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| Main Authors: | , , , , , , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.09233 |
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Table of Contents:
- 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 to reconcile post-training objectives 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 promotes 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 to preserve exploration and align the two post-training stages. Our code is available at https://github.com/zzy1127/GIFT.