Title: Where Did This Sentence Come From? Tracing Provenance in LLM Reasoning Distillation
Primary area: foundation or frontier models, including LLMs
Keywords: Reasoning Distillation

Abstract: Reasoning distillation, a cost-effective approach for enhancing student model performance, has attracted increasing attention. It typically leverages a large teacher model to generate reasoning paths, which are then used to fine-tune a student model so that it mimics the teacher's behavior in training contexts. 
However, previous approaches have lacked a detailed analysis of the origins of the distilled model's capabilities. It remains unclear whether the student can maintain consistent behaviors with the teacher in novel test-time contexts, or whether it regresses to its original output patterns, raising concerns about the generalization of distillation models.
To analyse this question, we introduce a cross-model Reasoning Distillation Provenance Tracing framework. For each action (e.g., a sentence) produced by the distilled model, we obtain the predictive probabilities assigned by the teacher, the original student, and the distilled model under the same context. By comparing these probabilities, we classify each action into four categories: (i) teacher-originated actions, (ii) student-originated actions, (iii) pre-existing actions in both models not enhanced by distillation, and (iv) pre-existing actions boosted through distillation. By systematically disentangling the provenance of each action, we experimentally demonstrate that, in test-time contexts, the distilled model can indeed generate teacher-originated actions, which correlate with and plausibly explain observed performance on distilled model. Building on this analysis, we further propose a teacher-guided data selection method. Unlike prior approach that rely on heuristics (e.g., selecting data most aligned with the student's original distribution), our method directly compares teacher–student divergences on the training data, providing a principled selection criterion. We validate the effectiveness of our approach across multiple representative teacher models (Deepseek-R1-671B, QwQ-32B, GPT-OSS-120B) and diverse student models (Qwen2.5-7B-Instruct, Qwen4-4B-Base, Qwen3-8B-Base, Qwen3-4B-Instruct-2507). The results highlight the utility of our provenance-tracing framework and underscore its promise for reasoning distillation. We hope to share Reasoning Distillation Provenance Tracing, along with our insights into reasoning distillation, with the community.