# Surveying the Effects of Quality, Diversity, and Complexity in Synthetic Data From Large Language Models

arXiv: https://arxiv.org/abs/2412.02980 · HTML: https://mlsanity.com/paper/2412.02980/

## Key facts

- Cited by 35 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 192 of its 247 references that are in the map.
- First posted on arXiv 4 Dec 2024.

## 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 192)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [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)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)

## Built on by (most cited first, 30 of 35)

- [Darwin Godel Machine: Open-Ended Evolution of Self-Improving Agents](https://mlsanity.com/paper/2505.22954/) (2025)
- [Big-Math: A Large-Scale, High-Quality Math Dataset for Reinforcement Learning in Language Models](https://mlsanity.com/paper/2502.17387/) (2025)
- [Prismatic Synthesis: Gradient-based Data Diversification Boosts Generalization in LLM Reasoning](https://mlsanity.com/paper/2505.20161/) (2025)
- [Demystifying Reinforcement Learning in Agentic Reasoning](https://mlsanity.com/paper/2510.11701/) (2025)
- [Demystifying Synthetic Data in LLM Pre-training: A Systematic Study of Scaling Laws, Benefits, and Pitfalls](https://mlsanity.com/paper/2510.01631/) (2025)
- [How Instruction and Reasoning Data shape Post-Training: Data Quality through the Lens of Layer-wise Gradients](https://mlsanity.com/paper/2504.10766/) (2025)
- [SPARQ: Synthetic Problem Generation for Reasoning via Quality-Diversity Algorithms](https://mlsanity.com/paper/2506.06499/) (2025)
- [Middo: Model-Informed Dynamic Data Optimization for Enhanced LLM Fine-Tuning via Closed-Loop Learning](https://mlsanity.com/paper/2508.21589/) (2025)
- [Learning Next Action Predictors from Human-Computer Interaction](https://mlsanity.com/paper/2603.05923/) (2026)
- [Survey and Experiments on Mental Disorder Detection via Social Media: From Large Language Models and RAG to Agents](https://mlsanity.com/paper/2504.02800/) (2025)
- [RePro: Training Language Models to Faithfully Recycle the Web for Pretraining](https://mlsanity.com/paper/2510.10681/) (2025)
- [Reasoning-Driven Synthetic Data Generation and Evaluation](https://mlsanity.com/paper/2603.29791/) (2026)
- [Detecting and Suppressing Reward Hacking with Gradient Fingerprints](https://mlsanity.com/paper/2604.16242/) (2026)
- [A Structured Review of Underwater Object Detection Challenges and Solutions: From Traditional to Large Vision Language Models](https://mlsanity.com/paper/2509.08490/) (2025)
- [Even Small Reasoners Should Quote Their Sources: Introducing the Pleias-RAG Model Family](https://mlsanity.com/paper/2504.18225/) (2025)
- [Filtering with Confidence: When Data Augmentation Meets Conformal Prediction](https://mlsanity.com/paper/2509.21479/) (2025)
- [Privasis: Synthesizing the Largest "Public" Private Dataset from Scratch](https://mlsanity.com/paper/2602.03183/) (2026)
- [Generating Pretraining Tokens from Organic Data for Data-Bound Scaling](https://mlsanity.com/paper/2605.17849/) (2026)
- [Mechanistic Circuit Identification for Controllable Data Generation](https://mlsanity.com/paper/2608.24065/) (2026)
- [Quality over Quantity: An Effective Large-Scale Data Reduction Strategy Based on Pointwise V-Information](https://mlsanity.com/paper/2507.00038/) (2025)
- [Data Value in the Age of Scaling: Understanding LLM Scaling Dynamics Under Real-Synthetic Data Mixtures](https://mlsanity.com/paper/2511.13640/) (2025)
- [EnterpriseLab: A Full-Stack Platform for developing and deploying agents in Enterprises](https://mlsanity.com/paper/2603.21630/) (2026)
- [Adversarial Arena: Crowdsourcing Data Generation through Interactive Competition](https://mlsanity.com/paper/2604.17803/) (2026)
- [QDTraj: Exploration of Diverse Trajectory Primitives for Articulated Objects Robotic Manipulation](https://mlsanity.com/paper/2604.22551/) (2026)
- [Transformers as Cross-Task Learners: Shared Structure Drives Sample Efficiency in In-Context Learning](https://mlsanity.com/paper/2609.29060/) (2026)
- [Language Models Might Not Understand You: Evaluating Theory of Mind via Story Prompting](https://mlsanity.com/paper/2506.19089/) (2025)
- [Input-Time Scaling: Adding Noise and Irrelevance into Less-Is-More Drastically Improves Reasoning Performance and Efficiency](https://mlsanity.com/paper/2508.13654/) (2025)
- [Waste-Bench: A Comprehensive Benchmark for Evaluating VLLMs in Cluttered Environments](https://mlsanity.com/paper/2509.00176/) (2025)
- [Complexity-Regularized Proximal Policy Optimization](https://mlsanity.com/paper/2509.20509/) (2025)
- [SPA: A Simple but Tough-to-Beat Baseline for Knowledge Injection](https://mlsanity.com/paper/2603.22213/) (2026)

## Abstract (arXiv)

Synthetic data generation with Large Language Models is a promising paradigm for augmenting natural data over a nearly infinite range of tasks. Given this variety, direct comparisons among synthetic data generation algorithms are scarce, making it difficult to understand where improvement comes from and what bottlenecks exist. We propose to evaluate algorithms via the makeup of synthetic data generated by each algorithm in terms of data quality, diversity, and complexity. We choose these three characteristics for their significance in open-ended processes and the impact each has on the capabilities of downstream models. We find quality to be essential for in-distribution model generalization, diversity to be essential for out-of-distribution generalization, and complexity to be beneficial for both. Further, we emphasize the existence of Quality-Diversity trade-offs in training data and the downstream effects on model performance. We then examine the effect of various components in the synthetic data pipeline on each data characteristic. This examination allows us to taxonomize and compare synthetic data generation algorithms through the components they utilize and the resulting effects on data QDC composition. This analysis extends into a discussion on the importance of balancing QDC in synthetic data for efficient reinforcement learning and self-improvement algorithms. Analogous to the QD trade-offs in training data, often there exist trade-offs between model output quality and output diversity which impact the composition of synthetic data. We observe that many models are currently evaluated and optimized only for output quality, thereby limiting output diversity and the potential for self-improvement. We argue that balancing these trade-offs is essential to the development of future self-improvement algorithms and highlight a number of works making progress in this direction.