Model merging, typically on Instruct and Thinking models, has shown remarkable performance for efficient reasoning.In this paper, we systematically revisit the simplest merging method that interpolates two weights directly.Particularly, we observe that model interpolation follows a three-stage evolutionary paradigm with distinct behaviors on the reasoning trajectory.These dynamics provide a principled guide for navigating the performancecost trade-off.Empirical results demonstrate that a strategically interpolated model surprisingly surpasses sophisticated model merging baselines on both efficiency and effectiveness.We further validate our findings with extensive ablation studies on model layers, modules, and decoding strategies.Ultimately, this work demystifies model interpolation and offers a practical framework for crafting models with precisely targeted reasoning capabilities.Code is available at Github.

Kullback-Leiber divergence has been widely used in Knowledge Distillation (KD) to compress Large Language Models (LLMs). Contrary to prior assertions that reverse Kullback-Leibler (RKL) divergence is mode-seeking and thus preferable over the mean-seeking forward Kullback-Leibler (FKL) divergence, this study empirically and theoretically demonstrates that neither mode-seeking nor mean-seeking properties manifest in KD for LLMs. Instead, RKL and FKL are found to share the same optimization objective and both converge after a sufficient number of epochs. However, due to practical constraints, LLMs are seldom trained for such an extensive number of epochs. Meanwhile, we further find that RKL focuses on the tail part of the distributions, while FKL focuses on the head part at the beginning epochs. Consequently, we propose a simple yet effective Adaptive Kullback-Leiber (AKL) divergence method, which adaptively allocates weights to combine FKL and RKL. Metric-based and GPT-4-based evaluations demonstrate that the proposed AKL outperforms the baselines across various tasks and improves the diversity and quality of generated responses.

Knowledge Distillation (KD), aiming to train a better student model by mimicking the teacher model, plays an important role in model compression. One typical way is to align the output logits. However, we find a common issue named mis-instruction, that the student would be misled when the predictions based on teacher logits do not follow the labels. Meanwhile, there is other useful dark knowledge in the logits such as the class discriminability, which is vital for distillation. In this paper, we propose a simple yet effective Logit Calibration (LoCa) method, which calibrates the logits from the teacher model based on the ground-truth labels. The key insight is to correct the prediction (to address the mis-instruction issue) and maintain useful dark knowledge simultaneously. Our proposed LoCa does not require any additional parameters. Empirical results on image classification and text generation tasks demonstrate that LoCa can effectively improve the performance of baselines.