On the data requirements of probing

As large and powerful neural language models are developed, researchers have been increasingly interested in developing diagnostic tools to probe them. There are many papers with conclusions of the form "observation X is found in model Y", using their own datasets with varying sizes. Larger probing datasets bring more reliability, but are also expensive to collect. There is yet to be a quantitative method for estimating reasonable probing dataset sizes. We tackle this omission in the context of comparing two probing configurations: after we have collected a small dataset from a pilot study, how many additional data samples are sufficient to distinguish two different configurations? We present a novel method to estimate the required number of data samples in such experiments and, across several case studies, we verify that our estimations have sufficient statistical power. Our framework helps to systematically construct probing datasets to diagnose neural NLP models.