ADEPT: A Unified Framework for Deep Learning Test Adequacy

Existing methods for testing deep neural networks (DNNs) primarily prioritize test inputs likely to reveal model faults under a fixed labeling budget. In practice, choosing that budget is difficult: too little testing misses failures, while too much incurs unnecessary labeling costs. This work studies the stopping problem in DNN testing. We formulate testing as a cost--benefit decision process in which labeling an input incurs cost $c$ and discovering a fault yields value $v$. Based on this formulation, we introduce \textit{AdaStop}, a framework that estimates the marginal fault discovery rate during testing and stops labeling when the estimated rate falls below the threshold $τ= c/v$. Experiments across multiple datasets, architectures, and selection strategies show that $65$--$84\%$ of faults can be discovered using only $9$--$31\%$ of the labeling budget.

Deep neural nets achieve remarkable performance when training and test data share the same distribution, but this assumption frequently breaks in real-world deployment, where data undergoes continual distributional shifts. Continual Test-Time Adaptation (CTTA) addresses this challenge by adapting pretrained models to non-stationary target distributions on-the-fly, without access to source data or labeled targets, while mitigating two critical failure modes: catastrophic forgetting of source knowledge and error accumulation from noisy pseudo-labels over extended time horizons. In this comprehensive survey, we formally define the CTTA problem, analyze the diverse continual domain shift patterns that characterize different evaluation protocols, and propose a hierarchical taxonomy that categorizes existing methods into three families: optimization-based strategies (entropy minimization, pseudo-labeling, parameter restoration), parameter-efficient methods (normalization layer adaptation, adaptive parameter selection), and architecture-based approaches (teacher-student frameworks, adapters, visual prompting, masked modeling). We systematically review representative methods within each category and present comparative benchmarks and experimental results across standard evaluation settings. Finally, we discuss the limitations of current approaches and highlight emerging research directions, including the adaptation of foundation models and black-box systems, thereby providing a roadmap for future research in robust continual test-time adaptation.

Many modern applications of deep learning involve training a neural network via a one-step prediction loss (e.g., $L^2$ regression, cross-entropy), but deploy the network by rolling out along its own predictions. Key examples include autoregressive language modeling, flow-based generative modeling, and robot policy learning. It is well-documented that these settings induce a phenomenon we call test-time feedback (TTF): the mismatch between the training/validation loss and downstream metrics of interest, such as task success rate and generation quality, which grows with task length. While data curation, architecture, and objective design have been proposed to combat train-test shift in TTF settings, this paper proposes optimization as a new design axis to mitigate error accumulation. Specifically, we introduce a new optimization paradigm called double-preconditioning (DoPr) uniquely tailored to the challenges of TTF. DoPr combines gradient-wise preconditioning, as in Adam and Muon, with activation-wise preconditioning (AP), such as in KFAC. We show that the addition of AP yields a drop-in intervention for increasing downstream model performance across a range of TTF settings. Interestingly, these gains in test-time performance do not consistently accompany improvements in validation loss, opening new questions about how to properly evaluate models trained with one-step supervised objectives.