Estimating Class Separability of Datasets Using Persistent Homology with Application to LLM Fine-Tuning

This paper proposes a method to estimate the class separability of an unlabeled text dataset by inspecting the topological characteristics of sentence-transformer embeddings of the text. Experiments conducted involve both binary and multi-class cases, with balanced and imbalanced scenarios. The results demonstrate a clear correlation and a better consistency between the proposed method and other separability and classification metrics, such as Thornton's method and the AUC score of a logistic regression classifier, as well as unsupervised methods. Finally, we empirically show that the proposed method can be part of a stopping criterion for fine-tuning language-model classifiers. By monitoring the class separability of the embedding space after each training iteration, we can detect when the training process stops improving the separability of the embeddings without using additional labels.