Scaling Laws For Dense Retrieval

Scaling laws have been observed in a wide range of tasks, particularly in language generation. Previous studies have found that the performance of large language models adheres to predictable patterns with respect to the size of models and datasets. This helps us design training strategies effectively and efficiently, especially as large-scale training becomes increasingly resource-intensive. Yet, in dense retrieval, such scaling law has not been fully explored. In this study, we investigate how scaling affects the performance of dense retrieval models. We implement dense retrieval models with different numbers of parameters, and train them with various amounts of annotated data. We propose to use the contrastive entropy as the evaluation metric, which is continuous compared with discrete ranking metrics and thus can accurately reflect model performance. Results indicate that the performance of dense retrieval models follows a precise power-law scaling related to the model size and the number of annotations across different datasets and annotation methods. Additionally, we show that the scaling laws help optimize the training process, such as resolving the resource allocation problem under a budget constraint. We believe that these findings significantly contribute to understanding the scaling effect of dense retrieval models and offer meaningful guidance for future research.