# Synthetic Text Generation for Training Large Language Models via Gradient Matching

arXiv: https://arxiv.org/abs/2502.17607 · HTML: https://mlsanity.com/paper/2502.17607/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 61 references that are in the map.
- First posted on arXiv 24 Feb 2025.

## Builds on (most cited first, 30 of 36)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Hierarchical Neural Story Generation](https://mlsanity.com/paper/1805.04833/) (2018)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [BloombergGPT: A Large Language Model for Finance](https://mlsanity.com/paper/2303.17564/) (2023)
- [CTRL: A Conditional Transformer Language Model for Controllable Generation](https://mlsanity.com/paper/1909.05858/) (2019)
- [Inverting Gradients -- How easy is it to break privacy in federated learning?](https://mlsanity.com/paper/2003.14053/) (2020)
- [Textbooks Are All You Need II: phi-1.5 technical report](https://mlsanity.com/paper/2309.05463/) (2023)
- [Dataset Condensation with Gradient Matching](https://mlsanity.com/paper/2006.05929/) (2020)
- [DiffuSeq: Sequence to Sequence Text Generation with Diffusion Models](https://mlsanity.com/paper/2210.08933/) (2022)
- [Dataset Distillation by Matching Training Trajectories](https://mlsanity.com/paper/2203.11932/) (2022)
- [Dataset Condensation with Distribution Matching](https://mlsanity.com/paper/2110.04181/) (2021)
- [Not All Samples Are Created Equal: Deep Learning with Importance Sampling](https://mlsanity.com/paper/1803.00942/) (2018)
- [Dataset Condensation with Differentiable Siamese Augmentation](https://mlsanity.com/paper/2102.08259/) (2021)
- [Large Language Model as Attributed Training Data Generator: A Tale of Diversity and Bias](https://mlsanity.com/paper/2306.15895/) (2023)
- [Does Fine-Tuning LLMs on New Knowledge Encourage Hallucinations?](https://mlsanity.com/paper/2405.05904/) (2024)
- [Dataset Meta-Learning from Kernel Ridge-Regression](https://mlsanity.com/paper/2011.00050/) (2020)
- [ZeroGen: Efficient Zero-shot Learning via Dataset Generation](https://mlsanity.com/paper/2202.07922/) (2022)
- [Generating Training Data with Language Models: Towards Zero-Shot Language Understanding](https://mlsanity.com/paper/2202.04538/) (2022)
- [Dataset Condensation via Efficient Synthetic-Data Parameterization](https://mlsanity.com/paper/2205.14959/) (2022)
- [Efficient Dataset Distillation Using Random Feature Approximation](https://mlsanity.com/paper/2210.12067/) (2022)
- [Soft-Label Dataset Distillation and Text Dataset Distillation](https://mlsanity.com/paper/1910.02551/) (2019)
- [Synthetic Data Generation with Large Language Models for Text Classification: Potential and Limitations](https://mlsanity.com/paper/2310.07849/) (2023)
- [TAG: Gradient Attack on Transformer-based Language Models](https://mlsanity.com/paper/2103.06819/) (2021)
- [Extremely Low Bit Neural Network: Squeeze the Last Bit Out with ADMM](https://mlsanity.com/paper/1707.09870/) (2017)
- [Controlled Text Generation via Language Model Arithmetic](https://mlsanity.com/paper/2311.14479/) (2023)
- [SmallToLarge (S2L): Scalable Data Selection for Fine-tuning Large Language Models by Summarizing Training Trajectories of Small Models](https://mlsanity.com/paper/2403.07384/) (2024)
- [Data Distillation for Text Classification](https://mlsanity.com/paper/2104.08448/) (2021)
- [DiLM: Distilling Dataset into Language Model for Text-level Dataset Distillation](https://mlsanity.com/paper/2404.00264/) (2024)

## Built on by (most cited first, 10 of 10)

- [SIPDO: Closed-Loop Prompt Optimization via Synthetic Data Feedback](https://mlsanity.com/paper/2505.19514/) (2025)
- [Approximating Language Model Training Data from Weights](https://mlsanity.com/paper/2506.15553/) (2025)
- [Synthetic Data-Driven Prompt Tuning for Financial QA over Tables and Documents](https://mlsanity.com/paper/2511.06292/) (2025)
- [Technical Report on Text Dataset Distillation](https://mlsanity.com/paper/2512.03967/) (2025)
- [DP-RFT: Learning to Generate Synthetic Text via Differentially Private Reinforcement Fine-Tuning](https://mlsanity.com/paper/2602.18633/) (2026)
- [Omnimodal Dataset Distillation via High-order Proxy Alignment](https://mlsanity.com/paper/2604.10666/) (2026)
- [Synthetic Worlds for Temporal Evaluation and Knowledge Updating in LLMs](https://mlsanity.com/paper/2609.00184/) (2026)
- [Is Human-Readable Text Necessary for Effective LLM Fine-Tuning?](https://mlsanity.com/paper/2609.35868/) (2026)
- [Synthetic Data Characterization via Training Dynamics](https://mlsanity.com/paper/2609.39447/) (2026)
- [Fisher-Guided Submodular Data Selection for Continual Pre-Training of Large Language Models](https://mlsanity.com/paper/2610.02593/) (2026)

## Abstract (arXiv)

Synthetic data has the potential to improve the performance, training efficiency, and privacy of real training examples. Nevertheless, existing approaches for synthetic text generation are mostly heuristics and cannot generate human-readable text without compromising the privacy of real data, or provide performance guarantees for training Large Language Models (LLMs). In this work, we propose the first theoretically rigorous approach for generating synthetic human-readable text that provides convergence, performance, and privacy guarantees for fine-tuning LLMs on a target task. To do so, we leverage Alternating Direction Method of Multipliers (ADMM) that iteratively optimizes the embeddings of synthetic examples to match the noisy gradient of the target training or validation data, and maps them to a sequence of text tokens with low perplexity. In doing so, the generated synthetic text guarantees convergence of the model to a close neighborhood of the solution obtained by fine-tuning on real data and preserves their privacy. Experiments on various classification tasks confirm the effectiveness of our proposed approach. Our code is available at https://github.com/BigML-CS-UCLA/GRADMM.