# Optimsyn: Influence-Guided Rubrics Optimization for Synthetic Data Generation

arXiv: https://arxiv.org/abs/2604.00536 · HTML: https://mlsanity.com/paper/2604.00536/

## 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 34 of its 42 references that are in the map.
- First posted on arXiv 1 Apr 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, 30 of 34)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [PubMedQA: A Dataset for Biomedical Research Question Answering](https://mlsanity.com/paper/1909.06146/) (2019)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [Instruction Tuning with GPT-4](https://mlsanity.com/paper/2304.03277/) (2023)
- [WildChat: 1M ChatGPT Interaction Logs in the Wild](https://mlsanity.com/paper/2405.01470/) (2024)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [HealthBench: Evaluating Large Language Models Towards Improved Human Health](https://mlsanity.com/paper/2505.08775/) (2025)
- [Data Selection for Language Models via Importance Resampling](https://mlsanity.com/paper/2302.03169/) (2023)
- [ChatDoctor: A Medical Chat Model Fine-Tuned on a Large Language Model Meta-AI (LLaMA) Using Medical Domain Knowledge](https://mlsanity.com/paper/2303.14070/) (2023)
- [MEDITRON-70B: Scaling Medical Pretraining for Large Language Models](https://mlsanity.com/paper/2311.16079/) (2023)
- [QuRating: Selecting High-Quality Data for Training Language Models](https://mlsanity.com/paper/2402.09739/) (2024)
- [MAmmoTH2: Scaling Instructions from the Web](https://mlsanity.com/paper/2405.03548/) (2024)
- [BIG-Bench Extra Hard](https://mlsanity.com/paper/2502.19187/) (2025)
- [MATES: Model-Aware Data Selection for Efficient Pretraining with Data Influence Models](https://mlsanity.com/paper/2406.06046/) (2024)
- [Data Selection via Optimal Control for Language Models](https://mlsanity.com/paper/2410.07064/) (2024)
- [Learning to Generate Instruction Tuning Datasets for Zero-Shot Task Adaptation](https://mlsanity.com/paper/2402.18334/) (2024)
- [ReasonMed: A 370K Multi-Agent Generated Dataset for Advancing Medical Reasoning](https://mlsanity.com/paper/2506.09513/) (2025)
- [Predictive Data Selection: The Data That Predicts Is the Data That Teaches](https://mlsanity.com/paper/2503.00808/) (2025)
- [Meta-rater: A Multi-dimensional Data Selection Method for Pre-training Language Models](https://mlsanity.com/paper/2504.14194/) (2025)
- [Condor: Enhance LLM Alignment with Knowledge-Driven Data Synthesis and Refinement](https://mlsanity.com/paper/2501.12273/) (2025)
- [Montessori-Instruct: Generate Influential Training Data Tailored for Student Learning](https://mlsanity.com/paper/2410.14208/) (2024)

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

- [Socratic-SWE: Self-Evolving Coding Agents via Trace-Derived Agent Skills](https://mlsanity.com/paper/2606.07412/) (2026)
- [INFUSER: Influence-Guided Self-Evolution Improves Reasoning](https://mlsanity.com/paper/2606.09052/) (2026)
- [CompassPlay: Rewarding the Proposer for Where It Moves the Solver](https://mlsanity.com/paper/2609.32228/) (2026)
- [Training-Aware Target Coverage for Synthetic Data Selection](https://mlsanity.com/paper/2610.00814/) (2026)
- [From Structure to Validity: Mechanism-Guided Generation and Refinement of LLM Rubrics](https://mlsanity.com/paper/2610.13375/) (2026)
- [AssetForge: Asset-Augmented Task Synthesis for Business Automation Agents](https://mlsanity.com/paper/2610.18330/) (2026)

## Abstract (arXiv)

Large language models (LLMs) achieve strong downstream performance largely due to abundant supervised fine-tuning (SFT) data. However, high-quality SFT data in knowledge-intensive domains such as humanities, social sciences, medicine, law, and finance is scarce because expert curation is expensive, privacy constraints are strict, and label consistency is hard to ensure. Recent work uses synthetic data, typically by prompting a generator over domain documents and filtering outputs with handcrafted rubrics. Yet rubric design is expert-dependent, transfers poorly across domains, and is often optimized through a brittle heuristic loop of writing rubrics, synthesizing data, training, inspecting results, and manually guessing revisions. This process lacks reliable quantitative feedback about how a rubric affects downstream performance. We propose evaluating synthetic data by its training utility on the target model and using this signal to guide data generation. Inspired by influence estimation, we adopt an optimizer-aware estimator that uses gradient information to quantify each synthetic sample's contribution to a target model's objective on specific tasks. Our analysis shows that even when synthetic and real samples are close in embedding space, their influence on learning can differ substantially. Based on this insight, we propose an optimization-based framework that adapts rubrics using target-model feedback. We provide lightweight guiding text and use a rubric-specialized model to generate task-conditioned rubrics. Influence score is used as the reward to optimize the rubric generator with reinforcement learning. Experiments across domains, target models, and data generators show consistent improvements and strong generalization without task-specific tuning.