Isotropic Representation Can Improve Dense Retrieval

The recent advancement in language representation modeling has broadly affected the design of dense retrieval models. In particular, many of the high-performing dense retrieval models evaluate representations of query and document using BERT, and subsequently apply a cosine-similarity based scoring to determine the relevance. BERT representations, however, are known to follow an anisotropic distribution of a narrow cone shape and such an anisotropic distribution can be undesirable for the cosine-similarity based scoring. In this work, we first show that BERT-based DR also follows an anisotropic distribution. To cope with the problem, we introduce unsupervised post-processing methods of Normalizing Flow and whitening, and develop token-wise method in addition to the sequence-wise method for applying the post-processing methods to the representations of dense retrieval models. We show that the proposed methods can effectively enhance the representations to be isotropic, then we perform experiments with ColBERT and RepBERT to show that the performance (NDCG at 10) of document re-ranking can be improved by 5.17\%$\sim$8.09\% for ColBERT and 6.88\%$\sim$22.81\% for RepBERT. To examine the potential of isotropic representation for improving the robustness of DR models, we investigate out-of-distribution tasks where the test dataset differs from the training dataset. The results show that isotropic representation can achieve a generally improved performance. For instance, when training dataset is MS-MARCO and test dataset is Robust04, isotropy post-processing can improve the baseline performance by up to 24.98\%. Furthermore, we show that an isotropic model trained with an out-of-distribution dataset can even outperform a baseline model trained with the in-distribution dataset.