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.
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