# OptiMer: Optimal Distribution Vector Merging Is Better than Data Mixing for Continual Pre-Training

arXiv: https://arxiv.org/abs/2603.28858 · HTML: https://mlsanity.com/paper/2603.28858/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 38 of its 49 references that are in the map.
- First posted on arXiv 30 Mar 2026.

## Builds on (most cited first, 30 of 38)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [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)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Don't Stop Pretraining: Adapt Language Models to Domains and Tasks](https://mlsanity.com/paper/2004.10964/) (2020)
- [C-Eval: A Multi-Level Multi-Discipline Chinese Evaluation Suite for Foundation Models](https://mlsanity.com/paper/2305.08322/) (2023)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [DoReMi: Optimizing Data Mixtures Speeds Up Language Model Pretraining](https://mlsanity.com/paper/2305.10429/) (2023)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [XL-Sum: Large-Scale Multilingual Abstractive Summarization for 44 Languages](https://mlsanity.com/paper/2106.13822/) (2021)
- [Continual Learning of Large Language Models: A Comprehensive Survey](https://mlsanity.com/paper/2404.16789/) (2024)
- [Evolutionary Optimization of Model Merging Recipes](https://mlsanity.com/paper/2403.13187/) (2024)
- [Arcee's MergeKit: A Toolkit for Merging Large Language Models](https://mlsanity.com/paper/2403.13257/) (2024)
- [Branch-Train-Merge: Embarrassingly Parallel Training of Expert Language Models](https://mlsanity.com/paper/2208.03306/) (2022)
- [Data Mixing Laws: Optimizing Data Mixtures by Predicting Language Modeling Performance](https://mlsanity.com/paper/2403.16952/) (2024)
- [RegMix: Data Mixture as Regression for Language Model Pre-training](https://mlsanity.com/paper/2407.01492/) (2024)
- [Tree-Structured Parzen Estimator: Understanding Its Algorithm Components and Their Roles for Better Empirical Performance](https://mlsanity.com/paper/2304.11127/) (2023)
- [Continual Pre-Training for Cross-Lingual LLM Adaptation: Enhancing Japanese Language Capabilities](https://mlsanity.com/paper/2404.17790/) (2024)
- [It's All in the Heads: Using Attention Heads as a Baseline for Cross-Lingual Transfer in Commonsense Reasoning](https://mlsanity.com/paper/2106.12066/) (2021)
- [Investigating Continual Pretraining in Large Language Models: Insights and Implications](https://mlsanity.com/paper/2402.17400/) (2024)
- [What Matters for Model Merging at Scale?](https://mlsanity.com/paper/2410.03617/) (2024)
- [Chat Vector: A Simple Approach to Equip LLMs with Instruction Following and Model Alignment in New Languages](https://mlsanity.com/paper/2310.04799/) (2023)
- [Neural Thickets: Diverse Task Experts Are Dense Around Pretrained Weights](https://mlsanity.com/paper/2603.12228/) (2026)
- [Mid-Training of Large Language Models: A Survey](https://mlsanity.com/paper/2510.06826/) (2025)
- [Command R7B Arabic: A Small, Enterprise Focused, Multilingual, and Culturally Aware Arabic LLM](https://mlsanity.com/paper/2503.14603/) (2025)

## Abstract (arXiv)

Continual pre-training is widely used to adapt LLMs to target languages and domains, yet the mixture ratio of training data remains a sensitive hyperparameter that is expensive to tune: they must be fixed before training begins, and a suboptimal choice can waste weeks of compute. In this work, we propose OptiMer, which decouples ratio selection from training: we train one CPT model per dataset, extract each model's distribution vector, which represents the parameter shift induced by that dataset, and search for optimal composition weights post-hoc via Bayesian optimization. Experiments on Gemma 3 27B across languages (Japanese, Chinese) and domains (Math, Code) show that OptiMer consistently outperforms data mixture and model averaging baselines with 15-35 times lower search cost. Key findings reveal that 1) the optimized weights can be interpreted as data mixture ratios, and retraining with these ratios improves data mixture CPT, and 2) the same vector pool can be re-optimized for a given objective without any retraining, producing target-tailored models on demand. Our work establishes that data mixture ratio selection, traditionally a pre-training decision, can be reformulated as a post-hoc optimization over distribution vectors, offering a more flexible paradigm for continual pre-training.