  Proposing scoring functions to effectively understand, analyze and learn
various properties of high dimensional hidden representations of large-scale
transformer models like BERT can be a challenging task. In this work, we
explore a new direction by studying the topological features of BERT hidden
representations using persistent homology (PH). We propose a novel scoring
function named "persistence scoring function (PSF)" which: (i) accurately
captures the homology of the high-dimensional hidden representations and
correlates well with the test set accuracy of a wide range of datasets and
outperforms existing scoring metrics, (ii) captures interesting post
fine-tuning "per-class" level properties from both qualitative and quantitative
viewpoints, (iii) is more stable to perturbations as compared to the baseline
functions, which makes it a very robust proxy, and (iv) finally, also serves as
a predictor of the attack success rates for a wide category of black-box and
white-box adversarial attack methods. Our extensive correlation experiments
demonstrate the practical utility of PSF on various NLP tasks relevant to BERT.
