Instead of directly distilling a language model, this study addresses the problem of aligning a base model with a target model in distribution by designing the domain mixture of training data for pretraining or continued pretraining as a fixed training recipe. We propose a method for determining domain weights by viewing models as points in log-likelihood space and aligning the training update direction with the direction toward the target model. Experiments with NanoGPT show that the proposed method consistently reduces the KL divergence between the trained base model and the target model relative to training with Pile-original weighting. Although knowledge distillation remains more effective when available, the proposed method achieves meaningful alignment, and downstream task performance also tends to become closer to that of the target model.

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.

Various studies have proposed methods to quantify and compare the rapidly growing number of large language models (LLMs). However, when constructing a macroscopic map of LLMs, there is a trade-off between estimation accuracy and computational cost, making the selection of evaluation texts critical. In this work, we propose Predictive Importance Sampling (PredIS), which selects informative texts by predicting likelihood variance from text-level features. Experiments on 100 LLMs across 25 domains demonstrate that our predictor generalizes robustly. Furthermore, we reveal that text importance cannot be explained by text length alone, as it is also closely tied to meaning reflected in the embedding space.

We address the computational cost of constructing a model map, which embeds diverse language models into a common space for comparison via KL divergence. The map relies on log-likelihoods over a large text set, making the cost proportional to the number of texts. To reduce this cost, we propose a resampling method that selects important texts with weights proportional to the variance of log-likelihoods across models for each text. Our method significantly reduces the number of required texts while preserving the accuracy of KL divergence estimates. Experiments show that it achieves comparable performance to uniform sampling with about half as many texts, and also facilitates efficient incorporation of new models into an existing map. These results enable scalable and efficient construction of language model maps.

Lexical semantic change detection aims to identify shifts in word meanings over time. While existing methods using embeddings from a diachronic corpus pair estimate the degree of change for target words, they offer limited insight into changes at the level of individual usage instances. To address this, we apply Unbalanced Optimal Transport (UOT) to sets of contextualized word embeddings, capturing semantic change through the excess and deficit in the alignment between usage instances. In particular, we propose Sense Usage Shift (SUS), a measure that quantifies changes in the usage frequency of a word sense at each usage instance. By leveraging SUS, we demonstrate that several challenges in semantic change detection can be addressed in a unified manner, including quantifying instance-level semantic change and word-level tasks such as measuring the magnitude of semantic change and the broadening or narrowing of meaning.