# Subset Selection for Fine-Tuning: A Utility-Diversity Balanced Approach for Mathematical Domain Adaptation

arXiv: https://arxiv.org/abs/2505.01523 · HTML: https://mlsanity.com/paper/2505.01523/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 14 references that are in the map.
- First posted on arXiv 2 May 2025.

## Builds on (most cited first, 8 of 8)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [SmallToLarge (S2L): Scalable Data Selection for Fine-tuning Large Language Models by Summarizing Training Trajectories of Small Models](https://mlsanity.com/paper/2403.07384/) (2024)
- [SMART: Submodular Data Mixture Strategy for Instruction Tuning](https://mlsanity.com/paper/2403.08370/) (2024)

## Abstract (arXiv)

We propose a refined approach to efficiently fine-tune large language models (LLMs) on specific domains like the mathematical domain by employing a budgeted subset selection method. Our approach combines utility and diversity metrics to select the most informative and representative training examples. The final goal is to achieve near-full dataset performance with meticulously selected data points from the entire dataset while significantly reducing computational cost and training time and achieving competitive performance as the full dataset. The utility metric incorporates both perplexity and Chain-of-Thought (CoT) loss to identify challenging examples that contribute most to model learning, while the diversity metric ensures broad coverage across mathematical subdomains. We evaluate our method on LLaMA-3 8B and Phi-3 models, comparing against several baseline approaches, including random selection, diversity-based sampling, and existing state-of-the-art subset selection techniques.