OptimSyn: Influence-Guided Rubrics Optimization for Synthetic Data Generation

Large language models (LLMs) achieve strong downstream performance largely due to abundant supervised fine-tuning (SFT) data that imparts problem-solving capabilities. However, as applications expand, high-quality SFT data in knowledge-intensive verticals (e.g., humanities and social sciences, medicine, law, finance) is exceedingly scarce: expert curation is costly, privacy constraints are strict, and label consistency is hard to guarantee. Recent work turns to synthetic data, typically prompting a teacher model over domain documents and filtering with handcrafted rubrics. Yet, rubric design is expert-dependent and rarely transfers across domains; moreover, prevalent heuristic optimization follows a brittle loop (write rubric $\rightarrow$ synthesize $\rightarrow$ train $\rightarrow$ inspect $\rightarrow$ guess tweaks) that lacks reliable, quantitative feedback about a rubric's true contribution to downstream performance. We argue for assessing synthetic data quality through its causal impact on the target model, using this feedback to guide data generation. Inspired by classic influence functions, we repurpose an optimizer-aware estimator that uses gradient information to quantify each synthetic sample's contribution to the objective of a given target model on specific tasks. Our analysis reveals a gap: although synthetic and real samples may be close in embedding space, their influence on learning can differ substantially. Building on this insight, we propose an optimization-based synthetic data framework that adapts rubrics with target-model feedback. Instead of manually engineering domain rubrics, we supply lightweight guiding text and delegate rubric generation to a rubric-specialized model conditioned on the task; crucially, rubric (and data) selection is supervised by estimated downstream impact rather than proxy formality. Empirically, the framework yields consistent gains across domains (HSS and health), target models (e.g., Qwen and Llama families), and data generators, demonstrating broad generalization and engineering portability without task-specific tuning.