Where Did This Sentence Come From? Tracing Provenance in LLM Reasoning Distillation
Authors: kaiyuan liu
Shaotian Yan
Rui Miao
Bing Wang
Chen Shen
Jun Zhang
Jieping Ye
Venue: ICLR 2026 Poster (2026)
Keywords: Reasoning Distillation
Primary area: foundation or frontier models, including LLMs

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.

Published as a conference paper at ICLR 2026
WHERE DID THIS SENTENCE COME FROM? TRACING PROVENANCE IN LLM REASONING DISTILLATION
Kaiyuan Liu', , Yan?, Rui Miao?, Bing Wang', Chen Shen Jun Zhang,, Jieping Yeat
"College of Computer Science and Technology. Zhejiang University
2 Alibaba Cloud Computing
School of Artificial Intelligence, Jilin University
*College of Computer Science and Technology, Jilin University
6 DDepartment of Mathematics, University of Michigan
1242128 @ @zju.edu.cn
ABSTRACT
Reasoning distillation, cost-effective approach for enhancing student model per- formance, has attracted increasing attention. It typically leverages a large teacher model to generate reasoning paths, which are then used to fine-tune student model so that it mimics the teacher's behavior in training contexts. However, pre- vious approaches have lacked detailed analysis of the origins of the distilled model's capabilities. It remains unclear whether the student can maintain consis- tent behaviors with the teacher in novel test-time contexts, or whether regresses to its original output patterns, raising concerns about the generalization of dis- tillation models. To analyse this question, we introduce cross- moosll Reason- ing Distillation Provenance Tracing framework. For each action (e.g., a sentence) produced by the distilled model, we obtaín 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) eacher-originater 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 ac- tion, we experimentally demonstrate that, in test-time contexts, the distilled model can indeed generate teacher-origines explain observed performance on distilled model. Building on this analysis, we further propose a teacher- gercherrguiedd data selection method. Unlike prior approach that rely on heuristics (c.g., selecting data most aligned with the student's 's original dis- tribution), our method directly compares teacher-student divergences on the train- ing data, providing principled selection criterion. We validate the effectiveness of our approach across multiple representative teacher models (Deepseek, QwQ, GPT-OSS-120BI and diverse student models (Qwen2.5-7B- Innttuuct, Qwen3-4B- Base, Qwen3-8B-Base ity of our provenance- -raannnneetttnngggng 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.
actions, which correlate with and plausibly
Fween--4--Instrutt-22
The results highlight the util-
INTRODUCTION
The rapid development of reinforcement learning (RL) techniques (Schulman et al.] 2017 Shao
et 2024 Ahmadian et al. 2024) and resulting large-scale reasoning models (DeepSeek-Ai 2025
AI Team] 2025b) has accelerated the growth of distillation researches, especially reason- ing distillation (Zhao et al. 2025 Guha et al. (025). Early work on reasoning distillation focused on creating high-quality open-source datasets (Zhao et al. [025 Guha et al. 2025 NVIDIA (025), and recent studies have focused on curating and filtering distillation samples to improve efficiency
and performance (Zhang et al. 2025 Li et al. 2025). However, these approaches primarily focus on
model performance and fail to provide explanatory analysis of the sources of the model's output
Corresponding author

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Published as a conference paper at ICLR 2026
in test-time contexts. As result, it remains unclear whether the student model has successfully inherited the knowledge and reasoning logic from the teacher model, raising concerns about the generalization of distillation models (Hinton et al. 2015b).
Concretely, as illustrated in Figure T reasoning distillation involves two main steps. First, specific contexts (e-g.. high-quality questions, or high-quality questions augmented with partially generated answers) are provided to the teacher model, which then produces the next action via sampling. Second, these context-action pairs are used to train the student model, encouraging the teacher's actions under the same contexts, At test time, however, the distilled student faces new contexts. It remains unclear whether the student will continue to follow the teacher's behavior instead of falling back on its original output distribution.
reproduce
To analyse the above problem, we propose a cross- model Reasoning Distillation Provenance Tracing frame- work. Concretely, we evaluate three open-source dis- tilled models: PrepSeeekDDitill--Ween AL 2025), DeepSeek-R1-OS22 -00---1--52--00 Qwen3-8B (DeepSeek-
Training Stage
Input
Sample
Teacher Model
(DeepSeek-
Training
Thaining Context
Next Sentence
AI. 2025), and LIMO-v2 model (Ye et al.] 2025). To analyze the patterns in distilled models' outputs under test contexts, we collect multiple responses from them on GPQA-D (Rein et al. 2024) and AIME24. Each re- sponse is re-input into the distilled model, the correspond- ing teacher model, and the original student model. This sce-
Student Model
Triinig Contect
Teacher Sentence
procedure allows us obtain, under the same nario, the probability assigned by each model to the next action produced by the distilled model. By comparing these probabilities, we can naturally trace the provenance of every action. For example, if the teacher model as- signs significantly higher probability to an action than the original student model does, we can attribute that action to feacher-originater actions, since the distilled model's ability to produce it mainly derives from teacher model's 's knowledge transferred during distillation. For further de- tails about other action types, see Section 3
Distilled Model
Testing
Context
Testing Stage
Figure 1: Motivation. In reasoning dis- tillation, the student model learns in the training stage to produce actions con- sistent with the teacher model within the training context. However, at test time, it remains unclear whether the dis- tilled model will continue to output ac- tions aligned with the teacher model in- stead of degrading to the outputs of the student model, raising concerns about the generalization of distillation models (Hinton et al.) 20155).
To this end, observe that distilled models re- produce teacher-originated actions in new test contexts. Moreover, these actions correlated with correct re- sponses on the test set, which helps explain the gener- alization gains achieved through distillation. This obser- vation further motivates our training design: we hypoth- esize that when the training data contains higher proportion of originated actions, the distilled model attains better final performance. To validate this hypothesis, we propose teacher- guided data selection strategy that compares the probabilities assigned by the teacher and student models on the training data and prioritizes examples that contain more teacher-originated actions. We then evaluate its effectiveness across multiple settings, including representative teacher models from different families (DeepSeck-RR R1---11-61111 IB (DeepSeck-Al 2025). QwQ-32B (Team 2025b), GPT-
OSS-120B (OpenAl 2025)) and various student models Jiwen2.5-7B-Instrice Qwen3-4h 40--3-4B-Base 4B-Base, Qwen3-8B- BBenn- 4 4B-Instruct-2507)
Our contributions can be summarised as follows: (1) We propose Reasoning Distillation Provenance Tracing, systematic method to disentangle the origins of each action, through fine-grained catego- rization into teacher-originated, student-orrginatee, shared, and boosted actions. This offers prin- cipled approach for analyzing whether distillation genuinely transfers reasoning ability or merely reinforces pre-existing patterns. (2) Through analysis on reasoning benchmarks, we show that dis- tilled models can generate teacher-originated actions even unseen test scenarios. These actions are correlated with correctness, offering a quantitative explanation for why reasoning distillation im- proves generalization. (3) Building on the provenance analysis, we introduce teacher-guie guided data selection strategy that prioritizes training samples rich in teacher-originated actions. Unlike heuristic method, our approach leverages explicit teacher-student divergence as a selection criterion. Experi- ments across diverse ceacher-studen pairs demonstrating performance gains in our settings.
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2 RELATED WORK
2.1 REASONING DISTILLATION
Distilling the reasoning abilities of large reasoning models has been an important problem since their emergence (Kim & Rush 2016; Ho et al., 2023 Ko et al., 2024 2025). DeepSeek (DeepSeek- AT 2025) pioneered this line of work by showing that supervised fine-tuning on the outputs of a reasoning teacher, which is also the approach we focus on in this paper. can dramatically en- hance the reasoning abilities of smaller models. Numerous subsequent projects (e.g.. HuggingFace (Guha et al.] 2025), a-m-team (Zhao et al. 2025), NVIDIA AceReason (Liuu et al.) 2025b), Alibaba
Openk1 (Hugging Face 2025), OpenThougee
(Guha et al. 2025), LIMO YYe et al. 2025). Tencent DeepMath (He et al. 2025)) have devoted substantial effort to constructing large-scale corpora of challenging reasoning problems paired with teacher responses, using rig- orous quality filtering, correctness checks, and diversity-aware curation. Most recently, GRAPE Zhang et al., 2025) preferentially selects examples whose likelihoods best match the student's cur- rent distribution, thereby steering training toward data that is already well aligned with the student. Rather than focusing solely on artificially designed rules and heuristic rules, we aim to quan- tify the sources of distilled model's capabilities and introduce data selection criterion that focuses on sentences whose probabilities indicate stronger oeaihee-originated behavior. This provenance-awane criterion complements prior student-only selection and provides an explicit cross-model signal for reasoning transfer.
2.2 MODEL AUDITING
Another closely related area is model auditing, growing line of work that studies (Song & Shmatikov 2019 Carlini et al. 2022, Dekoninck et al. 2024) auditing generative models to under- stand what data they memorize and to attribute outputs back underlying data sources. In contrast, our work targets model-level provenance in a distillation setting: rather than asking whether specific data are memorized, we aim to trace which upstream models are the sources of given output, shifting the focus from data membership to the lineage of the models themselves.
Due to page limitations, we provide further discussions on related work in the Appendix A.6
3 REASONING DISTILLATION PROVENANCE TRACING
In this section, first provide necessary notations in Subsection 3.1 and introduce Reasoning Distillation Provenance Tracing in Subsection 3.2 We then apply Reasoning Distillation Provenance Tracing three widely used open-source models (Deepscek-Distee Disteee--Dsilll--ee--B.... Qwen-7B, DeepSeek-RI RR-05528---5-- Qwen3-8B and LIMO-v2 model) and present the results of the analysis in Subsection 3.3
3.1 NOTATIONS
Specifically, let Mr denote the teacher model, Ms the student model, and {Q a set of high- quality training questions, where Virain denotes the i-th question. Reasoning distillation first sam- ples responses from MT on (Qirain yielding the training set Dirain = {(Q train T'), where T, = {a(a,) =1. -1....,,, L.} denotes the trajectory for the i-th question, consisting of L, actions gen- erated by Mr. The student model Mg is then trained by minimizing the cross-entropy loss between its predicted next-token-actions and the teacher's actions in trajectory т; under the same context (e.g., input (Q ((.1)): ((.,)).((i)))) output d(),) This ensures that distilled model MD produces reasoning trajectories mimicking to those of Mr when presented with the same context.
3.2 METHOО
As stated in the Section I our goal is to analyze whether the distilled model MD can still produce actions similar to those of the teacher model My in new contexts. The most direct approach is to input the same context into both models (My and MD) and compare their actions. Yet this approach faces two challenges. First, reasoning outputs are typically long, and even when segmented step by step, the number of sentences remains large. Iteratively truncating each sentence boundary and re-input both models to generate new actions is prohibitively expensive. Second, is difficult to accurately evaluate the similarity between the newly generated actions of the two models.
To address these issues, we shift perspective and instead sample exclusively from the distilled model MD the test set (Qiest). We first obtain the trajectory test set Diess {QQi r')}- Sub- sequently, we feed 7² back into the three models (My, Mg. and Mp) and analyse each component action ((t.))- For each action, since token-level comparison is sometimes difficult due possible
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An illustration of analysis using Reasoning Distillation Provenance Tracing. The hori- zontal axis denotes the action position (i.c., the sentence order), while the vertical axis shows the probability assigned by different models (indicated by colored curves in the foreground) in produc- ing that action under the same context. The background colors indicate the action types. Some example of different action types also shown at the top for illustration, where the blank spaces indicate the segmentation boundaries of the response.
Figure 2:
vocabulary mismatches between Mr and MD. We coarser alternative, comparing at the sen- tence level. In this way, we define the probability of producing a(i.j) as the geometric mean of per-token probabilities P(i.j) = expp(mean(log(py) where pş denote the probability of k-th token contained with the sentence ((i.j)-
obtain three output probabilities under the same context: Ple.) from My, P(.,) from Ms. and P(i.) from Mp. As shown in Figure the blue line corresponds to p the orange line to P(,a) and the green line to P((.))
For each ((i)))
Overall, since the trajectory r¹ is sampled from the distilled model Mp. the orange curve (Pit.)) tends be the largest average. Furthermore, four distinet patterns can be observed. Specifically:
Pre-existing actions in both models not enhanced by distillation (hereafter referred to as Shared Sentence ): This includes actions such as those hetween the 54th and 68th steps, where the output probabilities of all models are nearly identical. These actions are originally present in both the teacher and the student models, and distillation does not further increase their probabilities.
Pre-existing actions boosted through distillation (hereafter referred to as Boosted Sentence Similar to the first type, P(..j) and P(..)) remain close, but (b,)) differs significantly (and is typically higher in practice, since trajectories sampled from MD). These actions also exist in both the teacher and student models prior to distillation, but their probabilities are amplified through training with distilled data.
Student-orrginated actions (hereafter referred to as Student Sentence and teacher-originated actions (hereafter referred as Teacher Sentence ): When there is large discrepancy between P(.)) and P(. the distilled model MD still outputs the action, suggesting the action is sistent with the model assigning higher likelihood. Note that a Teacher Sentence does not imply that the action is entirely absent from the student model, but rather that it is primarily originated from the teacher. The same applies Student Sentence.
3.3 ANALYSIS ON OPEN-SOURCE MODELS
In this subsection, apply Reasoning Distillation Provenance Tracing SeepSeck-Distill-O5 7B (Ds-7B), DeepSeck-RR --nc--R--0522 (528-Qwen33 of each sentence produced by the distilled models in testing context. Specifically, sample the open-source models on two commonly used reasoning benchmarks: AIME24 and GPQA-D. AIME24 uses 16 completions per question, and GPQA-D uses 8.
(Ds-8B) and LIMO-v2 model to analyze the source
For each completed response, we segment the output according to the following rules: (1) Special tokens (e.g., <think>) treated individual actions, they carry specific
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Artwes Trncher
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Figure 3: Analysis results open-source models. We apply Reasoning Distillation Provenance Tracing to Deepseek-Distil-Qweee Distill-QQQe-- and DeepSeck-RI Deepsec-R1--022-022 -11-0528-Qwe3--8, analyzing the probabil- ity of producing different actions at each action position two reasoning benchmarks (AIME24 and GPQA-D). The x-axis denotes the action index, and the y-axis shows the probability of produc- ing that action.
mantics and represent important behavior. (2) For the remaining text, we split sentences using the pattern: punctuation + optional whitespace + uppercase letter, corresponding to: re wwo.oomlllloo Mempileln (x' ( (.. ([\s)n]+) (A-2))))). This segmentation procedure covers most common English sentence structures.
Then, we feed the sampled trajectories back into the corresponding teacher and student models to obtain the output probability for each token, and consequently (by taken geometric average of token probability). the probability for each action (p P(iy) and P(r.)) ). We then define AsD =
Plr, - P(.)) ATD P(a,)) phay and ATS = P((.)) P(a)) Using two thresholds, a and can perform the tracing provenance:
if(Aspl Sa A Artil Sa A |Arl I o)) else if( > 3). else ATS {) Boosted Sentence,
Shared Sentence,
Teacher Sentence,
Student Sentence,
else if([Assl $).
where play) Pla.) and pi.,,) denote the probabilities assigned to action a(a)) by the distilled model Mp. the student model Ms, and the teacher model My, respectively. We follow the evaluation order: Shared - Teacher + Student - Boosted. The role of a is to filter out relatively small probability differences (such those between sentences 55 and 65 in Figure 2 to prevent them from influencing the analysis. / helps to more clearly differentiate between various action types, and its value can be determined adaptively. Due page limitations, the selection of a and B is detailed in Appendix A.2
Based on this classification scheme, compute, for each action position, the proportion of each action type and interpret this proportion as the probability of outputting that action type at the given position. For example, for all answers at the third action position (i.e., the third sentence). we calculate the proportion of actions belonging to Teacher Sentence and treat it as the probability that the model outputs Teacher Sentence that position. It is worth noting that the number of actions varies across different answers; therefore, where sufficient data is available to yield reliable statistics. In addition, we compute the average number of tokens for all actions at each position, and, at 4k-token intervals, mark in the action positions corresponding to the average number of tokens required to reach that position. The results shown in Figure and Figure
focus primarily on the earlier action positions,
We observe three phenomena (see Appendix A.3 for more analyses) that help explain the observed benefits of reasoning distillation in novel test-time settings:
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Cormoct Anewer Trncher Sentencee
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Teacher Model: DeepSeek Ri on AIME24
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Figure 4: Analysis results on LIMO-v2 model (Ye et al. Provenance Tracing to LIMO-v2 model, analyzing the probability of producing different actions at each action position two reasoning benchmarks (AIME24 and GPQA-D). Since LIMO-v2 model uses multiple teacher models, we tried different teacher models on all samples. The x-axis denotes the action index, and the y-axis shows the probability of producing that action.
2025 We apply Reasoning Distillation
(1) Higher Teacher Sentence probability in the early inference stage.
As shown in Figure 3 and Figure 4 the light-green line ()) exhibits larger values in the early action index, meaning that the probability of outputting Teacher Sentence is relatively high in the early stages of inference. We attribute this to two factors. First, the student model lacks the ability to properly generate the token <think>, and subsequent steps may be influenced by the first action. However, this effect is limited, as evidenced by the rapid increase in the probability of Boosted Sentence (i.e., the light-yellow line (-) rises sharply in the early phase.). Figure 2 and Figure further illustrate this point, showing that other actions typically emerge after only a few steps. Second, we observe that many early actions focus on analyzing the input and planning subsequent steps. We hypothesize that forcing such behavior early on may be unique pattern of the teacher model, which explains why Teacher Sentences are more likely to appear the beginning of inference.
(2) Student-internal patterns are often activated but not uniformly beneficial during reasoning distillation.
In LIMO-v2 paper, the authors found that if a model already contains sufficient reasoning knowl- edge, reasoning distillation can activate it with minimal data scale and yield strong performance. In this work, we find that reasoning distillation not only activates reasoning knowledge, but also trig- gers other latent patterns embedded within the Boosted Sentence. As shown in Figure and Figure 4 we observe that the mean of the pointwise sum of the light-green (-) and light-yellow ( lines exceeds 0.7, indicating that at each position the predicted action is likely to be one of these two ac- tion types. This means that, in distilled models, the majority of output action types are either Teacher Sentences or Boosted Sentences. More Teacher Sentences originate from the student model learning directly from the teacher model. And more Boosted Sentences suggests that reasoning distillation consistently activates student-internal patterns.
To analyze how reasoning distillation helps in novel contexts, we further conduct quantitative analysis of action-type probabilities in correct versus incorrect responses. As shown in Figure 4 on LIMO-v2 model, Boosted Sentences emerge in later stages with consistently high probability in correct responses across different teacher models (i.c., in later stages, the light-yellow solid line remains above the light-yellow dashed line (--)).. ). In the early stages, correct responses are more likely to rely on Teacher Sentences (i.e., the light-green solid line (-) stays above the light-green
dashed line (- (). However, Figure 3 also reveals the opposite trend in smaller models: Boosted Sentences consistently appear with higher probability in incorrect responses. This suggests that not all coudent-internal patterns are worth activating. The authors of LIMO-v2 paper also find that small models (e.g., 7B) trained with the same method fail to achieve good performance. Taken together with our findings, one concludes that reasoning distillation often activates internal patterns in student model, but not all of these activations are beneficial.

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(3) Teacher sentences are highly correlated with performance gains.
As shown in Figure across different models (DeepSeek-RRI-i) 1-111-00022--n333 and DeepSeek- Distill-Qwen-7Br and test sets (AIME24 and GPQA-D), Teacher Sentence tends be assigned higher probabilities to correct answers (i.c.. the light-green solid line (-) stays above the light- green dashed line (---). This result is also intuitive: since the teacher model achieves higher performance on the test sets, the student model benefits from producing outputs more aligned with the teacher, thereby increasing its likelihood answering correctly.
It remains open question whether Teacher Sentence is equally beneficial for larger models, and believe further experimentation is needed. Although Figure X clearly shows that Teacher Sentence assigns higher probabilities correct answers in the early stages (while probabilities for correct and incorrect answers converge in later stages), the evidence is limited. LIMO-v2 dataset contains only 800 samples, designed primarily to activate original paper. Thus, it is unclear whether, at larger training scales, Teacher Sentence would still yield significantly higher probabilities for correct answers in the mid-to-late stages. resource constraints, this work focuses models of 8B parameters or fewer. We hope to validate our findings on larger models in future work.
patterns and validate conclusions in the
In summary, our Reasoning Distillation Provenance Tracing shows that in new test settings, distilled models not only produce sentences originating from the teacher, but these Teacher Sentence are especially prominent in early reasoning phases and associated with answer cor- rectness. At the same time, reasoning distillation can also activate patterns already latent within the student (Boosted Sentences), whose contributions vary by model size and reasoning phases, and are not uniformly beneficial.
4 BEYOND EXPLANATION, GUIDING TRAINING IN REVERSE: TEACHER -GUIDE DATA SELECTION
Building on the analysis in Section 3 natural training insight is: if we increase the proportion
of Teacher Sentence in the training data and explicitly leverage teacher-student divergences to select examples, we may front-load and amplity the observed generalization benefits. There-
fore, in this section, we first propose a teacher-guided data selection method in Section 4.1 Then we validate its effectiveness across multiple saccer-studeen pairs and benchmarks in Section
4.1
TEACHER -UUDDD DATA SELECTION
To validate our hypothesis, the first question we must address is: how can Reasoning Distillation Provenance Tracing be applied prior to training? At this stage, we only have access to the teacher model and the student model. Nevertheless, even with only these two models, it still possible to reliably distinguish between Teacher Sentences and Student Sentences. Specifically:
Teacher Model
(1) Sumple
Uhinng Duadd
Previous method
(2) Rnpor
(3) Heuristic
sclection
Stuskent
Midial
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motbod
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(i) Sample
Common Sentence
i((Ars] S (3,
Tmaning
Teacher-
(2) Re-Inpux
guided selection
Teacher Sentence
else if( (AT > (9)
Student
Model
Logits
Student Sentence
else if( Ars > (3)
where Common Sentence subsumes the previously de- fined Shared Sentence and Boosted Sentence. Through this approach, we are able to effectively filter training data to include more Teacher Sentence before training. Specif- ically, for each question with multiple responses from the same teacher model, we count the number of Teacher Sentences in each response and prioritize for training the response with the largest count.
Figure 5: Comparison between teacher- guided data selection and the previous method (Zhang et al.) 2025).
As shown in Figure 5 the previous method (Zhang al.) 2025) feeds the training data into the student model before training, computes heuristics metrics based on the logits of student model, and selects samples that more aligned with the student model's ''s original distribution. In contrast, our proposed method provides a clearer objective for data selection: prioritizing samples where the teacher and student models differ the most.
Moreover, our method introduces only an acceptable additional cost in practice. (1) When one wishes to sample responses, similar to the previous method (Zhang al. 2025). our approach
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incurs no extra overhead, since logits can be obtained directly during sampling. (2) When one wishes to leverage existing open-source distillation datasets for filtering. some additional cost is required. However, it is important to note that re-feeding the generated sequences into the model to extract logits only requires a single forward pass, which is significantly faster than token-by-token generation. Given sufficient GPU memory, consider the additional time cost to be acceptable. 4.2 EXPERIMENTS
We aim to evaluate the effectiveness teacher-guided data selection across diverse training settings. To this end, conduct experiments with three distinct teacher models (Deepseek- R1- R1B.. QwQ 32B, and GPT-OSS- 120B) and four student models: Qwen3-4B-B Bwenn----BBsee, Bowen3-8B-Bal Qwen2.5- 7B-Instruct, and Qwen3-4B-Imm 33344---nttruut25000) We use two high-quality reasoning datasets, AceReason- 1.1-STT (Liu et al.] 2025b) and Oponh"hought (Guha et al.] (025). Each question in these datasets is paired with multiple candidate answers sampled from the teacher model. Further de- tails are provided in Appendix |..5 For each question, we then select a single response using one of three strategies: (i) random selection, which performs similarly to vanilla reasoning distillation ("Vanilla"); (ii) GRAPE (Zhang et al. (025) ("GRAPE"); and (iii) our method ("Ours"). ). All strate- gies yield training sets of identical size.
For evaluation, we select four widely adopted benchmarks known for their challenging reasoning demands: AIME24, AIME25, MATH500 (Lightman et al. 2023). and OlympiadBench (He et al., 2024). We report the accuracy results.
4.2.1 MAIN EXPERIMENTS
As shown in Tables 1. method achieves the best performance. On average, it improves results
by 1.7%-2.5%.
Table I: Comparison with different data selection strategy. Each experimental setting is denoted as Teacher Model Student Model + Data Source.
AIME24 AIME25
MATHISOO
OlympiadBench
Average
Deepseek RI + Qwen3 4B Buse AceReason S.7-SFT
Vanilla
44.4
33,3
91.2
55.9
36.2
GRAPE
Zhang ct al. 2025
43.0
34.1
88.6
54.8
55.1
Ours
49.3+4.
37.9-46 1
90.8
56.6.0.7
58.7+2.5
Deepseck-Re RI + (wenn-88 -BB-BBase AceReason-
I.I-ST
Vanilla
55.1
39.9
912
57.5
60.9
GRAPE Zhang et ul. 2025
54.2
38.1
58.4
60.6
57.3
41.5_
92.8
58.7
62.6,
QwQ-32B
Qwen2. 5-7B Instructtt + Open OpenThouge Thought3
Vanilla
43.5
35.6
89.8
5
56.0
GRAPE
Zhang al. 2025
47.5
34.6
91.4
54.8
57.1
Ours
48.1
36.3
90.0+0.2
56.3
57.7+1.7
GPT-OSS- -S00 + Qwen3 4B- Instruct -507 + Ace I.1-SPT
Vanilla
75.9
62.5
93.6
64.0
74.0
GRAPE Zhang et al. 2025
76,8
66.5
92.6
62.5
74.6
Ours
77.9420
68.3
94.6
64.9
76.4244
Table 2: Influence of different selection metries.
AIME24
AIME25
MATH500
OlympiudBench
Average
Maximize Absolute Count
49.3
37.9
90.8
56,6
58.7
Longest
48.1
37.5
90.0
55.9
57.9
Relative Proportion
46.9
35.0
88.8
55.1
56.4
Vanilla
44.4
33.3
91.2
55.9
56.2
Minimize Absolute Count
42.9
35.2
87.8
$4.2
55.0
4.2.2 ABLATION EXPERIMENTS
(1) How Leverage Teacher Sentences for Data Se- lection? We generally aim to include more Teacher Sen- tences in training data, where "more" can be interpreted in two ways: by the absolute count of Teacher Sentences within a response ("Maximize Absolute Count") or by their relative proportion ("Relative Proportion"). Figure 3 shows that, across most action positions correct re- sponses, Teacher Sentences receive higher output proba-
Figure 6: Illustration of selection for the first training setting.
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bilities from the distilled model. This observation suggests two principles for effective data selec- tion: (i) choose responses that contain as many reasoning actions as possible ("Longest") so that the training signal can influence the maximum number of action positions, and (ii) increase the absolute number of those actions that correspond to Teacher Sentences ("Maximize Absolute Count") to raise the model's probability of producing them at those positions.
To compare these metrics, we conduct an ablation study using Deepseek-RI as the teacher, Qwen3- AB-Base as the student, and AceReason- I.I-SFT as the data source. The results in Table[]show that Maximize Absolute Count yields the best performance, whereas Minimize Absolute Count performs the worst, indirectly corroborating our hypothesis.
Table Impact of different 3 values on accuracy. OlympiadBBenh
AIME24
AIME25
MATH500
Average
3 = 0.05
47.9
37.1
89.8
57.0
58.0
= 0.1
49.3
37.9
90.8
56.6
58.7
8 = 0.15
46.3
37,5
90.2
56.3
57.6
(2) How to determine 3? In Section 3 we describe how to set 3 at test time. Here, we assess whether the same procedure is effective on the training data. We conduct validation experiments using DeepSeek- RI the teacher model, Qwen3-4B B-Bee as the student model, and AceReason- 1.1-SFT as the training data source. As shown in Figure 6 before training we observe that / = 0.1 produces the cleanest partition, with minimal overlap across action types. As shown in Table the optimal / determined before training achieved the best results in the ablation experiment. Moreover, other near-optimal 3 also outperform the Vanilla baseline, indicating that performance is not highly sensitive to the choice of B. Together, the post-training results, along with the pre-training analysis, consistently support our data-driven S-selection strategy as a principled, training- free, and effective approach. For further discussion, see Appendix A.2
(3) Effects in different domain. To evaluate the ef- fectiveness of our method in different domain, we used GPT-OSS-120B to sample 10k questions from Open- ScienceReasoning.. (NVIDIA Corporation (024), gen- crating nine candidate responses per question. We then selected single response for training using different se- lection strategies. Results are reported in Table We find that our method is effective in the scientific domain and, compared to GRAPE, exhibits stronger generalization in math domain. Analysis on the test set further indicates that the Teacher Sentence in science shares commonali- ties with that in mathematics, which we hypothesize helps explain why training on scientific data can improve per- formance on the math test set. Additional analyses are provided in Appendix A.3.3
can
Figure 7: Analysis results of the first training setting (Deepseek-R1 Qwen3-4B-Base SFT) on AIME24.
+ AceReason-1.1-
Table 4: Comparison with different data selection strategy on scientific domain.
GFQA-D
AIME24
AIME25
MATH500
OlympiadBench
APT-OSS-1208
Qwen 1-B
4B-Base Base OpenScience
Vanilla GRAPE (Zhang et al.
39.9
24,2
24,6
85,8
44,0
2025
40.9
24.6
22.1
84.2
44.3
Ours
42.9
25.2
24.8.0.2
87.4.
48.0
(4) Does the distilled model increase the probability of outputting the Teacher Sentence? We apply the Reasoning Distillation Provenance Tracing to our trained models. The results are shown in Figure 7 Compared with the Vanilla baseline, within the range where estimates are statistically reliable (e.g.. the first 800 action indices), our method increases the probability of outputting the Teacher Sentence and correspondingly decreases that of the Student Sentence.
CONCLUSION
In this work, we address a fundamental yet under-explored question in reasoning distillation: does the distilled model truly inherit the teacher's pattern? To answer this, we introduce Reasoning Distillation Provenance Tracing, observe phenomena and quantify the evidences that help explain the observed benefits of reasoning distillation. Building on these insights, we propose a teacher- guided data-selection strategy and demonstrate its effectiveness our provenance-tracte tracing framework will inspire future research on cross- model behavior analysis, domain-aware data selection, and more reliable distillation protocols for complex reasoning tasks.
multiple settings. We hope

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A APPENDIX
A.1
FUTURE WORK
Future work will pursue three directions: (1) when more logits information is available, combine sequential probability matching methods to improve data selection; (2) expand beyond the small- model regime studied here, imposed by resource constraints, to evaluate the effectiveness of our data-selection strategy larger models; and (3) move past the single-teacher setting investigate principled approaches to data selection when training with ensembles of diverse teacher models.
A.2 HOW TO DETERMINE AND B
A.2.1 HOw TO DETERMINE Cr
For it is used to filter out relatively small probability differences that would otherwise affect the analysis. To obtain a relatively objective threshold, we asked 10 annotators to judge the magnitude of probability differences. For each annotation, the annotators were shown sutput-probability line chart similar to that in Figure 2 Given all the sentences in the response, we asked them to identify those whose probability differences could be regarded relatively negligible, such sentences 55-65 in Figure 2 After we explained the definitions of the four sentence types and the goal of our analysis, the annotators manually selected the sentences that appeared more likely be Shared Sentences, and we then derived the final rounded value of a = 0.1 from their judgments.
Threshold-O.1
Threshold-0.15
Threshold-022
histogramms the proportion of actions
Action output probability
Figure 8: Illustration of 3 selection for Deepseek- Soikk-DiDtll--weeeee on AIME24.
A.2.2
How TO DETERMINE 3
0.55 53378
The parameter 3 serves primarily to facilitate clearer separation of the relative proportions of different ac- tion types, enabling more effective provenance analysis. Specifically, for each trajectory, we compute the propor- tion of sentence attributed each action type (e.g., in trajectory 1, 60% sentences are labeled as Teacher Sentence; in trajectory 2, 70%). We then construct his- tograms showing the distribution of these proportions across all samples for each action type (e.g., plotting the distribution of Teacher Sentence proportions using values such as [0.6, O.7.
05112
Overte
0.30
02004
0.5
42200
02202
0.05
0.0
0.15
6.0
025
0:30
Intuitively, we choose 8 to maximize the separation be- tween the distributions of different action types, so that their overlap is minimized, particularly for the action types that dominate in frequency. As shown in Figure g for instance, when 3 = 0.15, the his- togram reveals that most samples exhibit clear predominance of Teacher Sentence, providing clean characterization of the model's output behavior. contrast, when 8 = 0.2, the distribu- tions of Teacher Sentence and Boosted Sentence exhibit significant overlap, indicating that samples within the overlapping region are sensitive to minor fluctuations and may be ambiguously classified. A similar problem also exists with 0.1.
Figure 9: Illustration of f selection pro-
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Algorithm Search for Optimal |
Require: teacher model Mr, student model Ms. batch of data D Ensure: optimal threshold /*
1: Feed D into Mr and Ms to obtain sentence-level output probabilitiee.
2: Following Section 4.2.2) partition sentences and get sentence-level probabilities into: Common
Sentence set C, Teacher Sentence set T, Student Sentence set S.
3: best overlap: O* +- +.00
4: best 3: 3* <- None
5: for 3 E {0.05, 0.10,.... 1.0) do
6: Compute the histogram overlap between S and under threshold denote it as O
7: Compute the histogram overlap between C and TT under threshold 8, denote it as O2.
8: Current overlap + O1 + O2
9:
if < O* then
O 4- 0
11:
8* < B
12:
end if
13: if mean (Cean(C)= > mean(T) then
14: break
15: end if
16: end for
return 3
Therefore, for Deepseek-Distill-weeerr
on AIME24, we set 3 = 0.15. For the experiments in Section 3.3 we evaluate all values of in the range [0.05, 0.2] with a step size of 0.05. The final selected thresholds are: B 0.1 for Deepseck-Distill-Qeenl for wwt.SSee--R--SS2--wwenss
GPQA-D, 3 = 0.1 on AIME24, = 0.15 for DeepSeek-R1-0522 --ee2-QQeen-8BB on GPQA-D, 8 0.1 for LIMO-v2 model on AIME24 when using QwQ-32B teacher model, = 0.2 for LIMO-v2 model on GPQA-D when using QwQ-32B as teacher model. B 0.15 for LIMO-v2 model on AIME24 when using Deepseek-Rl teacher model, and 0.1 for LIMO-v2 model on AIME24 when using Deepseek-RI as teacher model.
In fact, threshold selection is also adaptive procedure rather than manually specified parameter that must be tuned via repeated training runs, which makes it fundamentally different from hyperpa- rameter selection in neural networks. Taking the training-time pipeline an example, the search using Algorithm [ For the four training configurations in Table [ the chosen 3 values are 0. 0.1, 0.15, and 0.2, respectively. addition, we show how this algorithm selects the value 0.2 for Table [. Setting 4, as illustrated in Figure
perform
A.2.3 SENSITIVITY ANALYSIS
We also illustrate threshold selection on first training setting (DeepSeek-RI + Owen3-4B-BB. 4B-Base AceReason-LL1- 1.1-SFT) in Figure 66 The corresponding quantitative results are reported in Table As can be seen, the threshold identified as optimal before training also yields the best performance after training. The post-training metries in Table 3 and the pre-training visualizations in Figure demonstrate that the proposed method is purely data-driven, requires additional training, and is practically applicable. Near-optimal 33 also outperform the Vanilla baseline, indicating that perfor- mance is not highly sensitive to the choice of B.
Additionally, we examine the sensitivity of our analysis to the choice of 3. As shown in Figure g the relative trends and distinctions in action-type output probability between correct and incorrect samples remain consistent across different 3 values, suggesting that our main conclusions are robust to the setting.
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Ds-7B on AIME24
Ds-8B on AIME24
0.
11%
DIN
Tha
Stdden Sanderce
Dusceed SertenLE
Waardd beddawe
Teacher Serforce
Studkmn Sentence
Deniie Sertence
Shared Sentence
Figure 10: Differences across action types. Using SEAL's behavioral categorization, we classify all actions and report the proportion of behavior types within each action type.
A.3 MORE ANALYSIS RESULTS
A.3.1 ALTHOOUGH DISTILLED MODELS GENERALLY EXIIBIT SUBSTANTIALLY STRONGER LONG-CONTEXT GENERATION CAPABILITIES, THE SOURCES OF THESE IMPROVEMENTS ARE NOT UNIFORM ACROSS MODELS.
As shown in Figure within DeepSeek- DeepSeek-Distill-OO Distiil--weer Swelll--we--T0e 7B, once the sequence length exceeds ap- proximately 4K tokens, the generated outputs are quickly transformed into Teacher Sentence. In contrast, this behavior not observed DeepSeek- R1-0528-Qwent
or LIMO-v2 model. We attribute this discrepancy to differences in the underlying student model: DeepSSek-Distill-ONee 7B distilled from Qwen2.5-Math-7 of approximately 4K tokens. Beyond this limit, the model's outputs predominantly reflect patterns inherited from the teacher model. By comparison, DeepSeek PrepSeck-R--SS-1 11-0528-wwent model are based Swee3-8B-Base (Tem 2025a) and Owwe2.5-332B-Ime
(Yang al. 2024), which an effective context length
and LIMO-v2 respectively. These models support substantially longer effective context lengths and thus avoid this limitation.
A.3.2 WHAT BEHAVIORS ARE INCLUDED IN DIFFERENT ACTION TYPES?
We categorize each action using SEAL (Chen et al. 2025, which defines three types of behaviors: execution, reflection, and transition. Execution refers steps that directly advance problem solv- ing, reflection denotes verification, checking, or questioning of the existing reasoning process, and transition represents an intentional change the current reasoning direction or strategy. Special tokens are excluded from the statistics. The results are shown in Figure TO from which we make the following three observations.
(1) Both student models exhibit certain degree of reflection and transition, and reasoning dis- tillation further activates and strengthens these behaviors. Specifically, Student Sentences already contain reflection and transition behaviors, while Boosted Sentences display more of these behav- iors than Student Sentences and Shared Sentences after distillation. Although there remains a gap between RL and reasoning distillation, this observation is similar with prior work (Wang et al., 2025 Gandhi et al., 2025). which suggests that reflection and transition abilities are already latent student models and that RL/Reasoning distillation
post-traine post-training method serves to activate them. (2) The vast majority of Shared Sentences are Execution. (3) The student model of Deepseek- 1--5528-Qeen3 (Ds-8B) shows stronger reflective ability than the student model of Deepseek- Distill-Qwen-T1 (Ds-7B), evidenced by the higher proportion of reflection behaviors in Student Sentences.
A.3.3 TEACHER SENTENCES ACROSS DOMAINS
As illustrated in Figure II we further examine the characteristics of Teacher Sentences across do- mains. In mathematics, Teacher Sentences primarily consist of explicit mathematical operations, followed by checks of these operations and validations of the solution logic. In science, they more often involve inspections of reasoning chains and targeted recall of relevant knowledge. Despite these differences. we observe common patterns: when reasoning stalls, Teacher Sentences prompt the recall of key facts and encourage reflective adjustments the reasoning process. We hypothe-
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D&-8B on GPQA-D
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Figure 11: Comparison of Teacher Sentences across domains. Teacher Sentences are highlighted in light green.
Table Training config.
Qwen3-4B-Band
Qwen3-8B-BB -B-Base
Qwen3 110---B-Innnttt Instruct-2507
Qwen2.5-7BB 7-B-Intuctt
learning_rat
3e-3
Se-5
3e-3
8.0e-5
cutoff_len
32k
64k
64k
16k
epoch
6
6
5
batchsize
32
32
32
512
Ir s..ccccullrr.og type min
cosine with min_Inn Ir
cosine with_min_tt
Dosine_with with_min_Jr min
cosine
lc-5
lc-5
le-5
0
warmup ratio
0.1
0.1
0.1
0.1
size that these shared behaviors explain why training scientific-domain data containing higher proportion of Teacher Sentences can also benefit performance on mathematics test sets.
A.4 MORE DISCUSSIONS
A.4.1 A NEW PERSPECTIVE ON UNDERSTANDING MODELS
Most existing approaches Lee et al. (025): Liu al. (2025a) to understanding model outputs oper- ate in human-centric semantic space. They typically seek to decompose intermediate activations or outputs into numan-interpretable units, such as natural language concepts, symbolic structures, or predefined semantic categories. While this line of work has yielded valuable insights, it implic- itly assumes that model behavior is best understood by mapping it onto human-designed semantic structures.
We agree that semantic/struetur-lleee analyses are important. But we believe that decomposing the outputs of reasoning model into human-interpretable semantic units is not the only way to
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understand model behavior. Instead, method offers novel and complementary perspective: construct a decomposition that naturally induced by the model itself and directly ties its outputs to performance on the test set. This model-centric view allows us to analyze how different components of the model's output contribute to its empirical performance, without requiring a predefined set of cuma-ninterpretable semantic units.
A.4.2 ALIGNMENT OF OUTPUT DISTRIBUTIONS
In the distillation setting, define better reasoning as closer alignment with the teacher model's output distribution. The goal of reasoning distillation is therefore twofold: (i) the student model should learn the teacher model's output distribution, and (ii) this alignment should yield better performance on the test set. In addition to the existing analysis the second point (in main text), further examine the first point. To examine (i), construct three sets of sentences: the teacher model's s outputs on the training set, the teacher model's outputs on the test set, and the distilled student model's outputs the test For each set, we feed every response into both the teacher model and the distilled student model, compute the difference between the output probabilities for each sentence, and then aggregate these differences obtain the empirical distribution histogram of probability discrepancies.
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Figure 12: Distribution of output probability differences. "Train Data", "Teacher Test Data", and "Student Test Data" represent the outputs of the teacher model on the training set, the outputs of the teacher model on the test set, and the outputs of the distilled student model on the test set, respectively.
The results, shown in the Figure 12, compare two different data-filtering strategies. Under both strategies, the probability discrepancy small on the training data (the teacher's outputs on the training set), which is expected because the training data are well fitted. The discrepancy on the teacher's outputs on the test set is slightly larger, indicating that, although the queries the training and test sets differ, the student model still largely follows the teacher model's output distribution when evaluated on the teacher's context. Remarkably, when evaluated on the distilled model's own context on the test set, our method achieves even smaller probability discrepancy than the train- ing data. This strongly suggests a high degree alignment with the teacher's s output distribution. It important to note that the teacher distribution is not directly observable. We only approximate indirectly via the probabilities assigned to sentences under different contexts. The fact, that the smallest probability discrepancy occurs the distilled model's own outputs the test set, indicates that our method allows the student model, in its own generation context, to closely align with the teacher model's output distribution.
A.4.3
CAN THE PROVENANCE METHODOLOGY BE USED TO IDENTIFY WHICH TEACHER MODEL DISTILLED THE REASONING CAPABILITY?
In short, our method is in principle capable of providing evidence about which teacher model con- tributed given reasoning capability. To demonstrate this ability, consider two different sce- narios and validate it in each of them."
(1) The student model is given, but its teacher model unknown.
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10
0.8
Probabiity
0.6
0.4
0.2
0.0
Action index
Figure 13: Analysis results on original teacher. We apply Reasoning Distillation Provenance Trac- ing to Disseekk-Dstill--ee----- and SeepSeek-R1-05225 2022--Qen3--B, analyzing the probability of producing different actions at each action position on two reasoning benchmarks (AIME24 and GPQA-D). The x-axis denotes the action index, and the y-axis shows the probability of producing that action.
1.0
Correct Answers, Thacher Sentence
Correct Answers, Student Sentence
0.8
Answers,
Shared Sentence
Probabiity
Incorrect Answers, Teacher Sentence Incorrect Answers, Student Sentence Incorrect Answers, Boosted Sentence
0.4
Incorrect Answers, Shared Sentence
0.2
200
400
600
800
1000
Action Index
Figure 14: Analysis results spurious teacher. We apply Reasoning Distillation Provenance Tracing to Deepsek-Distill-wwen--T and DeepSeek-RR BaroSeek-R1-05555 11-558-QQwen3-888 analyzing the probabil- ity of producing different actions at each action position on reasoning benchmarks (AIME24 and GPQA-D). The x-axis denotes the action index, and the y-axis shows the probability of produc- ing that action.
We employ the distilled model from setting in Table 1, which was in fact distilled from DeepSeek- candidate teacher models (i.e., DeepSeek-RI and
R1. We then apply our analysis method ppt-oss-120b) to determine which teacher was actually used for distillation.
The analysis results for DeepSeek-RI presented in the Figure 14 We observe that, when a spurious teacher model is used, the output probability of the Teacher Sentence is the lowest, while the output probability of the Student Sen- tence is relatively high. This indicates that our analysis method can, to some extent, identify the true teacher model behind distilled student model.
shown in Figure 13 while results for gpt-oss- 120b
(2) The student model is known to be distilled from multiple teacher models.
From methodological perspective, our provenance analysis can partially identify the extent to which the teacher model contributes to the student model's reasoning capability. For example. in our analysis of the LIMO-v2 model, we observe that, across all teacher models, the Teacher Sen- tence tends to be assigned a higher output probability on correct answers than incorrect ones. However, different teacher models exert heterogeneous influences on the student model. Concretely, the first 400 steps (those with relatively stronger statistical significance), lative difference between the output probability of the Teacher Sentence on correct versus incorrect answers, and obtain the following sums: gpqa-R1 (9.41), gpqa-QwQ (7.66), aime-R1 (7.09), aime- QwQ (7.88).
compute the cumu-
These results suggest that, although the exact proportions of R1- and QwQ -eneratedd data in the LIMO-v2 training set are unknown, the data produced by these two teacher models have heteroge- neous effects across domains. We tentatively hypothesize that, GPQA, the reasoning capability
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distilled from R1 is particularly beneficial for scientific questions. The result is consistent with the fact that DeepSeek-RL substantially outperforms QwQ on GPQA while performing comparably to QwQ on AIME. In future work, plan to further investigate how identify which teacher model has contributed the distilled reasoning capability to the student model on different domains.
A.5 TRAINING DETAILS
For the OpenTThought3-111 1.2M dataset, used only the mathematical problems and randomly sam- pled 50k questions. For each question, the official dataset provides 16 responses generated by QwQ: from these, we randomly selected responses form our initial training set.
1-FT dataset, we first randomly sampled 50k mathematical questions. For each question, the official dataset provides multiple responses generated by RI. We then addition- ally generated 1-5 responses per question using GPT-OSS- (configured with Reasoning: gi)h). Together, the RI and GPT-OSS- 120B responses served as our initial training set.
For the AceReason- 1-SFFF
The training configuration is provided in Table 5
A.6 RELATED WORK
A.6.1 LLM DISTILLATION
Knowledge Distillation. Knowledge distillation was first introduced by (Hinton et al. 2015a) as technique for transferring the dark knowledge of teacher model to a lightweight student model via soft labels, thereby enabling substantial model compression while preserving most of the original ac- curacy. Subsequent works (SF) 2014 Zagoruyko & Komodakis, 2016) has extended this framework from multiple perspectives, for example by distilling feature layers or intermediate representations and by introducing relational or structural distillation, so that the student not only mimics the output distribution but also aligns the structural properties of the hidden representation space. Later works (Ko et al. 2024 2025) further improve alignment by approximating sequence-level KL divergence, leading to more effective distillation. In practice, knowledge distillation (Gou et al. 2021) has been widely applied to tasks such as image classification, object detection, and natural language process- ing, and has become one of the mainstream approaches for model compression and acceleration.
Reasoning Distillation. Distilling the reasoning abilities of large language models has been an im- portant problem since their emergence (Kim & Rush] 2016 [H al. [023] Ko et al.) 2024 2025)
Before the advent of large-scale reasoning models such as Ol (Jaech et al. 2024). traditional rea-
soning distillation methods primarily transferred capabilities by aligning intermediate features or output probabilities between teacher and student models (Kim & Rush 2016
Ho et al. 2023 Ko
al. [2244] 2025). To teach reasoming more explicitly, prior work (Hsieh al. 2023] Kim & Rush,
2016 Ho et al.] [2023] Ko et al., 2024 2025) constructs responses that include detailed reasoning traces and trains the student on these signals, thereby strengthening its mastery of reasoning. In
the era of large-scale reasoning models such as R1 (DeepSeek-A]] 2025) and QwQ (Team) 2025b), which naturally exhibit chain-of-thought reasoning and achieve strong performance, distilling their capabilities into smaller models has become an effective and practical path toward improved effi- ciency. DeepSeek (DeepSeek-AI) 2025) pioneered this line of work by showing that supervised fine-tuning the outputs of a reasoning teacher, which is also the approach we focus in this paper, can dramatically enhance the reasoning abilities of smaller models. Numerous subsequent projects (e.g.. OpenRI (Hugging Face| 2025). OpenTTouughs (Guha et al., (025), a-m-team (Zhao et al. al.
2025), NVIDIA AceReason (Liu et al. (0255), OmniThought (Guha et al. 2025). LIMO (Ye
2025), Deep (He et al. (025)) have devoted substantial effort constructing and refining
large-scale corpora of challenging reasoning problems paired with teacher responses, using rigorous quality filtering, correctness checks, and diversity-aware curation. Most recently, GRAPE (Zhang et al. (023) scores candidate responses with the student model and preferentially selects examples whose likelihoods best match the student's 's current distribution, thereby steering training toward data that is already well aligned with the student. Rather than focusing solely on artificially designed rules and heuristic rules, we view reasoning distillation as a capability teacher to student. We aim to quantify the sources of distilled model's capabilities: given context, which actions in a trajectory from distilled model are more likely to originate from the teacher's behavior rather than the student's existing tendencies? Building this perspec-
problem from
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five, we introduce data selection criterion that jointly compares teacher-student output dis- tributions and focuses on sentences whose probabilities indicate stronger teacher-originated behavior. This provenance-aware criterion complements prior student-only selection in the following way: it provides an explicit cross-model signal for reasoning transfer. In Section show that provenance-aware selection outperforms student-only alignment in settings.
A.6.2 MODEL AUDITING
Another closely related area is model auditing, growing line of work that studies (Song & Shmatikov, 2019 Carlini et al. 2022 Dekoninck et al.] 2024) auditing generative models to un- derstand what data they memorize and to attribute outputs back underlying data sources. For example, prior work (Song & Shmatikov 2019) shows that rare tokens in the training data tend to be memorized by text generation models, and uses shadow models together with audit classifier (e.g., an SVM on boken-rank features) to distinguish whether user's data was included in training. Separately, subsequent work (Carlini et al. (022)) formalizes extractability as the ability of a model, given a prefix, to greedily regenerate the exact suffix from the training set, and systematically studies how repetition and sequence length affect the fraction of such extractable sequences. In contrast, our work targets model-level provenance in a distillation setting: rather than asking whether specific data are memorized, we aim to trace which upstream models are the sources of given output, shifting the focus from data membership to the lineage of the models themselves.
A.7 LLM USAGE
We used Qwen3 for polishing, followed by manual refinement.
20


Reviews:
[{"review_id": "1unyI8QXis", "reviewer": "Reviewer_CXTo", "summary": "This paper considers the problem of tracing provenance in LLM reasoning distillation. The paper proposes Reasoning Distillation Provenance Tracing, a method that quantifies the sources of a distilled model's capabilities: whether it is from the teacher, from the student, or both. Based on this, the paper then proposes a new teacher-guided data selection method, showing its efficacy across various teacher/student models.", "questions": "1. All the provenance analyses are done with open-source, already-distilled models only. What are the effects of different distillation methods? Do they lead to different provenance?\n2. If one utilizes distillation methodologies that explicitly matches sequential-level probabilities [5,6], then would this lead to more homogeneous provenance and potentially even better data selection? Some discussions on this and references therein would be helpful as well.\n\n\n\n[5] https://proceedings.mlr.press/v235/ko24c.html\n\n[6] https://proceedings.mlr.press/v267/ko25a.html", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- A timely, yet interesting topic\n- Well written\n- Several qualitatively interesting experimental results, and promising results for the newly proposed data selection method", "weaknesses": "- Although I'm not an expert in this field, it is still clear that the paper is lacking discussions of prior literature on knowledge distillation and model auditing/provenance [1,2]. Additionally, core literature on distilling LLM reasoning capabilities [3,4] is lacking.\n- Can the proposed provenance methodology be used to identify which teacher model distilled the reasoning capability?\n\n\n[1] https://dl.acm.org/doi/10.1145/3292500.3330885\n\n[2] https://openreview.net/forum?id=TatRHT_1cK\n\n[3] https://aclanthology.org/2023.acl-long.830/\n\n[4] https://aclanthology.org/2023.findings-acl.507/", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "GVPBjdsKVR", "reviewer": "Reviewer_8GhT", "summary": "This paper introduces Reasoning Distillation Provenance Tracing, a novel analytical framework for understanding where the behaviors of a distilled reasoning model originate, whether from the teacher model, the student’s prior patterns, or both. Building on these findings, they propose a teacher-guided data selection strategy, experiments across multiple teacher–student pairs show consistent improvements.", "questions": "Does producing more Teacher Sentences **cause** better reasoning, or merely co-occurs with it?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 4, "strengths": "- The paper is well organized and good written\n - RDPT introduces an interpretable framework for tracing the origin of reasoning steps, bridges the gap between explainability and distillation efficiency.\n - Proposes a simple yet effective teacher-guided data selection method.", "weaknesses": "- Lack of validation on larger-scale (e.g., 70B+) models questions scalability\n - The proposed teacher-guided selection requires re-feeding large corpora through both models for probability extraction, cost analysis is needed\n - The method is primarily validated on short- to medium-length reasoning traces, leaving its effectiveness in long-range or multi-step reasoning scenarios uncertain.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "CZj9IXSfpC", "reviewer": "Reviewer_GDUf", "summary": "This paper investigates the origin of student model behaviors in reasoning distillation and introduces a framework called Reasoning Distillation Provenance Tracing (RDPT). Instead of only measuring performance, the authors analyze where each generated sentence (action) in a distilled model comes from—whether it originates from the teacher model, the student model, both, or is newly boosted through distillation. By comparing predictive probabilities from the teacher, student, and distilled models under the same context, they categorize actions into four provenance types. Using this analysis, the paper shows that distilled models indeed generate “teacher-originated” actions even in unseen contexts, and these actions are correlated with correctness, offering an interpretable explanation for distillation’s generalization benefits.\nBuilding on this, the authors propose a teacher-guided data selection strategy that prioritizes examples with higher teacher–student divergence. Experiments across multiple teacher–student pairs (e.g., DeepSeek-R1, QwQ-32B, GPT-OSS-120B) and reasoning benchmarks (AIME24/25, GPQA-D, MATH500) demonstrate consistent performance improvements over prior heuristics such as GRAPE.", "questions": "The experiments focus exclusively on mathematical reasoning tasks (AIME, MATH500, OlympiadBench, etc.), while reasoning distillation is also widely applied to other domains such as common-sense reasoning and natural language inference. Could the authors clarify why the analysis and validation were limited to math reasoning? Are there specific challenges that make extending the proposed provenance-tracing framework to broader reasoning domains difficult or less meaningful?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "- Provides a novel analytical framework (RDPT) that quantitatively traces the provenance of reasoning actions, offering interpretability to the distillation process.\n- Empirical evidence that distilled models reproduce teacher-originated behaviors in unseen contexts, explaining why reasoning distillation generalizes.\n- The proposed teacher-guided data selection is simple yet principled, improving performance across diverse teacher–student configurations and datasets.\n- Strong experimental design and evaluation, with systematic analysis on multiple benchmarks and detailed ablation studies.\n- Offers insightful observations about how teacher- and student-originated patterns emerge and interact during reasoning, bridging the gap between empirical distillation and interpretability analysis.", "weaknesses": "- The proposed framework (RDPT) is primarily analytical and diagnostic rather than methodological. It provides interpretation of distillation outcomes but does not introduce new mechanisms that improve reasoning capability.\n- The provenance classification relies on manually set thresholds (α, β) and simple probability gaps between teacher and student. This rule-based design is heuristic and potentially unstable across datasets or model scales.\n- The definition of “teacher-originated” actions is superficial and token-level, lacking semantic or reasoning-structure grounding. High teacher probability does not necessarily imply genuine reasoning transfer.\n- Experimental coverage is limited to ≤8B models and a narrow set of teacher–student pairs; it remains uncertain whether the findings generalize to stronger or cross-architecture settings.\n- The teacher-guided data selection method is incremental over GRAPE, and its ~2% average gain is modest given the extra computational cost of obtaining teacher logits.\n- The analysis focuses entirely on quantitative trends, without qualitative or behavioral validation to substantiate the claim that “teacher-originated” sentences truly reflect reasoning inheritance.\n- The framework assumes access to teacher probabilities for all samples, which restricts scalability and practical applicability in closed-source or large-model scenarios.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "aK5pd2ThZa", "reviewer": "Reviewer_E2xa", "summary": "This submission studies reasoning distillation, where a smaller student model is fine-tuned on reasoning paths generated by a larger teacher model. It first proposes a method called Reasoning Distillation Provenance Tracing to categorize each reasoning step (\"action\") produced by a distilled model, based on the probabilities assigned to it by the distilled model, teacher model, and student model before distillation. The aim is to determine whether a reasoning step is more likely to originate from the teacher model, from the student before distillation, or be \"boosted\" by distillation even though the teacher does not assign it high probability. The authors present a study using Reasoning Distillation Provenance Tracing on open-source distilled models and reasoning datasets. The second part of the submission builds on the first by selecting examples for distillation where the probability of the example's actions being teacher-generated is higher. Experiments show that this data selection strategy outperforms random selection and a baseline called GRAPE in terms of the distilled model's performance on reasoning benchmarks.", "questions": "In order of importance:\n- Regarding weakness 4 above, how were the 4 combinations in Table 1 chosen? \n- I would appreciate responses to the clarity issues identified above.\n- Did the authors try splitting sentences using a natural language processor such as NLTK or spaCy? These may be more robust than the regex pattern used.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "- This work aims to go beyond performance on reasoning benchmarks to understand the effects that distillation has on a granular, step-by-step level. The proposed categorization of actions appears simple and reasonable.\n- The work also aims to close the loop by using the categorization to select more effective examples for distillation, with encouraging results.\n- An effort is made to experiment on multiple student models, teacher models, distillation datasets, and evaluation datasets.", "weaknesses": "1. The paper claims that distilled models reproduce teacher-originated actions in \"entirely new contexts,\" and the newness of test contexts is emphasized throughout. However, this newness is not substantiated. Moreover, newness as a binary notion misses the fact that similarity to training contexts lies on a spectrum. I think it would be better to quantify somehow the dissimilarity of test contexts from training contexts, at both the sample and dataset levels, and analyze results in terms of this dissimilarity.\n1. Figures are unclear, to the point of obscuring evidence for main claims of the paper (see especially the first point below).\n    - Figures 3 and 4: The solid and dashed lines are hard to distinguish. This makes it hard to be convinced of finding (3) in Section 3.3 in particular, i.e., the correlation between Teacher Sentences and correctness. Can this correlation be quantified so that the evidence is not just visual comparison of two curves? It is also hard to understand finding (2) in Section 3.3 from the current figures.\n    - Legends, tick labels, etc. are too small: This matters especially in Figures 3 and 4 because the line colors and line types are not described in the text.\n    - Figure 6: The x-axis is not labelled (and the tick labels are very small). This does not help in explaining the selection of $\\beta$ (see next point).\n    - Figure 7: Since the estimates are statistically reliable only for the first 800 action indices, a suggestion is to restrict the plot to this range so that it can be clearer.\n1. The selection of threshold $\\beta$ is described only in Appendix A.2. Given that $\\beta$ is needed in both Section 3 (provenance tracing) and 4 (data selection), and given the claim (in bold) about the selection of $\\beta$ (lines 442-445), this description should be in the main paper.\n    - As a secondary point, the selection of threshold $\\alpha$ is also unclear, specifically what is meant by \"manual binary classification\" (lines 243-244). What is the classification task? Why not set $\\alpha$ larger than 0.1 if \"the average probability difference for Shared\nSentence was found to be 0.097\"?\n1. Main results for data selection: With 3 teacher models x 4 student models x 2 data sources, there are 24 combinations. However, the main Table 1 shows only 4 combinations, and I did not find more in the appendix. There is thus no assurance that the combinations in Table 1 were not cherry-picked.\n1. Some sentences are unclear or should otherwise be improved. Below I list only ones where I am quite unsure of what is meant. That said, I consider this point to be less important than the other presentation issues above.\n    - Lines 155-156, \"minimal sentence level\": Why is it \"minimal\"? It is also not clear at this point that each reasoning step corresponds to a sentence.\n    - Lines 253-254, \"the Teacher Sentence curve in the figure\": Which figure?\n    - Lines 267-268, \"Figure 2 and Figure 10 further illustrate this point\": I do not see how these figures show emergence of other actions after a few steps.\n    - Lines 320-327: This paragraph about LIMO-v2 is unclear to me, especially \"LIMO-v2 contains only 800 samples.\" It appears that LIMO-v2 refers to both a model as well as a dataset. I do not understand the statements about the work being limited to models of $<8$B parameters. A quick look at LIMO-v2's GitHub page suggests the LIMO-v2 model has 32B parameters.\n    - Lines 360-361, \"for each question with multiple responses from teacher models\": This is confusing because it suggests that multiple teachers give responses to the same question, and the selection is between teachers, which does not seem to be the case later on.\n    - Section 4.2.2 ablation (3): What is the domain of the two main datasets, AceReason-1.1-SFT and OpenThought3-1.2M, if science is considered a different domain?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)