Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL) dominate the post-training landscape for mathematical reasoning, yet differ fundamentally in their reliance on expert trajectories. To understand the optimal way to harness these trajectories for maximizing performance, we propose the Plasticity-Ceiling Framework. This framework empirically grounds the post-training landscape by decomposing the final performance ceiling into the foundational SFT performance and the subsequent RL plasticity (i.e., the maximum improvement via RL). Through extensive benchmarking, we establish the Sequential SFT-then-RL pipeline as the superior standard, overcoming the stability and premature convergence deficits inherent in synchronized approaches. Furthermore, we derive precise scaling guidelines: (1) Transitioning to RL at the Stable or Mild Overfitting Regime of SFT maximizes the final ceiling by securing a robust SFT foundation with substantial RL plasticity; (2) Refuting the “Less is More” hypothesis in SFT-then-RL scaling, we demonstrate that Data Scale determines the primary post-training potential, while Trajectory Difficulty acts as a performance multiplier; and (3) The Minimum Validation Loss of SFT serves as a reliable indicator for selecting the expert trajectories that maximize the ultimate performance ceiling. Our findings provide actionable guidelines for extracting maximum value from expert trajectories.

Large language models (LLMs) struggle with maintaining accurate knowledge due to conflicting/outdated parametric memories. While locate-and-edit methods address this, their reliance on models’ internal representations leads to robustness failures in long-context reasoning and paraphrased queries. We identify a fundamental limitation of locate-and-edit methods: existing semantic keys (for memory localization) cannot simultaneously satisfy robustness (context-invariant activation) and specificity (precise knowledge discrimination). Through theoretical error-bound analysis, we establish formal criteria for effective editing.Our solution introduces Robust Edit Pathway (REP), a plug-and-play module that: (1) disentangles editing keys from native model representations; (2) dynamically adjusts keys via contrastive learning to achieve robustness-specificity balance. Extensive experiments across various editing methods (ROME/MEMIT/R-ROME/EMMET), existing LLMs (LLaMA2, QWen, Mistral), and datasets (CounterFact, ZsRE) show that REP improves success rate over robustness tests by up-to 66.4% while maintaining the success rate unaffected.