Temporal Scaling Law for Large Language Models

Recently, LLMs are widely adopted in a wide range of tasks, leading to increasing attention towards the research on how scaling LLMs affects their performance. Existing works, termed as Scaling Laws, have discovered that the loss of LLMs scales as power laws with model size, computational budget, and dataset size. However, the performance of LLMs throughout the training process remains untouched. In this paper, we propose the novel concept of Temporal Scaling Law and study the loss of LLMs from the temporal dimension. We first investigate the imbalance of loss on each token positions and develop a reciprocal-law across model scales and training stages. We then derive the temporal scaling law by studying the temporal patterns of the reciprocal-law parameters. Results on both in-distribution (IID) data and out-of-distribution (OOD) data demonstrate that our temporal scaling law accurately predicts the performance of LLMs in future training stages. Moreover, the temporal scaling law reveals that LLMs learn uniformly on different token positions, despite the loss imbalance. Experiments on pre-training LLMs in various scales show that this phenomenon verifies the default training paradigm for generative language models, in which no re-weighting strategies are attached during training. Overall, the temporal scaling law provides deeper insight into LLM pre-training.