When Easy Contexts Teach Less: Contextual Answerability-Guided Data Reformulation for LLM Training

The growing scarcity of high-quality natural corpora has made data reformulation and synthesis increasingly important for large language model training. However, existing document reformulation methods largely rely on human-designed heuristics, while identifying useful strategies typically requires expensive corpus generation and train-and-evaluate comparisons. In this work, we investigate whether feedback from the model itself can predict the knowledge-learning utility of reformulated data before training. We introduce Contextual Answerability, which measures how readily a model can recover a target fact when a reformulated document is provided as context. Interestingly, we uncover a consistent and counter-intuitive relationship: **reformulations from which the model can more readily recover factual knowledge yield smaller improvements in closed-book factual recall after training.** In other words, higher Contextual Answerability indicates lower knowledge learnability. Our gradient analysis suggests that readily answerable reformulations favor context-dependent processing, whereas less answerable reformulations provide comparatively stronger signals for parametric knowledge acquisition. Building on this analysis, we propose **Carve**, a self-evolving framework that uses Contextual Answerability as feedback to iteratively explore and refine effective corpus-level reformulation strategies under a factual-fidelity constraint. Experiments show that the reformulation selected by Carve outperforms the original corpus and reformulations without feedback during continuous training, reaching a score comparable to the final baselines with **27% fewer training tokens**. The same reformulation also transfers to pretraining from scratch across multiple model scales, where it consistently achieves the highest average performance.