Efficient Embedding-based Synthetic Data Generation for Complex Reasoning Tasks

Adapting small instruction-tuned models to specialized domains often relies on supervised fine-tuning (SFT) on curated instruction-response examples, which is expensive to collect at scale. Synthetic training examples generated by a teacher LLM from a domain corpus can reduce this cost, but existing pipelines can produce homogenized outputs and do not consistently capture cross-passage or cross-document dependencies. We introduce EmbGen, a synthetic data generation pipeline that decomposes a corpus into entity-description pairs, reassembles them using semantic structure inferred from embedding similarity, and then generates question-answer (QA) pairs via proximity, intra-cluster, and inter-cluster sampling with cluster-specialized system prompts. We evaluate EmbGen against EntiGraph, InstructLab and Knowledge-Instruct on three datasets of varied semantic heterogeneity, under fixed token budgets (5 and 20 million tokens). We use lexical overlap metrics, an LLM-as-a-judge rubric, and Binary Accuracy, a composed metric combining Factual Accuracy and Completeness for evaluation. EmbGen improves Binary Accuracy on the most heterogeneous dataset by 12.5% at 5M and 88.9% at 20M tokens budget, relative to the strongest baseline, while remaining competitive across other datasets with lower heterogeneity.

Synthetic data is a standard component in training large language models, yet systematic comparisons across design dimensions, including rephrasing strategy, generator model, and source data, remain absent. We conduct extensive controlled experiments, generating over one trillion tokens, to identify critical factors in rephrasing web text into synthetic pretraining data. Our results reveal that structured output formats, such as tables, math problems, FAQs, and tutorials, consistently outperform both curated web baselines and prior synthetic methods. Notably, increasing the size of the generator model beyond 1B parameters provides no additional benefit. Our analysis also demonstrates that the selection of the original data used for mixing substantially influences performance. By applying our findings, we develop FinePhrase, a 486-billion-token open dataset of rephrased web text. We show that FinePhrase outperforms all existing synthetic data baselines while reducing generation costs by up to 30 times. We provide the dataset, all prompts, and the generation framework to the research community.

What are the limits of controlling language models via synthetic training data? We develop a reinforcement learning (RL) primitive, the Dataset Policy Gradient (DPG), which can precisely optimize synthetic data generators to produce a dataset of targeted examples. When used for supervised fine-tuning (SFT) of a target model, these examples cause the target model to do well on a differentiable metric of our choice. Our approach achieves this by taking exact data attribution via higher-order gradients and using those scores as policy gradient rewards. We prove that this procedure closely approximates the true, intractable gradient for the synthetic data generator. To illustrate the potential of DPG, we show that, using only SFT on generated examples, we can cause the target model's LM head weights to (1) embed a QR code, (2) embed the pattern $\texttt{67}$, and (3) have lower $\ell^2$ norm. We additionally show that we can cause the generator to (4) rephrase inputs in a new language and (5) produce a specific UUID, even though neither of these objectives is conveyed in the generator's input prompts. These findings suggest that DPG is a powerful and flexible technique for shaping model properties using only synthetic training examples.