  We propose an approach to estimate the number of samples required for a model
to reach a target performance. We find that the power law, the de facto
principle to estimate model performance, leads to large error when using a
small dataset (e.g., 5 samples per class) for extrapolation. This is because
the log-performance error against the log-dataset size follows a nonlinear
progression in the few-shot regime followed by a linear progression in the
high-shot regime. We introduce a novel piecewise power law (PPL) that handles
the two data regimes differently. To estimate the parameters of the PPL, we
introduce a random forest regressor trained via meta learning that generalizes
across classification/detection tasks, ResNet/ViT based architectures, and
random/pre-trained initializations. The PPL improves the performance estimation
on average by 37% across 16 classification and 33% across 10 detection
datasets, compared to the power law. We further extend the PPL to provide a
confidence bound and use it to limit the prediction horizon that reduces
over-estimation of data by 76% on classification and 91% on detection datasets.
