Semantic Properties of cosine based bias scores for word embeddings

Plenty of works have brought social biases in language models to attention and proposed methods to detect such biases. As a result, the literature contains a great deal of different bias tests and scores, each introduced with the premise to uncover yet more biases that other scores fail to detect. What severely lacks in the literature, however, are comparative studies that analyse such bias scores and help researchers to understand the benefits or limitations of the existing methods. In this work, we aim to close this gap for cosine based bias scores. By building on a geometric definition of bias, we propose requirements for bias scores to be considered meaningful for quantifying biases. Furthermore, we formally analyze cosine based scores from the literature with regard to these requirements. We underline these findings with experiments to show that the bias scores' limitations have an impact in the application case.