Reverse Kullback-Leibler (RKL) divergence is widely favored over forward KL (FKL) in large language models (LLM) distillation, yet this preference is largely based on comparisons that omit the temperature τ, overlooking its central role in softening teacher distributions and improving knowledge transfer. In this work, we revisit temperature in LLM distillation and show that it fundamentally changes the comparison between FKL and RKL. Our analysis reveals an asymmetric effect: temperature substantially enriches FKL with non-dominant token signals, whereas it mainly rescales RKL gradients, causing FKL to benefit much more from τ scaling than RKL. This asymmetry overturns the standard empirical conclusion: although RKL outperforms FKL at τ=1, FKL consistently surpasses RKL at higher temperatures across instruction-following benchmarks. Moreover, the impact of temperature is not limited to FKL; it improves a broader family of distillation objectives, enabling simple KL-based methods to achieve competitive performance against recent state-of-the-art LLM distillation approaches.
Knowledge distillation is central to LLM post-training, yet its design space remains poorly understood, especially alongside reinforcement learning (RL). We show that the prevailing paradigms, off-policy distillation and on-policy distillation (OPD), implicitly couple two orthogonal choices: prefix source and token-level KL direction. This follows from decomposing sequence-level KL over autoregressive response distributions: forward KL pairs teacher prefixes with token-level forward KL, and reverse KL pairs student prefixes with token-level reverse KL. We argue this coupling is not intrinsic: decoupling the two axes yields four valid objectives. We establish gradient-level identities showing forward KL gives SFT-style cross-entropy matching with teacher soft targets, whereas reverse KL gives an RL-style policy-gradient objective with a dense teacher-student log-ratio reward, connecting them to off-policy SFT, DAgger-style on-policy SFT, offline-RL-style distillation, and OPD. We conduct an extensive controlled study on math reasoning, evaluating the four objectives both as standalone methods and as initializations for subsequent RL. The results reveal three tradeoffs: KL direction induces an accuracy-entropy tradeoff, prefix source a quality-compute tradeoff, and training length an accuracy-stability tradeoff. Motivated by these findings, we propose KL mixing and an entropy-gated length curriculum. KL mixing shows long-sequence distillation requires substantial forward-KL weight to prevent entropy collapse and length inflation without sacrificing accuracy. The entropy-gated length curriculum improves Avg@k and Pass@k by 3.6 and up to 5.8 points, and cuts average response length by roughly 3x versus fixed long-horizon training. Our results provide a framework and practical methods for designing reasoning distillation objectives that balance accuracy, diversity, compute, and RL behavior.
Knowledge distillation (KD) is a key technique for compressing Large Language Models (LLMs), yet methods relying on a single KL objective often fail to balance primary distribution fitting with long-tail probability modeling, limiting both generation quality and generalization. To address this, we analyze the complementary roles of forward and reverse KL divergence (FKL/RKL) in distribution alignment from theoretical and empirical perspectives. We then propose a reinforcement-learning-based adaptive KL-weighted distillation framework, in which a policy network dynamically assigns weights to FKL and RKL based on teacher-student distributional characteristics, guided by immediate reward signals to achieve dual alignment on principal and long-tail modes. Extensive experiments demonstrate consistent improvements across Rouge-L and BertScore metrics, surpassing greedy heuristics by 0.4-0.6 points and outperforming other baseline methods on diverse benchmarks.
Knowledge distillation (KD) transfers knowledge from a high-capacity teacher to a compact student by matching their predictive distributions, with temperature scaling serving as a central mechanism for smoothing teacher predictions and exposing informative "dark knowledge" beyond the hard label. However, the standard fixed-temperature design is inherently sample-agnostic. Since samples differ in logit scale and learning difficulty, a single global temperature produces teacher soft labels with highly inconsistent entropy: some predictions remain overly sharp and provide limited inter-class information, whereas others become over-smoothed and lose class-discriminative information. Moreover, sharing the same temperature between teacher and student further imposes rigid logit-scale alignment despite their capacity mismatch. To address these limitations, we propose CIST (Consistently Informative Soft-label Temperature), which assigns separate sample-wise adaptive temperatures to the teacher and student. This design produces consistently informative teacher soft labels while relaxing rigid teacher--student logit-scale matching. It also reweights the distillation objective according to teacher confidence and student learning difficulty. Theoretically, we show that teacher-label entropy is largely governed by the ratio between the maximum teacher logit and the temperature, providing a principled basis for adaptive smoothing. Empirically, CIST mitigates the inconsistency induced by fixed temperature, and experiments on both vision and language distillation tasks show consistent improvements over standard KD and strong baselines with negligible computational overhead.