GIFT: Unlocking Global Optimality in Post-Training via Finite-Temperature Gibbs Initialization

• URL: http://arxiv.org/abs/2601.09233v1
• Date: Wed, 14 Jan 2026 07:13:57 GMT
• Title: GIFT: Unlocking Global Optimality in Post-Training via Finite-Temperature Gibbs Initialization
• Authors: Zhengyang Zhao, Lu Ma, Yizhen Jiang, Xiaochen Ma, Zimo Meng, Chengyu Shen, Lexiang Tang, Haoze Sun, Peng Pei, Wentao Zhang,
• Abstract summary: We reformulateSupervised Fine-Tuning (SFT) within a unified post-training framework and propose Gibbs Initialization with Finite Temperature (GIFT)<n>GIFT incorporates supervision as a finite-temperature energy potential, establishing a distributional bridge that ensures objective consistency throughout the post-training pipeline.
• Score: 9.388803723263392
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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