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

arXiv: https://arxiv.org/abs/2610.20086 · HTML: https://mlsanity.com/paper/2610.20086/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 38 references that are in the map.
- First posted on arXiv 14 Oct 2026.

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

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [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)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Don't Stop Pretraining: Adapt Language Models to Domains and Tasks](https://mlsanity.com/paper/2004.10964/) (2020)
- [Know What You Don't Know: Unanswerable Questions for SQuAD](https://mlsanity.com/paper/1806.03822/) (2018)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [When Not to Trust Language Models: Investigating Effectiveness of Parametric and Non-Parametric Memories](https://mlsanity.com/paper/2212.10511/) (2022)
- [Mass-Editing Memory in a Transformer](https://mlsanity.com/paper/2210.07229/) (2022)
- [DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs](https://mlsanity.com/paper/1903.00161/) (2019)
- [REPLUG: Retrieval-Augmented Black-Box Language Models](https://mlsanity.com/paper/2301.12652/) (2023)
- [Phi-4 Technical Report](https://mlsanity.com/paper/2412.08905/) (2024)
- [Compositional Semantic Parsing on Semi-Structured Tables](https://mlsanity.com/paper/1508.00305/) (2015)
- [DataComp-LM: In search of the next generation of training sets for language models](https://mlsanity.com/paper/2406.11794/) (2024)
- [Measuring short-form factuality in large language models](https://mlsanity.com/paper/2411.04368/) (2024)
- [Are We Done with MMLU?](https://mlsanity.com/paper/2406.04127/) (2024)
- [Rephrasing the Web: A Recipe for Compute and Data-Efficient Language Modeling](https://mlsanity.com/paper/2401.16380/) (2024)
- [Nemotron-CC: Transforming Common Crawl into a Refined Long-Horizon Pretraining Dataset](https://mlsanity.com/paper/2412.02595/) (2024)
- [Synthetic continued pretraining](https://mlsanity.com/paper/2409.07431/) (2024)
- [Injecting New Knowledge into Large Language Models via Supervised Fine-Tuning](https://mlsanity.com/paper/2404.00213/) (2024)
- [SimpleQA Verified: A Reliable Factuality Benchmark to Measure Parametric Knowledge](https://mlsanity.com/paper/2509.07968/) (2025)

## Abstract (arXiv)

Synthetic data is increasingly used in language-model pretraining. Existing knowledge-corpus synthesis pipelines, including WRAP and Nemotron-CC, usually take a source passage or document segment as input and generate rewritten or QA-style samples from that text. This can improve surface form and prompt diversity, but it does not explicitly require fine-grained source facts -- especially secondary entities, list/table entries, and precise temporal attributes -- to appear in the synthesized corpus. We propose AFCS (Atomic-Fact-Conditioned Synthesis), a pipeline that first extracts source-supported atomic facts and then uses each retained fact to drive generation. AFCS uses structure-aware extraction over the document tree, source-grounded verification, local context expansion, and multi-format generation. In continued-pretraining experiments with OLMo-3-7B and a 32B base on the same FineWiki source corpus, AFCS outperforms WRAP and Nemotron-CC on SimpleQA, SimpleQA Verified, PopQA, and HotpotQA. Granularity ablations show that fact-level synthesis improves over chunk-level, paragraph-level, and entity-level synthesis; and a 100B-token mid-training integration improves factual benchmarks and raises the 12-task general benchmark average by +1.09.