Enhancing Knowledge Injection with Surrounding Backgrounds in Continual Training LLMs

Updating the parametric knowledge of Large Language Models (LLMs) post-training remains a significant challenge, a scenario we term \textit{Epistemic Fluidity}. Both model editing and Continual Pre-training are ill-suited: the former suffers from progressive parameter interference under sequential edits, while the latter is cost-prohibitive for sparse factual updates. While Supervised Fine-tuning (SFT) is promising and computationally efficient, our controlled experiments across a six-task evaluation protocol spanning from direct recall to scenario simulation reveal a critical gap: naive or semantically-flat rewrites yield only spurious memorization of co-occurring tokens, falling short of genuine internalization for retrieval and future reasoning. To close this gap, we introduce \ours, a framework of 12 structured rewriting strategies organized into an atom-to-interactive four-level taxonomy, spanning counterfactual data from seven domains. Our experiments with different sets of rewriting strategies on three LLMs reveal three key insights: 1) sufficient knowledge exposure is a necessary condition for internalization; 2) under sufficient exposure, data diversity dominates over quantity; and 3) explicit contrastive reasoning combined with anchor-knowledge bridging drives the deepest internalization. These findings provide a systematic, data-centric foundation for transforming static LLMs into continuously updatable knowledge bases.