# Instruction Data Selection via Answer Divergence

arXiv: https://arxiv.org/abs/2604.10448 · HTML: https://mlsanity.com/paper/2604.10448/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 37 references that are in the map.
- First posted on arXiv 12 Apr 2026.

## Builds on (most cited first, 27 of 27)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [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)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [LIMA: Less Is More for Alignment](https://mlsanity.com/paper/2305.11206/) (2023)
- [C-Eval: A Multi-Level Multi-Discipline Chinese Evaluation Suite for Foundation Models](https://mlsanity.com/paper/2305.08322/) (2023)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [Layer by Layer: Uncovering Hidden Representations in Language Models](https://mlsanity.com/paper/2502.02013/) (2025)
- [From Quantity to Quality: Boosting LLM Performance with Self-Guided Data Selection for Instruction Tuning](https://mlsanity.com/paper/2308.12032/) (2023)
- [Superfiltering: Weak-to-Strong Data Filtering for Fast Instruction-Tuning](https://mlsanity.com/paper/2402.00530/) (2024)
- [A Survey on Data Selection for LLM Instruction Tuning](https://mlsanity.com/paper/2402.05123/) (2024)
- [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)
- [Smaller Language Models are capable of selecting Instruction-Tuning Training Data for Larger Language Models](https://mlsanity.com/paper/2402.10430/) (2024)
- [FinCARDS: Card-Based Analyst Reranking for Financial Document Question Answering](https://mlsanity.com/paper/2601.06992/) (2026)
- [Take the essence and discard the dross: A Rethinking on Data Selection for Fine-Tuning Large Language Models](https://mlsanity.com/paper/2406.14115/) (2024)
- [MIG: Automatic Data Selection for Instruction Tuning by Maximizing Information Gain in Semantic Space](https://mlsanity.com/paper/2504.13835/) (2025)
- [Data Selection for Multi-turn Dialogue Instruction Tuning](https://mlsanity.com/paper/2604.07892/) (2026)
- [Evaluating Generalization and Representation Stability in Small LMs via Prompting, Fine-Tuning and Out-of-Distribution Prompts](https://mlsanity.com/paper/2506.17289/) (2025)

## Built on by (most cited first, 3 of 3)

- [Beyond Semantic Relevance: Counterfactual Risk Minimization for Robust Retrieval-Augmented Generation](https://mlsanity.com/paper/2605.01302/) (2026)
- [Generating Effective CoT Traces for Mitigating Causal Hallucination](https://mlsanity.com/paper/2604.12748/) (2026)
- [Chain of Evidence: Pixel-Level Visual Attribution for Iterative Retrieval-Augmented Generation](https://mlsanity.com/paper/2605.01284/) (2026)

## Abstract (arXiv)

Instruction tuning relies on large instruction-response corpora whose quality and composition strongly affect downstream performance. We propose Answer Divergence-Guided Selection (ADG), which selects instruction data based on the geometric structure of multi-sample outputs. ADG draws several high-temperature generations per instruction, maps responses into an embedding space, and computes an output divergence score that jointly encodes dispersion magnitude and shape anisotropy. High scores correspond to instructions whose answers are both far apart and multi-modal, rather than clustered paraphrases along a single direction. Across two backbones and three public instruction pools, fine-tuning on only 10K ADG-selected examples consistently outperforms strong selectors on six benchmarks spanning reasoning, knowledge, and coding. Analyses further show that both dispersion magnitude and shape anisotropy are necessary, supporting answer divergence as a practical signal for instruction data selection. Code and appendix are included in the supplementary materials.