Scaling LLM Knowledge Boundaries via Distribution-Optimized Synthesis

Large language models (LLMs) rely on static pretraining corpora, causing their knowledge to become outdated over time. Existing approaches for evaluating knowledge edits either suffer from rapid contamination or rely on counterfactual edits that conflict with rigid existing knowledge. In this work, we propose a synthetic, simulation-driven framework for studying knowledge insertion in LLMs. We introduce {\sc ParallelEvents}, a benchmark of fictional yet realistic future worlds that generates coherent event trajectories for controlled evaluation, avoiding contamination while preserving consistency. Building on this dataset, we develop {\sc Synapse}, a training framework that uses model-generated data to update model parameters via mid-training and instruction tuning. This synthetic pipeline enables scalable knowledge integration without costly human-curated data. Empirically, {\sc Synapse} outperforms existing methods by 14.23%, demonstrating that simulation-based synthetic training leads to robust and coherent knowledge insertions.

LLM pretraining is shifting from a compute-bound to a data-bound regime, where available human (organic) text falls far short of scaling demands. However, reaching the data-bound regime does not mean the model has fully utilized its organic corpus. In this paper, we introduce SynPro, a synthetic data generation framework that helps LLMs more thoroughly learn from limited organic data. SynPro applies two operations, rephrasing and reformat, that present the same organic source in diverse forms to facilitate deeper learning without introducing external information. Both generators are optimized via reinforcement learning with quality, faithfulness, and data influence rewards, and are continuously updated as pretraining plateaus to target content the model has yet to absorb. We pretrain 400M and 1.1B models with 10% of their Chinchilla-optimal tokens (0.8B and 2.2B) from DCLM-Baseline, reflecting a realistic data-bound regime in frontier pretraining. Our results reveal that organic data is significantly underutilized by standard repetition: SynPro unlocks 3.7-5.2x the effective tokens of repetition, even surpassing the non-data-bound oracle that trains on equivalent unique data at the 1.1B scale. Analyses confirm that faithful, model-aware synthesis sustains data-bound scaling without causing distribution collapse. We open-source our code at https://github.com/cxcscmu/SynPro.

High-quality, diverse data are vital for large language models (LLMs) but remain scarce and costly. Data synthesis is a viable alternative and succeeds on closed tasks, yet the humanities and social sciences (HSS) are overlooked, and their open-ended nature makes synthesis challenging. Moving beyond prior capability-centric, fragmented attempts, we adopt a subject-centric paradigm, define the first HSS domain system covering 14 mainstream fields, and introduce HSS-Synth, the first data synthesis pipeline for HSS. HSS-Synth comprises: (1) constructing seed documents from web corpora via multi-step filtering and text refinement evaluated by a judge; (2) specifying "requirements + persona" to backtranslate seed documents into diverse yet faithful instructions with a strict Q&A alignment check; and (3) breaking LLM response limits via teacher-forced Answering that feeds seed documents during response generation to anchor semantics, reduce hallucinations, and preserve tone and integrity. HSS-Synth yields 237k high-quality, diverse instruction-tuning samples that outperform 14 leading baselines on 16 benchmarks. The fine-tuned Qwen3-8B-Base sets a new SOTA and approaches the official Qwen3-8B, improving both human preference and knowledge capabilities without performance seesaws. Extensive experiments demonstrate HSS-Synth's robustness and transferability. Our code is publicly available at https://github.com/pengr/HSS-Synth.