AFCS: Atomic-Fact-Conditioned Synthesis for Factual Knowledge Pretraining

Synthetic data rephrasing has emerged as a powerful technique for enhancing knowledge acquisition during large language model (LLM) pretraining. However, existing approaches operate at the single-document level, rewriting individual web pages in isolation. This confines synthesized examples to intra-document knowledge, missing cross-document relationships and leaving facts with limited associative context. We propose WRAP++ (Web discoveRy Amplified Pretraining), which amplifies the associative context of factual knowledge by discovering cross-document relationships from web hyperlinks and synthesizing joint QA over each discovered document pair. Concretely, WRAP++ discovers high-confidence relational motifs including dual-links and co-mentions, and synthesizes QA that requires reasoning across both documents. This produces relational knowledge absent from either source document alone, creating diverse entry points to the same facts. Because the number of valid entity pairs grows combinatorially, this discovery-driven synthesis also amplifies data scale far beyond single-document rewriting. Instantiating WRAP++ on Wikipedia, we amplify ~8.4B tokens of raw text into 80B tokens of cross-document QA data. On SimpleQA, OLMo-based models at both 7B and 32B scales trained with WRAP++ substantially outperform single-document approaches and exhibit sustained scaling gains, underscoring the advantage of cross-document knowledge discovery and amplification.

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.