# InstructDiff: Domain-Adaptive Data Selection via Differential Entropy for Efficient LLM Fine-Tuning

arXiv: https://arxiv.org/abs/2601.23006 · HTML: https://mlsanity.com/paper/2601.23006/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 45 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## Builds on (most cited first, 30 of 31)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [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)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [What Disease does this Patient Have? A Large-scale Open Domain Question Answering Dataset from Medical Exams](https://mlsanity.com/paper/2009.13081/) (2020)
- [LIMA: Less Is More for Alignment](https://mlsanity.com/paper/2305.11206/) (2023)
- [BigCodeBench: Benchmarking Code Generation with Diverse Function Calls and Complex Instructions](https://mlsanity.com/paper/2406.15877/) (2024)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [What Makes Good Data for Alignment? A Comprehensive Study of Automatic Data Selection in Instruction Tuning](https://mlsanity.com/paper/2312.15685/) (2023)
- [Magpie: Alignment Data Synthesis from Scratch by Prompting Aligned LLMs with Nothing](https://mlsanity.com/paper/2406.08464/) (2024)
- [From Quantity to Quality: Boosting LLM Performance with Self-Guided Data Selection for Instruction Tuning](https://mlsanity.com/paper/2308.12032/) (2023)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [QuRating: Selecting High-Quality Data for Training Language Models](https://mlsanity.com/paper/2402.09739/) (2024)
- [Superfiltering: Weak-to-Strong Data Filtering for Fast Instruction-Tuning](https://mlsanity.com/paper/2402.00530/) (2024)
- [Pass@K Policy Optimization: Solving Harder Reinforcement Learning Problems](https://mlsanity.com/paper/2505.15201/) (2025)
- [AceMath: Advancing Frontier Math Reasoning with Post-Training and Reward Modeling](https://mlsanity.com/paper/2412.15084/) (2024)
- [Knowledge Transfer from High-Resource to Low-Resource Programming Languages for Code LLMs](https://mlsanity.com/paper/2308.09895/) (2023)
- [Entropy Law: The Story Behind Data Compression and LLM Performance](https://mlsanity.com/paper/2407.06645/) (2024)
- [SelectIT: Selective Instruction Tuning for LLMs via Uncertainty-Aware Self-Reflection](https://mlsanity.com/paper/2402.16705/) (2024)
- [LIMI: Less is More for Agency](https://mlsanity.com/paper/2509.17567/) (2025)
- [Entropy-guided sequence weighting for efficient exploration in RL-based LLM fine-tuning](https://mlsanity.com/paper/2503.22456/) (2025)
- [FANNO: Augmenting High-Quality Instruction Data with Open-Sourced LLMs Only](https://mlsanity.com/paper/2408.01323/) (2024)
- [Top Pass: Improve Code Generation by Pass@k-Maximized Code Ranking](https://mlsanity.com/paper/2408.05715/) (2024)
- [How Do Your Code LLMs Perform? Empowering Code Instruction Tuning with High-Quality Data](https://mlsanity.com/paper/2409.03810/) (2024)
- [Uncertainty Under the Curve: A Sequence-Level Entropy Area Metric for Reasoning LLM](https://mlsanity.com/paper/2508.20384/) (2025)

## Built on by (most cited first, 1 of 1)

- [Weak-Driven Learning: How Weak Agents make Strong Agents Stronger](https://mlsanity.com/paper/2602.08222/) (2026)

## Abstract (arXiv)

Supervised fine-tuning (SFT) is fundamental to adapting large language models, yet training on complete datasets incurs prohibitive costs with diminishing returns. Existing data selection methods suffer from severe domain specificity: techniques optimized for general instruction-following fail on reasoning tasks, and vice versa. We observe that measuring entropy differences between base models and minimally instruction-tuned calibrated models reveals a pattern -- samples with the lowest differential entropy consistently yield optimal performance across domains, yet this principle manifests domain-adaptively: reasoning tasks favor entropy increase (cognitive expansion), while general tasks favor entropy decrease (cognitive compression). We introduce InstructDiff, a unified framework that operationalizes differential entropy as a domain-adaptive selection criterion through warmup calibration, bi-directional NLL filtering, and entropy-based ranking. Extensive experiments show that InstructDiff achieves 17% relative improvement over full data training on mathematical reasoning and 52% for general instruction-following, outperforming prior baselines while using only 10% of the data.