# QAQ: Bidirectional Semantic Coherence for Selecting High-Quality Synthetic Code Instructions

arXiv: https://arxiv.org/abs/2603.12165 · HTML: https://mlsanity.com/paper/2603.12165/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 36 references that are in the map.
- First posted on arXiv 12 Mar 2026.

## Builds on (most cited first, 25 of 25)

- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [DeepSeek-Coder: When the Large Language Model Meets Programming -- The Rise of Code Intelligence](https://mlsanity.com/paper/2401.14196/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [WizardCoder: Empowering Code Large Language Models with Evol-Instruct](https://mlsanity.com/paper/2306.08568/) (2023)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [Magpie: Alignment Data Synthesis from Scratch by Prompting Aligned LLMs with Nothing](https://mlsanity.com/paper/2406.08464/) (2024)
- [From Quantity to Quality: Boosting LLM Performance with Self-Guided Data Selection for Instruction Tuning](https://mlsanity.com/paper/2308.12032/) (2023)
- [Magicoder: Empowering Code Generation with OSS-Instruct](https://mlsanity.com/paper/2312.02120/) (2023)
- [A Theory of Usable Information Under Computational Constraints](https://mlsanity.com/paper/2002.10689/) (2020)
- [Superfiltering: Weak-to-Strong Data Filtering for Fast Instruction-Tuning](https://mlsanity.com/paper/2402.00530/) (2024)
- [Rho-1: Not All Tokens Are What You Need](https://mlsanity.com/paper/2404.07965/) (2024)
- [Answers Unite! Unsupervised Metrics for Reinforced Summarization Models](https://mlsanity.com/paper/1909.01610/) (2019)
- [Large-Scale Data Selection for Instruction Tuning](https://mlsanity.com/paper/2503.01807/) (2025)
- [D3: Diversity, Difficulty, and Dependability-Aware Data Selection for Sample-Efficient LLM Instruction Tuning](https://mlsanity.com/paper/2503.11441/) (2025)
- [Token Weighting for Long-Range Language Modeling](https://mlsanity.com/paper/2503.09202/) (2025)
- [T-SHIRT: Token-Selective Hierarchical Data Selection for Instruction Tuning](https://mlsanity.com/paper/2506.01317/) (2025)
- [ProDS: Preference-oriented Data Selection for Instruction Tuning](https://mlsanity.com/paper/2505.12754/) (2025)

## Abstract (arXiv)

Synthetic data has become essential for training code generation models, yet it introduces significant noise and hallucinations that are difficult to detect with current metrics. Existing data selection methods like Instruction-Following Difficulty (IFD) typically assess how hard a model generates an answer given a query (A|Q). However, this metric is ambiguous on noisy synthetic data, where low probability can distinguish between intrinsic task complexity and model-generated hallucinations. Here, we propose QAQ, a novel data selection framework that evaluates data quality from the reverse direction: how well can the answer predict the query (Q|A)? We define Reverse Mutual Information (RMI) to quantify the information gain about the query conditioned on the answer. Our analyses reveal that both extremes of RMI signal quality issues: low RMI indicates semantic misalignment, while excessively high RMI may contain defect patterns that LLMs easily recognize. Furthermore, we introduce a selection strategy based on the disagreement between strong and weak models to identify samples that are valid yet challenging. Experiments across three datasets spanning code generation (WarriorCoder, Magpie-Qwen2.5-Coder-Pro-300K) and math reasoning (OpenR1-Math-220k) demonstrate that selecting just 25% of data using stratified RMI matches full-data performance while being consistently competitive with or better than existing data selection methods. Our approach highlights the importance of bidirectional semantic coherence in synthetic data curation, offering a scalable pathway to reduce computational costs without sacrificing model capability. Code is available at https://github.com/XXSg559/QAQ.