Establishing a Scale for Kullback-Leibler Divergence in Language Models Across Various Settings

Ryo Kishino; Yusuke Takase; Momose Oyama; Hiroaki Yamagiwa; Hidetoshi Shimodaira

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arXiv · 2505.15353

Establishing a Scale for Kullback-Leibler Divergence in Language Models Across Various Settings

Ryo Kishino·Yusuke Takase·Momose Oyama·Hiroaki Yamagiwa·Hidetoshi Shimodaira

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Abstract

Log-likelihood vectors define a common space for comparing language models as probability distributions, enabling unified comparisons across heterogeneous settings. We extend this framework to training checkpoints and intermediate layers, and establish a consistent scale for KL divergence across pretraining, model size, random seeds, quantization, fine-tuning, and layers. Analysis of Pythia pretraining trajectories further shows that changes in log-likelihood space, as measured by the scaling behavior of KL divergence, are much smaller than in weight space, resulting in subdiffusive learning trajectories and early stabilization of language-model behavior despite weight drift.

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Ryo Kishino, Yusuke Takase, Momose Oyama, Hiroaki Yamagiwa, Hidetoshi Shimodaira. 2026-04-20. Establishing a Scale for Kullback-Leibler Divergence in Language Models Across Various Settings. https://arxiv.org/abs/2505.15353

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