# Training-Aware Target Coverage for Synthetic Data Selection

arXiv: https://arxiv.org/abs/2610.00814 · HTML: https://mlsanity.com/paper/2610.00814/

## Key facts

- No citing papers in the map yet (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 29 of its 36 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## 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, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [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)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Distilling Step-by-Step! Outperforming Larger Language Models with Less Training Data and Smaller Model Sizes](https://mlsanity.com/paper/2305.02301/) (2023)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Textbooks Are All You Need](https://mlsanity.com/paper/2306.11644/) (2023)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [Scaling Synthetic Data Creation with 1,000,000,000 Personas](https://mlsanity.com/paper/2406.20094/) (2024)
- [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)
- [The Vendi Score: A Diversity Evaluation Metric for Machine Learning](https://mlsanity.com/paper/2210.02410/) (2022)
- [Self-Consuming Generative Models Go MAD](https://mlsanity.com/paper/2307.01850/) (2023)
- [Prioritized Training on Points that are Learnable, Worth Learning, and Not Yet Learnt](https://mlsanity.com/paper/2206.07137/) (2022)
- [GLISTER: Generalization based Data Subset Selection for Efficient and Robust Learning](https://mlsanity.com/paper/2012.10630/) (2020)
- [Limitations of the Empirical Fisher Approximation for Natural Gradient Descent](https://mlsanity.com/paper/1905.12558/) (2019)
- [Synthetic Data (Almost) from Scratch: Generalized Instruction Tuning for Language Models](https://mlsanity.com/paper/2402.13064/) (2024)
- [Gone Fishing: Neural Active Learning with Fisher Embeddings](https://mlsanity.com/paper/2106.09675/) (2021)
- [Prismatic Synthesis: Gradient-based Data Diversification Boosts Generalization in LLM Reasoning](https://mlsanity.com/paper/2505.20161/) (2025)
- [Let's Synthesize Step by Step: Iterative Dataset Synthesis with Large Language Models by Extrapolating Errors from Small Models](https://mlsanity.com/paper/2310.13671/) (2023)
- [Fill In The Gaps: Model Calibration and Generalization with Synthetic Data](https://mlsanity.com/paper/2410.10864/) (2024)
- [High-dimensional Analysis of Synthetic Data Selection](https://mlsanity.com/paper/2510.08123/) (2025)
- [SPICE: Submodular Penalized Information-Conflict Selection for Efficient Large Language Model Training](https://mlsanity.com/paper/2601.23155/) (2026)
- [Escaping Model Collapse via Synthetic Data Verification: Near-term Improvements and Long-term Convergence](https://mlsanity.com/paper/2510.16657/) (2025)
- [Optimsyn: Influence-Guided Rubrics Optimization for Synthetic Data Generation](https://mlsanity.com/paper/2604.00536/) (2026)

## Abstract (arXiv)

Synthetic data are increasingly used to scale LLM training, yet more synthetic data do not necessarily produce better models. Useful synthetic data must add information relevant to the target task without introducing errors that offset their benefit, and the value of an example can change as the training set grows. We develop a linear theory that characterizes this tradeoff and determines where synthetic data are useful, how much should be added, and the marginal value of adding one example to an existing set. The analysis shows the conditions when input coverage alone is sufficient and when synthetic errors must also be considered. Guided by these results, we introduce Training-Aware Target Coverage (TATC), a synthetic data selection method for LLM fine-tuning. TATC identifies candidates whose training effects are beneficial to the target task and selects among them to expand coverage of target-relevant directions not already represented by the available data. Experiments on text and image data verify the linear theory. With mathematical reasoning tasks, TATC selects synthetic solutions for fine-tuning Qwen2.5-Math-1.5B-Instruct and outperforms alternative synthetic-data selection methods on GSM8K across selection budgets. In summary, we provide a principled approach to synthetic data selection by quantifying and maximizing its value to the target task.