methods: their neglect of time-varying covariance reflects the influence of the gradient noise. To address this gap, we propose a novel steady-state adaptation (SSA) algorithm that balances covariance dynamics during adaptation. SSA is derived through the solution of a stochastic differential equation for the TTA process and online inference. The resulting algorithm incorporates a covariance-aware learning rate adjustment mechanism. Through extensive experiments, we demonstrate that SSA consistently improves state-of-the-art methods in various TTA scenarios, datasets, and model architectures, establishing its effectiveness in instability and adaptability.

In our daily lives, artificial intelligence (AI) systems—like those in autonomous vehicles or smart devices—often face new and changing environments. These changes can confuse the AI, leading to a drop in performance. Our research tackles the challenge of helping AI systems adapt to new data in real-time, even when correct answers aren’t available for learning.We found that traditional methods for real-time learning can unintentionally damage the system’s knowledge. To address this, we propose Bayesian Weight Enhancement with Steady-State Adaptation. This technique uses probability and mathematical modeling to adjust the system smoothly, avoiding damage and improving adaptability.This framework and algorithm consistently enhance the performance of state-of-the-art methods, provide a theoretical explanation of real-time learning, and reveal key principles behind performance improvements. Our work strengthens the practical stability and theoretical foundation of AI systems operating in dynamic environments.