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 likelihood maximization in SFT induces distributional collapse, thereby exhausting the exploration space necessary for subsequent RL. Motivated by the Gibbs optimum of KL-regularized RL, we derive a token-level variational surrogate that makes the SFT target structurally compatible with the subsequent RL stage, and propose Gibbs Initialization with Finite Temperature (GIFT). Standard SFT emerges as a degenerate zero-temperature limit of this surrogate, while a finite temperature preserves structural diversity. Our experiments demonstrate that GIFT outperforms standard SFT and surpasses competitive baselines when utilized for RL initialization. Our code is available at https://github.com/zzy1127/GIFT.

Large Language Models (LLMs) often produce unnecessarily lengthy reasoning traces, which significantly increase computational cost and latency. Existing approaches typically rely on fixed length penalties, but such penalties are hard to tune and fail to adapt to the evolving reasoning abilities of LLMs, leading to suboptimal trade-offs between accuracy and conciseness. To address this challenge, we propose LEASH (adaptive LEngth penAlty and reward SHaping), a reinforcement learning framework for efficient reasoning in LLMs. We formulate length control as a constrained optimization problem and employ a Lagrangian primal–dual method to dynamically adjust the penalty coefficient. When generations exceed the target length, the penalty is intensified; when they are shorter, it is relaxed. This adaptive mechanism guides models toward producing concise reasoning without sacrificing task performance. Experiments on Deepseek-R1-Distill-Qwen-1.5B and Qwen3-4B-Thinking-2507 show that LEASH reduces the average reasoning length by 60% across diverse tasks—including in-distribution mathematical reasoning and out-of-distribution domains such as coding and instruction following—while maintaining competitive performance. Our work thus presents a practical and effective paradigm for developing controllable and efficient LLMs that balance reasoning capabilities with computational budgets.