The prevailing post-training paradigm for Large Reasoning Models (LRMs)--Supervised Fine-Tuning (SFT) followed by Reinforcement Learning (RL)--suffers from an intrinsic optimization mismatch: the rigid supervision inherent in SFT induces distributional collapse, thereby exhausting the exploration space necessary for subsequent RL. In this paper, we reformulate SFT within a unified post-training framework and propose Gibbs Initialization with Finite Temperature (GIFT). We characterize standard SFT as a degenerate zero-temperature limit that suppresses base priors. Conversely, GIFT incorporates supervision as a finite-temperature energy potential, establishing a distributional bridge that ensures objective consistency throughout the post-training pipeline. Our experiments demonstrate that GIFT significantly outperforms standard SFT and other competitive baselines when utilized for RL initialization, providing a mathematically principled pathway toward achieving global optimality in post-training. Our code is available at https://github.com/zzy1127/GIFT.

翻译：大型推理模型（LRMs）当前的主流后训练范式——监督微调（SFT）后接强化学习（RL）——存在内在的优化失配问题：SFT中固有的刚性监督会导致分布坍缩，从而耗尽后续RL所需的探索空间。本文在一个统一的后训练框架内重新形式化了SFT，并提出了有限温度吉布斯初始化（GIFT）。我们将标准SFT刻画为一种抑制基础先验的退化零温极限。相反，GIFT将监督信息作为一个有限温度的能量势引入，建立了一个分布桥梁，确保在整个后训练流程中目标函数的一致性。实验表明，当用于RL初始化时，GIFT显著优于标准SFT及其他竞争基线方法，为在后训练中实现全局最优性提供了一条数学上严谨的路径。我们的代码可在 https://github.com/zzy1127/GIFT 获取。