# Towards Active Synthetic Data Generation for Finetuning Language Models

arXiv: https://arxiv.org/abs/2512.00884 · HTML: https://mlsanity.com/paper/2512.00884/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in LLM synthetic data generation, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 53 of its 71 references that are in the map.
- First posted on arXiv 30 Nov 2025.

## Placed in

- Synthetic data and self-improvement for LLMs / [LLM synthetic data generation](https://mlsanity.com/synth/llm-synthetic-data-generation/)

## Builds on (most cited first, 30 of 53)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [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)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [Instruction Tuning with GPT-4](https://mlsanity.com/paper/2304.03277/) (2023)
- [LLM Evaluators Recognize and Favor Their Own Generations](https://mlsanity.com/paper/2404.13076/) (2024)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Deep Batch Active Learning by Diverse, Uncertain Gradient Lower Bounds](https://mlsanity.com/paper/1906.03671/) (2019)
- [RewardBench: Evaluating Reward Models for Language Modeling](https://mlsanity.com/paper/2403.13787/) (2024)
- [BatchBALD: Efficient and Diverse Batch Acquisition for Deep Bayesian Active Learning](https://mlsanity.com/paper/1906.08158/) (2019)
- [What Makes Good Data for Alignment? A Comprehensive Study of Automatic Data Selection in Instruction Tuning](https://mlsanity.com/paper/2312.15685/) (2023)
- [Selection via Proxy: Efficient Data Selection for Deep Learning](https://mlsanity.com/paper/1906.11829/) (2019)
- [Language Models Are Greedy Reasoners: A Systematic Formal Analysis of Chain-of-Thought](https://mlsanity.com/paper/2210.01240/) (2022)
- [Not All Samples Are Created Equal: Deep Learning with Importance Sampling](https://mlsanity.com/paper/1803.00942/) (2018)
- [From Quantity to Quality: Boosting LLM Performance with Self-Guided Data Selection for Instruction Tuning](https://mlsanity.com/paper/2308.12032/) (2023)
- [Small Language Models are the Future of Agentic AI](https://mlsanity.com/paper/2506.02153/) (2025)
- [Prioritized Training on Points that are Learnable, Worth Learning, and Not Yet Learnt](https://mlsanity.com/paper/2206.07137/) (2022)
- [Orca-Math: Unlocking the potential of SLMs in Grade School Math](https://mlsanity.com/paper/2402.14830/) (2024)

## Built on by (most cited first, 6 of 6)

- [Exploring Autonomous Agentic Data Engineering for Model Specialization](https://mlsanity.com/paper/2605.30407/) (2026)
- [When the Strongest Teacher Is Not the Best Teacher: Student-Centric Answer Selection](https://mlsanity.com/paper/2605.26872/) (2026)
- [What Drives Interactive Improvement from Feedback?](https://mlsanity.com/paper/2606.30774/) (2026)
- [QVAC Genesis III: A Large-Scale, High-Quality Open Synthetic STEM Corpus for Efficient Language Model Pre-Training](https://mlsanity.com/paper/2609.19513/) (2026)
- [AutoDataBench: Can Agents Write the Data That Feeds the Self-Improvement Loop?](https://mlsanity.com/paper/2609.35025/) (2026)
- [G"odel Forest: Balancing Search Depth and Breadth for Data-Centric Recursive Self-Improvement](https://mlsanity.com/paper/2609.36675/) (2026)

## Abstract (arXiv)

A common and effective means for improving language model capabilities involves finetuning a ``student'' language model's parameters on generations from a more proficient ``teacher'' model. Termed ``synthetic data'', these generations are often produced before any student finetuning, but some work has considered generating new synthetic samples as training progresses. This paper studies and advocates for the latter case, where data are generated in an iterative, closed-loop fashion that is guided by the current state of the student model. For a fixed budget of generated samples, or a budget in terms of compute spent querying a teacher, we show that this curation of finetuning data affords improved student performance over static generation. Further, while there have been several LLM-specific methods proposed that operate in this regime, we find that simple, inexpensive selection criteria from the active learning literature tend to be most performant. We validate these claims across four mathematical and logical reasoning datasets using four different small language models.