Yiqun Liu

Yan Fang, Jingtao Zhan, Qingyao Ai et al. · tsinghua

Scaling up neural models has yielded significant advancements in a wide array of tasks, particularly in language generation. Previous studies have found that the performance of neural models frequently adheres to predictable scaling laws, correlated with factors such as training set size and model size. This insight is invaluable, especially as large-scale experiments grow increasingly resource-intensive. Yet, such scaling law has not been fully explored in dense retrieval due to the discrete nature of retrieval metrics and complex relationships between training data and model sizes in retrieval tasks. In this study, we investigate whether the performance of dense retrieval models follows the scaling law as other neural models. We propose to use contrastive log-likelihood as the evaluation metric and conduct extensive experiments with dense retrieval models implemented with different numbers of parameters and trained with different amounts of annotated data. Results indicate that, under our settings, the performance of dense retrieval models follows a precise power-law scaling related to the model size and the number of annotations. Additionally, we examine scaling with prevalent data augmentation methods to assess the impact of annotation quality, and apply the scaling law to find the best resource allocation strategy under a budget constraint. We believe that these insights will significantly contribute to understanding the scaling effect of dense retrieval models and offer meaningful guidance for future research endeavors.

Junxi Yan, Zixi Wei, Jingtao Zhan et al. · tsinghua

The cross-entropy scaling law has long served as a key tool for guiding the development of large language models. It shows that cross-entropy loss decreases in a predictable power-law rate as the model size increases. However, recent evidence indicates that this law breaks down at very large scales: the loss decreases more slowly than expected, which causes significant trouble for developing large language models. In this paper, we hypothesize that the root cause lies in the fact that cross-entropy itself does not truly scale; instead, only one of its hidden components does. To investigate this, we introduce a novel decomposition of cross-entropy into three parts: Error-Entropy, Self-Alignment, and Confidence. We show both theoretically and empirically that this decomposition precisely captures the training dynamics and optimization objectives. Through extensive experiments on multiple datasets and 32 models spanning five orders of magnitude in size, we find that only error-entropy follows a robust power-law scaling, while the other two terms remain largely invariant. Moreover, error-entropy constitutes the dominant share of cross-entropy in small models but diminishes in proportion as models grow larger. This explains why the cross-entropy scaling law appears accurate at small scales but fails at very large ones. Our findings establish the error-entropy scaling law as a more accurate description of model behavior. We believe it will have wide applications in the training, understanding, and future development of large language models.