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 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.