  This paper investigates how Transformer language models (LMs) fine-tuned for
acceptability classification capture linguistic features. Our approach uses the
best practices of topological data analysis (TDA) in NLP: we construct directed
attention graphs from attention matrices, derive topological features from
them, and feed them to linear classifiers. We introduce two novel features,
chordality, and the matching number, and show that TDA-based classifiers
outperform fine-tuning baselines. We experiment with two datasets, CoLA and
RuCoLA in English and Russian, typologically different languages. On top of
that, we propose several black-box introspection techniques aimed at detecting
changes in the attention mode of the LMs during fine-tuning, defining the LM's
prediction confidences, and associating individual heads with fine-grained
grammar phenomena. Our results contribute to understanding the behavior of
monolingual LMs in the acceptability classification task, provide insights into
the functional roles of attention heads, and highlight the advantages of
TDA-based approaches for analyzing LMs. We release the code and the
experimental results for further uptake.
