Mask-based pretraining has become a cornerstone of modern large-scale models across language, vision, and recently biology. Despite its empirical success, its role and limits in learning data representations have been unclear. In this work, we show that the behavior of mask-based pretraining can be directly characterized by test risk in high-dimensional minimum-norm ("ridge-less") linear regression, without relying on further model specifications.

Understanding how the test risk scales with model complexity is a central question in machine learning. Classical theory is challenged by the learning curves observed for large over-parametrized deep networks. Capacity measures based on parameter count typically fail to account for these empirical observations. To tackle this challenge, we consider norm-based capacity measures and develop our study for random features based estimators, widely used as simplified theoretical models for more complex networks. In this context, we provide a precise characterization of how the estimator's norm concentrates and how it governs the associated test error. Our results show that the predicted learning curve admits a phase transition from under-to over-parameterization, but no double descent behavior. This confirms that more classical U-shaped behavior is recovered considering appropriate capacity measures based on models norms rather than size. From a technical point of view, we leverage deterministic equivalence as the key tool and further develop new deterministic quantities which are of independent interest.

Encountering shifted data at test time is a ubiquitous challenge when deploying predictive models. Test-time adaptation (TTA) methods address this issue by continuously adapting a deployed model using only unlabeled test data. While TTA can extend the model's lifespan, it is only a temporary solution. Eventually the model might degrade to the point that it must be taken offline and retrained. To detect such points of ultimate failure, we propose pairing TTA with risk monitoring frameworks that track predictive performance and raise alerts when predefined performance criteria are violated. Specifically, we extend existing monitoring tools based on sequential testing with confidence sequences to accommodate scenarios in which the model is updated at test time and no test labels are available to estimate the performance metrics of interest. Our extensions unlock the application of rigorous statistical risk monitoring to TTA, and we demonstrate the effectiveness of our proposed TTA monitoring framework across a representative set of datasets, distribution shift types, and TTA methods.

The Appendix is organized as follows.

Chain-of-thought (CoT) is a method that enables language models to handle complex reasoning tasks by decomposing them into simpler steps.

Scaling machine learning models significantly improves their performance. However, such gains come at the cost of inference being slow and resource-intensive.

The principle of multi-task learning, which encompasses concepts such as "learning to learn" and "knowledge transfer," offers an efficient paradigm that mirrors human intelligence.