# Find Your Optimal Teacher: Personalized Data Synthesis via Router-Guided Multi-Teacher Distillation

arXiv: https://arxiv.org/abs/2510.10925 · HTML: https://mlsanity.com/paper/2510.10925/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Placed in Code and instruction data synthesis, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 31 of its 52 references that are in the map.
- First posted on arXiv 13 Oct 2025.

## Placed in

- Synthetic data and self-improvement for LLMs / [Code and instruction data synthesis](https://mlsanity.com/synth/code-and-instruction-data-synthesis/)
- Knowledge distillation / [General knowledge distillation methods](https://mlsanity.com/distill/general-knowledge-distillation-methods/)

## Builds on (most cited first, 30 of 31)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition](https://mlsanity.com/paper/2504.21801/) (2025)
- [On LLMs-Driven Synthetic Data Generation, Curation, and Evaluation: A Survey](https://mlsanity.com/paper/2406.15126/) (2024)
- [Large Language Models for Data Annotation and Synthesis: A Survey](https://mlsanity.com/paper/2402.13446/) (2024)
- [Distilling Reasoning Capabilities into Smaller Language Models](https://mlsanity.com/paper/2212.00193/) (2022)
- [Small Models Struggle to Learn from Strong Reasoners](https://mlsanity.com/paper/2502.12143/) (2025)
- [Beyond Pass@1: Self-Play with Variational Problem Synthesis Sustains RLVR](https://mlsanity.com/paper/2508.14029/) (2025)
- [SwS: Self-aware Weakness-driven Problem Synthesis in Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.08989/) (2025)
- [Evaluating Language Models as Synthetic Data Generators](https://mlsanity.com/paper/2412.03679/) (2024)
- [TreeReview: A Dynamic Tree of Questions Framework for Deep and Efficient LLM-based Scientific Peer Review](https://mlsanity.com/paper/2506.07642/) (2025)
- [ToolFlow: Boosting LLM Tool-Calling Through Natural and Coherent Dialogue Synthesis](https://mlsanity.com/paper/2410.18447/) (2024)
- [SMoA: Improving Multi-agent Large Language Models with Sparse Mixture-of-Agents](https://mlsanity.com/paper/2411.03284/) (2024)
- [Chain-of-Reasoning: Towards Unified Mathematical Reasoning in Large Language Models via a Multi-Paradigm Perspective](https://mlsanity.com/paper/2501.11110/) (2025)
- [SimRAG: Self-Improving Retrieval-Augmented Generation for Adapting Large Language Models to Specialized Domains](https://mlsanity.com/paper/2410.17952/) (2024)
- [PromptKD: Distilling Student-Friendly Knowledge for Generative Language Models via Prompt Tuning](https://mlsanity.com/paper/2402.12842/) (2024)
- [Initialization using Update Approximation is a Silver Bullet for Extremely Efficient Low-Rank Fine-Tuning](https://mlsanity.com/paper/2411.19557/) (2024)
- [BPO: Towards Balanced Preference Optimization between Knowledge Breadth and Depth in Alignment](https://mlsanity.com/paper/2411.10914/) (2024)
- [Genetic Instruct: Scaling up Synthetic Generation of Coding Instructions for Large Language Models](https://mlsanity.com/paper/2407.21077/) (2024)
- [Learning from Committee: Reasoning Distillation from a Mixture of Teachers with Peer-Review](https://mlsanity.com/paper/2410.03663/) (2024)
- [Multilingual Large Language Models and Curse of Multilinguality](https://mlsanity.com/paper/2406.10602/) (2024)
- [Task Oriented In-Domain Data Augmentation](https://mlsanity.com/paper/2406.16694/) (2024)
- [GuiLoMo: Allocating Expert Number and Rank for LoRA-MoE via Bilevel Optimization with GuidedSelection Vectors](https://mlsanity.com/paper/2506.14646/) (2025)
- [Fostering Natural Conversation in Large Language Models with NICO: a Natural Interactive COnversation dataset](https://mlsanity.com/paper/2408.09330/) (2024)
- [Multiple Choice Learning of Low-Rank Adapters for Language Modeling](https://mlsanity.com/paper/2507.10419/) (2025)

## Built on by (most cited first, 15 of 15)

- [ToolPRMBench: Evaluating and Advancing Process Reward Models for Tool-using Agents](https://mlsanity.com/paper/2601.12294/) (2026)
- [Sustainable Hybrid Document-Routed Retrieval for Financial RAG: Resolving the Robustness-Precision Trade-off](https://mlsanity.com/paper/2603.26815/) (2026)
- [Bridging Reasoning Trajectories in On-Policy Distillation via Near-Future Guidance](https://mlsanity.com/paper/2606.00305/) (2026)
- [Cornerstones or Stumbling Blocks? Deciphering the Rock Tokens in On-Policy Distillation](https://mlsanity.com/paper/2605.09253/) (2026)
- [Why Supervised Fine-Tuning Fails to Learn: A Systematic Study of Incomplete Learning in Large Language Models](https://mlsanity.com/paper/2604.10079/) (2026)
- [Reason Only When Needed: Efficient Generative Reward Modeling via Model-Internal Uncertainty](https://mlsanity.com/paper/2604.10072/) (2026)
- [Residual Decoding: Mitigating Hallucinations in Large Vision-Language Models via History-Aware Residual Guidance](https://mlsanity.com/paper/2602.01047/) (2026)
- [MIS-HCC: Hierarchical Channel Clustering for Efficient Medical Image Segmentation](https://mlsanity.com/paper/2607.17329/) (2026)
- [MUSE: Resolving Manifold Misalignment in Visual Tokenization via Topological Orthogonality](https://mlsanity.com/paper/2605.05646/) (2026)
- [Polyglot Teachers: Evaluating Language Models for Multilingual Synthetic Data Generation](https://mlsanity.com/paper/2604.11290/) (2026)
- [When the Strongest Teacher Is Not the Best Teacher: Student-Centric Answer Selection](https://mlsanity.com/paper/2605.26872/) (2026)
- [IMAGINE: Adaptive Schema-Imagery Enhanced Composition for Composed Video Retrieval](https://mlsanity.com/paper/2606.08144/) (2026)
- [Energy-Efficient On-Device RAG on a Mobile NPU: System Design and Benchmark on Snapdragon X Elite](https://mlsanity.com/paper/2606.11257/) (2026)
- [MOSAIC: Orchestrating Collaborative Knowledge Tracing with Hierarchical Semantic Alignment](https://mlsanity.com/paper/2606.29049/) (2026)
- [Hallucination Self-Play: Bootstrapping Reinforced Detector via Evolved Generator](https://mlsanity.com/paper/2607.07993/) (2026)

## Abstract (arXiv)

Training student models on synthetic data generated by strong teacher models is a promising way to distilling the capabilities of teachers. However, recent studies show that stronger models are not always optimal teachers, revealing a mismatch between teacher outputs and student learnability. To address this issue, we propose PerSyn (Personalized data Synthesis), a novel synthesis strategy that operates under a new ``Route then Generate'' paradigm to create data tailored to each student model, enabling it to learn more effectively. Specifically, PerSyn first assigns each prompt to its optimal teacher via a query-level router that jointly considers student learnability and teacher response quality. Each teacher then synthesizes data only for its assigned prompts, making the process more efficient than the conventional ``Generate then Select'' paradigm, where all teachers must generate parallel responses for the entire prompt set before constructing the final dataset. Extensive experiments across different model families and scales demonstrate that PerSyn consistently achieves superior or comparable performance to all baselines in instruct tuning and math reasoning settings. Further analysis verifies the effectiveness of PerSyn and offers extra insights to propel future research.