# Domain Mixture Design via Log-Likelihood Differences for Aligning Language Models with a Target Model

arXiv: https://arxiv.org/abs/2603.16622 · HTML: https://mlsanity.com/paper/2603.16622/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in LLM preference optimization methods, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 26 of its 38 references that are in the map.
- First posted on arXiv 17 Mar 2026.

## Placed in

- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)

## Builds on (most cited first, 26 of 26)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [LIMA: Less Is More for Alignment](https://mlsanity.com/paper/2305.11206/) (2023)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [DoReMi: Optimizing Data Mixtures Speeds Up Language Model Pretraining](https://mlsanity.com/paper/2305.10429/) (2023)
- [A Survey on Data Selection for Language Models](https://mlsanity.com/paper/2402.16827/) (2024)
- [RegMix: Data Mixture as Regression for Language Model Pre-training](https://mlsanity.com/paper/2407.01492/) (2024)
- [CodeGemma: Open Code Models Based on Gemma](https://mlsanity.com/paper/2406.11409/) (2024)
- [Organize the Web: Constructing Domains Enhances Pre-Training Data Curation](https://mlsanity.com/paper/2502.10341/) (2025)
- [Nemotron-CLIMB: CLustering-based Iterative Data Mixture Bootstrapping for Language Model Pre-training](https://mlsanity.com/paper/2504.13161/) (2025)
- [DDK: Distilling Domain Knowledge for Efficient Large Language Models](https://mlsanity.com/paper/2407.16154/) (2024)
- [Signal and Noise: A Framework for Reducing Uncertainty in Language Model Evaluation](https://mlsanity.com/paper/2508.13144/) (2025)
- [Massive Supervised Fine-tuning Experiments Reveal How Data, Layer, and Training Factors Shape LLM Alignment Quality](https://mlsanity.com/paper/2506.14681/) (2025)
- [Olmix: A Framework for Data Mixing Throughout LM Development](https://mlsanity.com/paper/2602.12237/) (2026)
- [Why Less is More (Sometimes): A Theory of Data Curation](https://mlsanity.com/paper/2511.03492/) (2025)
- [Mapping 1,000+ Language Models via the Log-Likelihood Vector](https://mlsanity.com/paper/2502.16173/) (2025)
- [Establishing a Scale for Kullback-Leibler Divergence in Language Models Across Various Settings](https://mlsanity.com/paper/2505.15353/) (2025)
- [Likelihood Variance as Text Importance for Resampling Texts to Map Language Models](https://mlsanity.com/paper/2505.15428/) (2025)

## Abstract (arXiv)

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.