# Not All Synthetic Data Is Yours to Learn From

arXiv: https://arxiv.org/abs/2605.31126 · HTML: https://mlsanity.com/paper/2605.31126/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in LLM preference optimization methods, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 30 of its 33 references that are in the map.
- First posted on arXiv 29 May 2026.

## Placed in

- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)
- Synthetic data and self-improvement for LLMs / [LLM synthetic data generation](https://mlsanity.com/synth/llm-synthetic-data-generation/)
- LLM safety and security / [Machine unlearning](https://mlsanity.com/safety/machine-unlearning/)

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

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Extracting Training Data from Large Language Models](https://mlsanity.com/paper/2012.07805/) (2020)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [ZeRO: Memory Optimizations Toward Training Trillion Parameter Models](https://mlsanity.com/paper/1910.02054/) (2019)
- [Quantifying Memorization Across Neural Language Models](https://mlsanity.com/paper/2202.07646/) (2022)
- [TOFU: A Task of Fictitious Unlearning for LLMs](https://mlsanity.com/paper/2401.06121/) (2024)
- [Knowledge Unlearning for Mitigating Privacy Risks in Language Models](https://mlsanity.com/paper/2210.01504/) (2022)
- [Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models](https://mlsanity.com/paper/2312.06585/) (2023)
- [Self-Consuming Generative Models Go MAD](https://mlsanity.com/paper/2307.01850/) (2023)
- [Spurious Rewards: Rethinking Training Signals in RLVR](https://mlsanity.com/paper/2506.10947/) (2025)
- [Reasoning with Sampling: Your Base Model is Smarter Than You Think](https://mlsanity.com/paper/2510.14901/) (2025)
- [Llama-Embed-Nemotron-8B: A Universal Text Embedding Model for Multilingual and Cross-Lingual Tasks](https://mlsanity.com/paper/2511.07025/) (2025)
- [Beyond Model Collapse: Scaling Up with Synthesized Data Requires Verification](https://mlsanity.com/paper/2406.07515/) (2024)
- [Embarrassingly Simple Self-Distillation Improves Code Generation](https://mlsanity.com/paper/2604.01193/) (2026)
- [Self-Improving Diffusion Models with Synthetic Data](https://mlsanity.com/paper/2408.16333/) (2024)
- [Scalable Power Sampling: Unlocking Efficient, Training-Free Reasoning for LLMs via Distribution Sharpening](https://mlsanity.com/paper/2601.21590/) (2026)
- [Common Corpus: The Largest Collection of Ethical Data for LLM Pre-Training](https://mlsanity.com/paper/2506.01732/) (2025)
- [Soft Contamination Means Benchmarks Test Shallow Generalization](https://mlsanity.com/paper/2602.12413/) (2026)
- [Model Collapse Is Not a Bug but a Feature in Machine Unlearning for LLMs](https://mlsanity.com/paper/2507.04219/) (2025)
- [Neon: Negative Extrapolation From Self-Training Improves Image Generation](https://mlsanity.com/paper/2510.03597/) (2025)
- [From P(y|x) to P(y): Investigating Reinforcement Learning in Pre-train Space](https://mlsanity.com/paper/2604.14142/) (2026)
- [A Model Can Help Itself: Reward-Free Self-Training for LLM Reasoning](https://mlsanity.com/paper/2510.18814/) (2025)

## Abstract (arXiv)

Can a language model improve from plain text sampled from itself, with no prompts, no teacher, no verifier, and no reward model? Yes, but only when the synthetic corpus is compatible with the student, a relational property of the source-student pair rather than an intrinsic property of the data. We call this the latent capability resurfacing hypothesis: weak self-training can amplify capabilities already present in the pretrained model, but only under this compatibility condition. We study this in the minimal setting of prompt-free unconditional self-training, where base language models are fine-tuned on text generated from the BOS token alone, with no task specification or external supervision. We report three findings. First, synthetic utility is relational rather than intrinsic: self-generated data is the most effective source, same-lineage transfer outperforms stronger but differently trained sources, and cross-family transfer is substantially weaker. Second, common intrinsic proxies fail: neither benchmark-level semantic similarity nor average per-token likelihood under the student predicts which corpora help. Third, this regime produces a surprising byproduct. In controlled Pythia experiments, capability and verbatim memorization decouple: benchmark utility is preserved or improved while held-out exact-match extraction drops by over 95 percent, with no forget set, privacy objective, or targeted unlearning. Together, these results suggest that prompt-free self-training works by amplifying what the student already knows, not by importing structure from the data. They also reveal a regime in which capability and verbatim memorization can be separated without any explicit unlearning objective.