Relative-Based Scaling Law for Neural Language Models

Scaling laws aim to accurately predict model performance across different scales. Existing scaling-law studies almost exclusively rely on cross-entropy as the evaluation metric. However, cross-entropy provides only a partial view of performance: it measures the absolute probability assigned to the correct token, but ignores the relative ordering between correct and incorrect tokens. Yet, relative ordering is crucial for language models, such as in greedy-sampling scenario. To address this limitation, we investigate scaling from the perspective of relative ordering. We first propose the Relative-Based Probability (RBP) metric, which quantifies the probability that the correct token is ranked among the top predictions. Building on this metric, we establish the Relative-Based Scaling Law, which characterizes how RBP improves with increasing model size. Through extensive experiments on four datasets and four model families spanning five orders of magnitude, we demonstrate the robustness and accuracy of this law. Finally, we illustrate the broad application of this law with two examples, namely providing a deeper explanation of emergence phenomena and facilitating finding fundamental theories of scaling laws. In summary, the Relative-Based Scaling Law complements the cross-entropy perspective and contributes to a more complete understanding of scaling large language models. Thus, it offers valuable insights for both practical development and theoretical exploration.

A Universal Unbiased Method for Classification from Aggregate Observations

In conventional supervised classification, true labels are required for individual instances. However, it could be prohibitive to collect the true labels for individual instances, due to privacy concerns or unaffordable annotation costs. This motivates the study on classification from aggregate observations (CFAO), where the supervision is provided to groups of instances, instead of individual instances. CFAO is a generalized learning framework that contains various learning problems, such as multiple-instance learning and learning from label proportions. The goal of this paper is to present a novel universal method of CFAO, which holds an unbiased estimator of the classification risk for arbitrary losses -- previous research failed to achieve this goal. Practically, our method works by weighing the importance of each label for each instance in the group, which provides purified supervision for the classifier to learn. Theoretically, our proposed method not only guarantees the risk consistency due to the unbiased risk estimator but also can be compatible with arbitrary losses. Extensive experiments on various problems of CFAO demonstrate the superiority of our proposed method.