Rethinking the Teacher-Student Framework for Test-Time Adaptation

Test-Time Adaptation (TTA) has recently emerged as a promising strategy that allows the adaptation of pre-trained models to changing data distributions at deployment time, without access to any labels. To mitigate error accumulation, researchers have widely adopted the teacher-student framework, though its long-term stability is often taken for granted. In this work, we challenge the common strategy of setting the teacher weights to an exponential moving average of the student by showing that error accumulation still occurs, although it is mostly apparent on longer sequences compared to those commonly utilized. We analyze the stability-plasticity trade-off within the teacher-student framework and propose to use an intransigent teacher that does not update its weights. Surprisingly, we show that this simple change allows TTA methods to significantly improve their performance on multiple datasets with longer scenarios and result in increased robustness to changes in hyperparameters. Finally, we show that those changes can be seamlessly and effectively applied to various architectures and experimental setups, including semantic segmentation. The code is available at https://github.com/dmn-sjk/intransigent_teacher.

Theoretical Foundations of Continual Learning via Drift-Plus-Penalty

In many real-world settings, data streams are nonstationary and arrive sequentially, requiring learning systems to adapt continuously without retraining from scratch. Continual learning (CL) addresses this challenge by incorporating new tasks while mitigating catastrophic forgetting, where learning new information degrades performance on previously acquired knowledge. We introduce a control-theoretic perspective on CL that explicitly regulates the evolution of forgetting, framing adaptation as a controlled process subject to long-term stability constraints. We focus on replay-based CL, where a finite memory buffer stores representative samples from prior tasks. We propose COntinual Learning with Drift-Plus-Penalty (COLD), a continual learning framework based on the Drift-Plus-Penalty (DPP) principle from stochastic optimization. To facilitate analysis, we also consider an oracle variant, COLD-ORACLE, as a reference benchmark. At each task, both methods minimize the current task loss while maintaining a virtual queue that tracks deviations from long-term stability on previously learned tasks, capturing the stability-plasticity trade-off as a regulated dynamical process. We establish stability and convergence guarantees that characterize this trade-off through a tunable control parameter. Experiments on standard benchmarks demonstrate that COLD consistently outperforms a broad range of state-of-the-art CL methods while providing competitive and controllable forgetting behavior through explicit regulation of stability and plasticity.