The Quest for Efficient Reasoning: A Data-Centric Benchmark to CoT Distillation
Authors: Ruichen Zhang
Rana Shahroz
Zhen Tan
Dawei Li
Song Wang
Tianlong Chen
Venue: ICLR 2026 Poster (2026)
Keywords: Chain-of-Thought
Knowledge Distillation
Large Language Models
Benchmarking
Data Augmentation
Data Selection
Data Mixing
Primary area: datasets and benchmarks
TL;DR: DC-CoT is the first benchmark for data-centric CoT distillation, testing how augmentation, selection, and mixing impact student LLMs. It evaluates multiple teachers and students  across multimodel reasoning tasks, focusing on IID, OOD, and transfer.

Abstract: Data-centric distillation, including data augmentation, selection, and mixing, offers a promising path to creating smaller, more efficient student Large Language Models (LLMs) that retain strong reasoning abilities. However, there still lacks a comprehensive benchmark to systematically assess the effect of each distillation approach. This paper introduces DC-CoT, the first data-centric benchmark that investigates data manipulation in chain-of-thought (CoT) distillation from method, model and data perspectives. Utilizing various teacher models (e.g., o4-mini, Gemini-Pro, Claude-3.5) and student architectures (e.g., 3B, 7B parameters), we rigorously evaluate the impact of these data manipulations on student model performance across multiple reasoning datasets, with a focus on in-distribution (IID) and out-of-distribution (OOD) generalization, and cross-domain transfer. Our findings aim to provide actionable insights and establish best practices for optimizing CoT distillation through data-centric techniques, ultimately facilitating the development of more accessible and capable reasoning models. The nonymous codebase can be accessed https://anonymous.4open.science/r/DC-COT-FF4C/

Published as a conference paper ICLR 2026
THE QUEST FOR EFFICIENT REASONING: A DATA-CENTRIC BENCHMARK TO COT DISTILLATION
Ruichen Zhang Rana Muhammad Shahroz Khan"1, Zhen Tan", Dawei LI,, Song Wang", Tianlong Chen
University of North Carolina at Chapel Hill, Arizona State University, University of Virginia
ABSTRACT
Data-centric distillation, including data augmentation, selection, and mixing, offers promising path to creating smaller, more efficient student Large Language Models (LLMs) that retain strong reasoning abilities. However, there still lacks a comprehensive benchmark to systematically assess the effect of each distillation approach. This paper introduces DC-CoT, the first data-centric benchmark that investigates data manipulation in chain-of- thought (CoT) distillation from method, model and data perspectives. Utilizing various teacher models (c.g., o4-mini, Gemini -Pro,, Claude-3. 5) and student architectures (e.g., 3B, 7B parameters), we rigorously evaluate the impact of these data manipulations on stu- dent model performance across multiple reasoning datasets, with a focus on in-distribution (IID) and out-of-distribution (OOD) generalization, and cross-domain transfer. Our find- ings aim to provide actionable insights and establish best practices for optimizing CoT distillation through data-centric techniques, ultimately facilitating the development of more capable reasoning models. The codebase can be accessed here
1 INTRODUCTION
Large language models (LLMs) achieve strong rea- soning performance when combined with ohain-of- thought (CoT) prompting (Wei et al. (022). but the best performance typically comes from expensive models with tens or hundreds of billions of param- eters. To address it, knowledge distillation (KD) stands out to transfer reasoning skills to lighter stu- dents (e.g. 3-8 B) at low inference cost (Hinton et al.)
Teacher
Data-Centric Munipulations
Augmentation
Selection
Mixing
G
Clande
Qucetiva Bephraaing
Tencher Cherecttoos
Jilcciu
Quees
GPT
Q/A
Muslent
hN
2015
et al. 2022b) Among various KD strategies for CoT Xu al. (2024); Tan et al. (2024), data-centric muethods-such as augmentation, selection, and mix- ing ing-have gained popularity for being architecture- agnostic and cost-efficient Xu et al. (2023). How- ever, systematic assessment still lacking eval- uate the effectiveness of these techniques.
Ho et al. 2022 Mukherjee et al.) 2023 Wang
Gemini
Thislingg
Judge
Teadwer
Theeskeak
IID OOD
Exaluation
n/
GONOK
ANLI
Datee
Wetherene
Figure 1: Overview of DC-CoT pipeline.
To address this, building data-centric benchmark is essential. Such a benchmark will provide a clearer understanding of the performance of existing data-centric
Equal contribution.

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Published as a conference paper ICLR 2026
methods by systematically evaluating and answering fundamental questions, such how to effectively synthe- size, select, and mix various CoT samples to robustly boost the student models' performance. Furthermore, a data-centric benchmark will serve as a valuable and controlled evaluation resource for future research and the development of new techniques in this area. In this work, we introduce DC-CoT, the first benchmark designed to investigate data-centrie CoT distillation systematically, answering the following research questions:
Method Perspective: How can various data-centric CoT distillation methods for LLMs be categorized, and what is their comparative performance in enhancing student model reasoning?
Model Perspective: How do the relative sizes and architectures of teacher and student models influence the effectiveness of data-centric CoT distillation?
@ Data Perspective: How do different data characteristics and settings, such as in-distribution (IID) versus out-of-distribution (OOD) data, casy-to-hard generalization, and data availability, impact the outcomes of Thouuht distillation?
Regarding the Method Perspective, DC-CoTT investigates various data manipulation strategies across three core axes: (i) Augmentation: Techniques like reverse reasoning and question/answer re- re-phrasing beyond vanilla COT. (ii) Selection: Compare heuristics such teacher-correct filtering, student-crror prioritization, and LLM-based quality judges (iū) Mixing: Explore blending CoT data based on length, domain, and teacher origin. To explore the Model Perspective, DC-CoT incorporates diverse teacher models (e.g., GPT-4o, Claude 3.5, Gemini- 1.5-Pro) and various open-source student model families and sizes (e.g.. LLaMA, Qwen, Gemma 3-8B parameters). To address the Data Perspective, evaluations conducted across reasoning datasets, specifically examining performance in in-distribution (IID) and out-of-distribution (OOD) settings.
Through extensive experiments, we present key findings and insights guided by research questions across multiple perspectives. From the Method Perspective, we find data augmentation to be generally the most effective approach and provide fine-grained analyses for each manipulation method across task types. From the Model Perspective, we confirm the roles of compatibility and learnability, highlighting their non-trivial impact on distillation and explaining why certain teacher student pairs may fail. From the Data Perspective, we reveal distinct scaling behaviors across augmentation methods and quantify the generalization capabilities of student LLMs across datasets. All these insights will help guide future research toward more effective and efficient CoT distillation paradigms.
In Summary, our work makes the following contributions:
① We present DC-CoT, unified, data-centric benchmark that explores data manipulation in distillation from method, model and data perspectives.
We conduct extensive experiments across diverse teacher-student pairs, tasks, and datasets, offering the first large-scale empirical overview of CoT distillation.
We distill actionable guidelines-e, e.gg. which augmentation boosts generalization, which filtering criterion balances quality and coverage, and when heterogeneous teacher mixtures thereby charting a path toward smaller yet more capable reasoning models.
2 RELATED WORKS
Reasoning in LLMs. Ohain-of-Thoughh (CoT) elicits explicit intermediate reasoning steps. making LLM inference more transparent and markedly more accurate on multi-step tasks (Wei ct al. 2022 Kojima et al. 2022). Based this, newer long-Co'I methods e.g. Tree-of-Thought iterative self self-reflection, and self- correction secaltiion-salleeeeeee CoT by exploring multiple paths and refining answers through critique (Yao et al. 2023a
Madaan al. 2023
Yu et al. 2025 Li et al. 2025c).
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Knowledge Distillation in LLMs. Knowledge distillation transfers the behaviour of large teacher LLM
to smaller, cheaper student. Beyond the original "soft-label" paradigm (Buciluã et al. 2006 Hinton et al. 2015), recent work treats LLM- -LM--geeratee instructions, responses, and rationales as synthetic supervision
for supervised fine-tuning or alignment tuning (Kim et al., 2023 Tong et al. 2024 Ouyang et al. 2022 Zhang et al. 2024] Wang et al. 2024). A particularly effective variant reasoning or chain-of-thought
(CoT) distillation: instead of imitating only the final answer, the student is trained to follow the intermediate
reasoning produced by the teacher, which has proved crucial when capacity or architectural gaps exist (Hsich) ct al. 2023 Mukherjee et al. [023] Lewkowycz et al. 2022) Yu et al. 2023). Despite promising gains, the field still lacks principled guidance on (i) which teachers, (ii) which rationales, and (iii) what selection or
mixing strategies yield maximal benefit for given student, motivating more data-centric exploration of
CoT distillation. More detailed related work is given in Appendix D
3
METHODOLOGY: A DATA-CENTRIC COT DISTILLATION BENCHMARK
3.1 DATA-CENTRIC MANIPULATION
The central theme of our DC-CoT is the systematic evaluation of data-centric manipulations applied to CoT exemplars for knowledge distillation. These manipulations manipulations encompass various strategic opera- tions to transfer the initial dataset Doouree to the tar- get dataset forget for small student model training, potentially guided by set of parameters rules O Dtarget = M(D Q). Here, M represents the abstract data transformation function encompass- ing augmentation, selection, and mixing. For aug- mentation strategies, we denote L the number of synthetic samples generated per source instance. DC-CoT is designed to deconstruct and analyze the impact of instantiating .M through three primary types of data-centric operations: O Data Augmen- tation (Section 3.1.1 @ Data Filtering (Section and @ Data Mixing (Section 3.1.3).
Data Sourse
Rephrase
Quuestion Angmentation
Data Turget
Answwer Auguentation
Revveree Thinking
Quattion
Figure 2: Data-centric augmentation flow. Teacher CoT traces are independently transformed by four op- erations: Rephrase Question, Question Augmentation, Answer Augmentation, and Reverse Thinking.
3.1.2
3.1.1
DATA AUGMENTATION
Data Augmentation is crucial in CoT distillation by enriching and diversifying the training data (Dsouree) available for the student model, to expose the student to various reasoning patterns, question formulations, and explanatory styles for enhancing their reasoning capabilities and generalization. Within the DC-CoT benchmark, we investigate several data augmentation strategies follows:
Question Rephrasing: This method, introduced in MetaMath (Yu et al. 2023). aims to increase question diversity by having the teacher LLM T paraphrase existing question Qi while preserving its underlying meaning and original answer AT: ( TQQ Preph) ) 1 Here Q; and Preph the original question and rephrasing prompt. For each rephrased question Q, the teacher T generates CoT rationale Rt and answer AY. one augmentation is retained if Ai matches the original answer.
This strategy focuses on creating entirely new questions Qnews to broaden the topical coverage or complexity of the training data, based on set of seed questions Q (Li et al., 2024a): Q = T(Q, PQ.). Poa here is a prompt for generating novel questions. After that, the same generation- then-filter process will be adopted to produce answers and CoTs for the augmented questions,
Question Augmentation:
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introduced in the Question Rephrasing method. Unlike general instruction-tuning methods (c.g.. Self-Instruct), this operation is strictly constrained to Reasoning Transfer. The prompt PQ forces the generation of parallel reasoning problems (e.g., altering numerical values in math or subjects in logic puzzles) to ensure the student learns the underlying reasoning pattern rather than memorizing specific answers.
Answer Augmentation: It involves prompting the teacher LLM to generate multiple diverse CoT rationales R that all lead to the same correct ground-truth answer A (Yu et al. 2023). Given (Qi. A7) E Doouree, and using CoT generation prompt PAA. the teacher model generates candidate rationales and answers as follows: {(R A (Q,.. PAA, temp) To mitigate the risk of reasoning hallucinations,, the prompt explicitly conditions the teacher on the ground-truth answer A; Our empirical results suggest that the benefit of exposing the student to diverse valid reasoning paths outweighs the noise of occasional imperfect traces, as the student learns the intersection of valid logic across the augmented set.
e Reverse Thinking Augmentation Reverse Thinking was introduced in the RevThink (Chen et al. 2024b). The goal is to enrich the data by generating forward CoT reasoning Ry. a corresponding backward question
Q' and backward reasoning Rg. For each A.) E Deource we do the following:
Generate Forward Reasoning: R2 T(Q Py) for some prompt Py. This is filtered to ensure that the
outcome of Ry is the ground truth A,,
Generate Backward Question: Using prompt Pog. the teacher T generates question that inverts the original problem: Q3 T A,, Poy).
Generate Backward Reasoning: The teacher then generates the CoT for this backward question: Rt T(q Por) for some prompt Por-
Consistency Filtering: A consistency check c = T(;;, A,, Qi Ri, Poon) is performed for making sure the backward and the forward questions are related and consistent with each other Yang et al. (025). Only consistency quadruplets (Q,, Ryy Q8 Rj) where are retained.
3.1.2 DATA FILTERING
Data Filtering, or selection, is critical step applied to either initial source data D or augmented data to create a high-quality training set Diroin for the student model. Since not all CoT instances are equally beneficial, as some are noisy incorrect, filtering aims to identify and retain the most valu- able exemplars to optimize learning. Our DC-CoT investigates the following data selection strategies:
Data Souree
Forward Reasoning
Consistency Filtering
?
yelated and concktveary
Answar
Quadion
Rossniin
Antove
Backward Reasoning
Data Targel
Filtering by Teacher Correctness: This strat- egy used in (Ho et al., 2022), retains CoT instances where the teacher's final answer A, matches the ground-truth answer A:: Dearget {(Q,, R, A.) A; A This ensures the student lears from CoTs lead to correct outcomes.
Q
Qf
Figure 3: Reverse- augmentation pipeline: from each (question, answer) pair, generate forward reasoning, synthesize backward question with its reasoning, then keep only examples whose forward- backward chains pass a consistency check.
Filtering by Student Error: This filtering strat- egy focuses student learning on its weaknesses by selecting instances where the student model yields
an incorrect answer: Dtarget_ = ((Q,, R2, Ac) A, + A7). This concentrated learning can focus on students' underperformed areas.
auddee Filtering: Inspired by I-SHEEP Liang et al. 2024 this method uses an external LLM judee to assess CoT instance quality based on criteria like coherence, correctness, and clarity, allowing for nu-
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anced quality assessment Li al. 2024b 2025a): Score, Ljudge (Ai, Ri, Qi, Perat). Instances are retained if their score meets threshold making the final dataset become: Dsouree = {Qi,, R., A,) [Score 2 r). To validate the reliability of this automated judge, we conducted human evaluation on a random sample of 100 filtered instances from SQA and GSM8K. We observed a Cohen's ss Kappa (k) of 0.84, indicating strong agreement between the LLM Judge (GPT-4o) and human experts, with the Judge exhibiting a slight preference for strictness- desirable bias for high-quality distillation.
3.1.3 DATA MIXING
Beyond augmentation and selection, Data Mixing offers another avenue for data-centric manipulation in CoT distillation. This strategy involves strategi- cally combining CoT instances from different dis- tributions with varying characteristics to create more diverse training dataset Daagget for the student model. The core idea is that blend of reasoning styles, complexities, or teacher provenances can lead student model with more robust and generaliz- able reasoning capabilities.
Teeeher- Generated (CVT Dataseei
'tucchr-Corrret Fihuring
Quigl-Qallity Training
Anoust AL
Gnornd Truth s.peeeee -o---
Student Pesoritiation
Anarver
Student
Cunation G.
Stidett Anserd Gromnd G
11M-aa-Julle lilterin
Length-based CoT Mixing: Length- mix- ing, introduced in (Li et al. 2025b), combines CoT examples of varying reasoning length to help bridge this learnability gap for smaller models and offers complexity for larger models. This mix, controlled by a ratio a, aims to provide balanced curriculum, exposing students to detailed and concise reasoning.
Gerand
Groznd
Aneave A. Grord Truth G. Lodeeroolll
Figure 4: Data-filtering pipeline in DC-CoT. A teacher- generated CoT pool is refined through three selectors.
Teacher-based CoT Mixing: This method blends CoTss generated by different teachers (Li et al. 2025b).
The mixed dataset is again guided by ratio providing balanced set of reasoning examples and preventing smaller students from being overwhelmed while still offering sophisticated examples.
4
EXPERIMENT RESULT & ANALYSII
4.1 BENCIIMARK SETUP
Teacher Models. We use SoTA LLMs known for strong reasoning to generate CoT rationales: (1) Gemini- 1.5-Pro Team et al. 2024a), (2) GPT-4 (Achiam et al. (2023). (3) Claude-3.5 Sonnet (Anthropic) 2024]. (4) G mini (OpenAl 2024a), (5) 04 mini (OpenAl 2024b). Utilizing multiple teachers allows us to study the impact of teacher diversity. Data filtering is performed with task-specific Judge LLMs: LLama-2-70BB for textual tasks, GPT-40-mini (Achiam et al. 2023) for agentic tasks, and GPT-4/4. 1miin for visual tasks.
Student Models. We test these open-source models as students: (1) L. 1-8B (Grattafiori et al. 2024
(2) LLaam-3... 1-8B-R1 Distilled (Guo et al. 22025) . (3) Mistral-7B (Jiang et al. 2023). (4) Gemma-78 7B Team ct al. 2024b). and (5) Qwen-2.5-7B Yang et al. 2024). Baselines. For Baseline comparison, we evaluate the models for (1) Zero Shot performance on the tasks, (2) Generate Zero-Shot CoT (Kojima et al. (022). (3) Fine-tune the model on the dataset without any COT, and (4) Vanilla CoT generated by the teacher model
with no pwanenttttion/llteinngmmiaeeee
Datasets. Student performance assessed on diverse reasoning datasets covering various skills and complexi-
ties. We evaluate textual reasoning tasks on: Commonsense Reasoning Tasks: StrategyQA (SQA; (Geva et al.
202I)). CommonscnseQA (CSQA; (Talmor et al., (211)), ARC-challenge (ARC: (Clark et al. (2018)) Math
Reasoning: GSM8K (GSM8K; (Cobbe et | (001)), MATH (MATH; (Hendrycks et al. (2221)). Natural Language Inference: ANLI (ANLI; (Nie et al. 2020). ). Logical Reasoning: Date Understanding (Date;
(Srivastava et al. 2022)) ) We evaluate agentic reasoning tasks on WEBARENA (Zhou et al. 2023) and
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Table Accuracy of augmentation, selection and mixing strategies on Llama-3. 1-8B. Textual scores are the mean of three independent runs.
Agenic
Visual
Textual
AVG
WebArana
Visual-CaT
OK-NQA
CLEVV
CSQA
MATH
VisullAAmmiic
Auguesttttio
Zemo Shot
5.66
42.
65.60)
$6.88
$7.64
43.08
48.46
9.32
19.54
13.83
49.70
23.85
57.38
Zero Shot CoT
8.25
44.52
61.84
58.36
65.55
53.56
67..4
11.76
21.00
39.92
62.13
26.39
45.90
No CuT
30,05
46.66
62.18
52.12
59.89
65.36
60.41
7.39
20.74
35.42
50.37
38.36
42.80
Vanilla CsT
22.
59.94
4:35
57.02
34.11
Rephrase Question
Question Aug
61.47
20.31
44.03
41.25
61.07
51.27
Answer Aug
64
64.
$1.61
36.84
$3.48
40.29
61 80
57.58
Reverse Thinking
72.49
78.46
$2.17
35.52
76.35
49.75
70.41
66.45
Selection
7.39
Fillering with Teacher
14
45.50
61.43
70.72
5.04
30.27
24.11
69
30.08
44.73
Filtering with Studort
27.59
45.90
66.30
57.02
60.20
70.85
60.30
5.21
26.97
25.40
58. 04
36.75
43.87
Jodge LLM
15.64
46.54
59.42
$4.12
$4.83
62.49
57.46
3:43
22.72
26.51
59.85
31,09
41.01
Dara Mixing
7.39
Length Mixing
21.84
Teacher Mixing
21.18
45.48
61.7
$3.6
56.75
66.94
62.82
5.96
19.57
29.45
52.30
33.33
41.97
evaluate visual reasoning on Visual-CoT (Shao et al. 2024), OK-VQA (Marino et al. 2019). and CLEVR
(Johnson al. 2017). We classify Shopping, Map, and Reddit webarena-easy, and others as hard. For task descriptions, please refer to
4.2 METHIOD-LEVEL RESULTS
This section delves into the performance of various data-centric manipulation strategies by posing key questions and deriving insights from our experimental findings. The analysis primarily references Table [ It is important to note that the results discussed in Table all pertain to the Llama-3. 1-8B student model. Furthermore, the teacher model for visual tasks was GPT-4-mini (Achiam al. (023), for agentic tasks
Claude-3.5 (Anthropic. 2024), and for textual tasks, (emmini-13-Pro-00) (Team al. 2024a) was used. For the mixing, we use the models as described in Table and
and
Q1: How do the broad categories of data-centric manipulation compare in terms of overall effectiveness? Table D shows that Data Augmentation strategies yield the most substantial average performance uplift over the Vanilla CoT baseline. For instance, Reverse improves average accuracy all eight tasks by 24.64%1. Filtering with Teacher Correctness (Textual Average: 44.7%) improves by +1.93 over Vanilla CoT. The best mixing strategy, Teacher Mixing (Textual Average: 41.97%), shows marginal decrease of 0.83% over Vanilla COT. This confirms that for a moderately sized student (7-8B), creating diverse rationales is more impactful than selecting or reshuffling existing ones. Data selection vital for quality control, and data
mixing helps tailor its composition.
Comparison with Logit-based Distillation. While DC-CoT focuses on black-box distillation (where teacher logits are unavailable), we assessed its com- petitiveness against white-box methods using open-weights teacher (Llama-3.1-- 1-70B on the ARC- Challenge. As shown in Table 2, DC-CoT (Reverse Thinking) achieved 69.2%. significantly outperform- ing standard Logit-based KD 64.8%. This suggests that transferring explicit reasoning steps via data aug- mentation is more effective for reasoning tasks than minimizing divergence the output distribution alone.
Table 2: Comparison of Data-Centric Distillation vs. Logit- KD on ARC-Challenge (Teacher: Llama-3.1-70B),
Method
Access Required
Accuracy (%)
Teacher Baselinc
Weights/Logits
92.4
Standard KD (KL Div.)
Weights/Logits Black-box (Text)
64.8
Vanilla CoT (SFT)
60.4
DC-CoT (Reverse)
Black-box (Text)
69.2
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Table 3: augmented distillation results for different teacher student combinations on textual tasks; numbers are three-run averages.
Student Model
Teacher Model
SQA
CSQA
ARC
MATH
GSM8K
ANLI
Date
AVG.
Gemini-1.5-
72.49
78.46
82.17
35.52
76.35
49.75
70.41
66.45
Llama-3.1-90
GPT-4
70.74
71,93
83.64
34.60
70.72
51.37
68.51
64.50
Gemini-1 Pro
69.43
71.74
74.23
36.82
69.45
47.08
70.41
62.74
Llama-3,1-8 1-8B-R1
GPT-4
70.95
68.40
76.84
36.27
70,94
50.58
67.80
63,11
Gemini- 1.5ii-1..... 1.5.
72.05
75.53
76.96
16.12
59.21
45.00
59.17
57.72
Mistral-7B
GPT-4
71.08
72.63
76.85
15.39
58.86
55.62
60.19
57.23
Bemmini-1.5-P Pro
68.12
74.86
73.46
16.54
53.45
40.92
31.36
51.24
Gemma-7B
GPT-4
69.08
73.81
75.60
16.18
54.49
41.65
30.57
51.63
Q2: Which techniques are most effective for each data manipulation? From Table I Reverse consistently excels, especially for structure logical deduction (MATH, GSM8K, Date). It likely fosters deeper under- standing by teaching bi-directional reasoning. Answer Augmentation also performs robustly, particularly for commonsense reasoning (SQA, CSQA), by exposing the student to varied solution paths, enhancing flexibility, While Question Augmentation and Rephrasing increase diversity, the more profound alterations from Reverse and Answer Augmentation generally yield larger gains. Among the selection techniques, LLM-as-a --ddee filtering is highly effective, often surpassing simpler heuristics due to its nuanced assessment of rationale quality (coherence, soundness) beyond mere answer correctness. However, filtering by Teacher Correctness is a strong baseline, ensuring students learn from factually accurate paths and consistently improve over no selection or other methods. When compared to the No Mixing baseline, data mixing strategies show varied effects. Length Mixing (Average: 41.43%) results in slight decrease of 1.37%) on average for textual tasks. However, while underperforming on others, it shows improvements on specific textual datasets like CSQA, GSM8K, and Date. Teacher Mixing also shows a slight decrease of 0.83%) on average for textual tasks compared to No Mixing. These results suggest that the benefits of the tested mixing strategies are not universally additive over strong No Mixing baseline for textual tasks on average, but they can offer advantages for specific datasets or modalities, likely by tailoring the data complexity or teacher style to particular student needs or task characteristics.
Q3: Which data-centric methods show particular strengths for specific reasoning tasks?Optimal
strategies vary by task demands, and combining effective augmentation with suitable filtering or mixing can yield further improvements:
1. Textual Reasoning (SQA, CSQA, ANLJ): Answer Augmentation and Question Rephrasing enhance lin- guistic diversity. These should be combined with LLM-as-a-Judge filtering to ensure the high quality and coherence of the textual rationales. Teacher Mixing could also be beneficial after augmentation for tasks with varying teacher capabilities.
2. Mathematical Reasoning (GSM8K, MATH, Date): Reverse Thinking excels due to the need for backward deduction. Answer Augmentation is also valuable. These augmented datasets should then be rigorously filtered using Filtering by Teacher Correctness to eliminate any incorrect mathematical procedures. Subsequently, Length Mixing can be applied to balance the complexity of Co'Ts presented to the student.
3. Agentic Reasoning ( (WebArena): Given the complexity and potential for action chain errors, the augmented data should be curated using LLM-as-a-Judde filtering to enhance correctness.
4. Visual Reasoning Visual-Cot), It is critical to use LLM-as-Judge filtering ensure rationales are not only logically sound but also accurately reflect and reference the visual content.
4.3 MODEL-LEVEL RESULTS
We explored the effect of Teacher and Student types/sizes as well. For detailed results on Student Models, please refer to Appendix
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Agentic: Claude 3.5
Visual: GPT-4
Visual: GPT-4.1 mini
Average Accuracy (S)
40
Average Accuraty
no CoT
no CoT
no CoT
20
30
20
Avarape
10
0%
100%
0%
100%
Seed Data %
Seed Daña
Seed Data %
Figure 5: Accuracy of different seed-data sizes and teachers for WebArena and Visual-CoT. 4.3.1 TEACHER MODEL ANALYSIS
We investigate the interplay between teacher and student models, summarized in Tables 3 and 4 For textual reasoning tasks, we utilize the best- perffrring augmentation approach, Reverse, and for visual as well as agentic tasks, we report the performance on vanilla COT.
Q4. How does the choice of a teacher model impact the performance of different student models on textual reasoning tasks? Is there a universally "best" teacher for all students? rreeess that for textual reasoning, stronger models like Gemini-1.5. 1..-in and GPT-4 generally yield better results when distilling to capable student mod- els such as -lama-3-8.1 1.8.1B.. B. For instance, 1.ama-3.1-88 achieves a high average textual score for both teachers, suggesting that long the teacher is powerful enough and the student has adequate capacity, transferring com-
Table 4: Impact of teacher model on agentic (We- bArena) and visual (Visual-CoT) performance.
Student Model
Teacher Model
WebArena
Visual CoT
Clande-3.5
22.78
1.lma-3.1-88
GPT-4o
24.51
Claude-3.5
11.33
Llana 3.1 8B
GPT-40
13.79
GPT-4
42.92
Qwen-2,5-VL-3B
GPT-4-mini
45.44
04-mini
45,20
plex reasoning using Knowledge Distillation is quite effective. However, universally "best" teacher is not apparent. While Gemini-1.5 shows slight edge for LLama-3.1 I-BB on average, GPT-4 can be comparable better on specific datasets (e.g., ARC for Llama-3.1-8B2 For Mistral Gemini-1.5 slightly outperforms GPT-4, whereas for Gemma-78 7B, GPT-4 is marginally better than the other. This variability indicates that optimal teacher-student pairings are nuanced, likely influenced by factors like architectural alignment or specific knowledge domains.
Q5. What does performance on agentic and visual tasks indicate about teacher model suitability? Table 4 which exam- ines agentic and visual tasks, provides strong support for the small model learnability gap. This concept suggests that smaller student models (e.g., < 3B parameters) may not al- ways benefit most from the largest available teachers, as they might learn more effectively from slightly smaller teachers whose reason- ing complexity better matches their own ca- pacity. Our results for the Qwen-2.5- V.5- student on Visual-CoTT clearly demonstrate this: distillation from smaller, capable teach- ers like GPT-4-mini (45.44% acc.) and 04- mini (45.20 20% acc.) leads to superior perfor- mance when compared to the largest GPT-4 (42.92% acc.). This implics that the CoTs from very large models like GPT-4 might be overly complex for smaller, specialized model like Qwen- 2.5-VL VL-3B to internalize effectively. The more digestible reasoning patterns of GPT-4-mini and -m-ii likely facilitate better knowledge transfer, highlighting that sheer teacher strength does not guarantee optimal
Table 5: Performance of Llama-3.1 1-BB and Mistral-7B when varying the percentage of seed data.
Student
Auguesttation Type
SQA
ARC
CSMMKK
AVG:
7ero-Shot
Novi
$7.64
45.46
19.64
49.70
43.86
25%
Vanilla Col
60.70
79.95
42.99
64.48
60.78
Vanilla CwT
7380
60:12
36.30
Lluma-3.1-8B
Reverse
79.95
75%
Vanilla CWT
Reverse
67.69
68.12
71.78
80.79
59.67
73.96
$7.09
70.64
100%
Vanilla CoT
Revess sc
$8.08
72.49
82.17
55.34
76.35
24.30
59.41
70.41
75.36
69.28
Zcro-Shot
Nose
$5.02
50.94
20.34
46.75
43.24
25%
Vanilla CHT
Reverse
71.18
20.46
69.52
73.98
$4.13
44.09
62.72
63.58
61.91
65.50
Mistral-BB
50%
Vanilla CIT
Reverse
68.56
64.91
76.11
70.04
$3.90
39.25
58.53
64.59
65.79
58.18
75%
Vanilla CoT
Revesse
62.14
71.98
77.30
64.02
26,91
50.69
66.28
50.95
72.05
76.96
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distillation if the student struggles with the complexity. Q6. Considering textual, agentic, and visual tasks, what general principles can be inferred for selecting an optimal teacher? Several interesting observations lead to emerging principles: (1) The "Learnability Gap" Affects Smaller//pecializzd Students. For smaller specialized students, the strongest teacher is not always the best. A teacher with more aligned reasoning complexity, even if smaller, can yield better results. (2) Student's Prior Distillation History Impacts Recep- tiveness. The Llama-3. 1-8B-R1 model, previously distilled from DeepSeek-R1 shows slightly lower average performance on textual tasks compared to base Llama-3.1 3-BBBBBBBBBBBBBB- when further distilled by either Gemini- GPT-4, This suggests that student's 's prior specializations or distillation experiences can hinder learning from new teachers if their strengths don't 't align, leading to less effective knowledge transfer.
4.3.2 STUDENT ARCHITECTURE AND ADVANCED SELECTION
While we discuss the scaling laws of standard dense stu- dent models in Appendix F. it is crucial validate the universality of DC-CoT across diverse architectures and assess more complex data selection heuristics. To this end, we extended our evaluation to DeepSeek-VL2 (a Mixture- of-Experts model) and Qwen-2.5-VL-8B on visual rea- soning tasks (OK-VQA, CLEVR). Furthermore, we intro- duced an Uncertainty-basee Selection strategy, which prioritizes training instances where the student model ex- hibits high entropy (> 0.5) in zero-shot inference.
Table Performance on Visual Reasoning tasks across Dense (Qwen) and MoE (DeepSeek) ar- chitectures.
Model
Qwen-2.5 VL BB (Dense)
DeepSeok-VP VL.2 (MoE)
Dataset
OK-VQA
CLEVR
OK-VQA
Auginentation
Zero Shot
65 60
56.88
11.60
Zero Shot CoT
61.84
58, 38.36
12.92
Vimilla CoT
59 94
54.04
45,46
Selection
No Selection
59.94
$4.04
45:46
Teacher Filter
63 30
67.60
$1.82
As presented in Table 6 DC-CoT strategies remain ef- fective for the MoE architecture. For instance, Teacher Filtering improves DeepSeek- VL2'ss performance OK- VQA from 45.46% (Vanilla) to 51.82%. Regarding data selection, while Uncertainty-baaee selection yields com- petitive results (e.g.. 59.54% on heuristic methods (Student/Teacher Filtering). This suggests that the foundational primitives defined in DC-CoT are both robust and efficient for diverse student architectures including MoEs.
Student Filter
66.30
57.02
43.46
Judge
Model Uncertainty
59.54
50.26
43.78
Date Milting
No
54.04
45.46
Teacher Mixing 61.70
55.00
48.04
with Qwen), it does not consistently outperform our proposed
4.4 DATA-LEVEL RESULTS
4.4.1 EFFECT OF DATA VOLUME
We investigate the relationship between the volume of seed data used for distillation and the resulting student model performance, referencing Table 5 for the textual reasoning task with Gemini-1.5-4 1.5-Pro as the teacher and Reverse augmentation, and Figure 5 for agentic and visual tasks with Claude 3.5 as the teacher and COT.
Q7. How does increasing the percentage of seed data generally impact student model performance for Vanilla CoT and Reverse on textual tasks? How do these two methods compare? On textual tasks, increasing seed data for Vanilla CoT does not consistently yield linear performance improvements. For Llama-3.1-88 Vanilla CoT performance peaks 50% seed data, then declines. Mistral with Vanilla Cot shows a similar non-linear trend, peaking earlier at 25%. This suggests that additional raw teacher traces might introduce noise or less informative examples beyond an optimal point, potentially hindering learning. In contrast, Reverse augmentation generally shows more consistent benefits with increased data. For both models, Reverse results in better performance at higher data volumes. This indicates that the richer signal from Reverse is more effectively leveraged data volume increases. Q8. Does the "more data always leads to better results" scaling law hold true across these experiments? The traditional scaling law does not universally hold in our experiments. This is particularly evident for Vanilla CoT on textual tasks, where
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performance can degrade with excessive data. However, more data tends be beneficial up to the tested volumes for more sophisticated augmentations like Reverse on textual data, and generally for agentic tasks.
4.4.2 GENERALIZATION CAPABILITY ANALYSIS
We investigate how well reasoning skills learned through CoT distilla- tion on source dataset transfer to related but distinct target datasets, The analysis primarily references Table 4, while all experimental settings are explained in Appendix
Table 7: Zero-shot (7S) versus OOD fine-tuning accuracy with Llama-3.1- 8B.
Training
Testing
Setting
ACC.
9. How does fine-tuning on source dataset generally impact Out-of-Distribution (OOD) performance compared to Zero-Shot performance on the target dataset? Table consistently shows that fine-tuning on source dataset, even if different from the target, generally leads to substantial improvements OOD performance on the target dataset compared to its Zero-Shot accuracy. For instance, after training on SQA, OOD performance on BoolQ improves. Sim- ilarly, training ARC boosts OBQA performance. This trend holds across textual, mathematical, agentic, and even some visual task pairings, indicating that the reasoning skills learned via CoT distil- lation possess a notable degree of transferability. Q10. Are there specific task categories pairings where OOD generalization is particularly strong or weak? Does fine-tuning on source task always guarantee better OOD performance than its Zero-Shot counterpart on the target task? The degree of generalization varies across task categories and specific pairings as observed in T Strong generalization is evident when transferring between similar textual reasoning tasks. For example, training on SQA significantly boosts BoolQ. and ARC training enhances OBQA performance. Mathematical reasoning also shows strong positive transfer, particularly when training on the more complex MATH dataset and testing on GSM8K, and also from GSM8K to its reversed version, GSM8K- -Rvv. Agentic tasks within be
SQA
BoolQ
0OD
64.16
54.75
74.58
ARC
OBQA
0OD
81.60
78
49.74
ANLJ
ESNLI
59.75
GSM8K- Rev
16.74
GSMSK
0OD
38.89
MATH
78
9.32
0OD
8.75
MATH
GSM8K
0OD
80.74
19.64
Webarene-hard
Webarens-casy
Z8
14.18
0OD
19,90
2.44
Weburenn-aasy
Wehurenz
0OD
11.95
42.10
Visual-CoT
OK-VQA
0OD
38.90
OK- VQA
Visual-CoT
ZS
0OD
44.62
44.52
WebArena also demonstrate good generalization across difficulty levels. However, generalization mixed or weak in other scenarios. For instance, while MATH to GSM8K is strong, the reverse (GSM8K to MATH) shows decrease. Visual tasks also present varied results; training on OK-VQA improves Visual-Cot, but training on Visual-Cot leads to a drop on OK-VQA.
For detailed analysis of the computational efficiency and token-level costs of our data-centric pipeline, please refer to Appendix
5 CONCLUSION
This paper addresses the challenge of transferring reasoning from large to small models via CoT distillation, a domain where data-centric strategies have been underexplored. We introduce DC-CoT, comprehensive benchmark designed to systematically investigate how data augmentation, selection, and mixing influence
CoT distillation efficacy. Our findings reveal that data-centric manipulations significantly enhance distillation. Data augmentation, in particular, offers the most substantial performance gains by enriching the diversity of reasoning traces. Furthermore, we distill our findings into heuristic framework for practitioners: (1) Structured Logic tasks (Math, Code) benefit most from Reverse Thinking combined with Teacher Cor- rectness filtering to enforce logical consistency. (2) Open-Enne Ended Linguistic tasks (Commonsense,, NLI) require Answer Augmentation paired with LLM-as-a-June Judge to capture diverse reasoning paths without semantic drift. (3) Agentic and Visual tasks necessitate LL---ss---Jdde
filtering, as simple heuristics fail verify the grounding of rationales in observation contexts. Future work will expand this benchmark include non- Transformer architectures and investigate more complex selection metrics, paving the way to democratize advanced reasoning.
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ACKNOWLEDGEMENT
This work is generously supported by Amazon Research Award, Cisco Faculty Award, UNC Accelerating Al Awards, NAIRR Pilot Award, OpenAI Researcher Access Award, and Gemma Academic Program GCP Credit Award.
ETHICS STATEMENT
We adhere to the ICLR Code of Ethics. No private, sensitive, or personally identifiable data are involved. Our work does not raise foreseeable ethical concerns produce harmful societal outcomes.
REPRODUCIBILITY STATEMENT
Reproducibility is central to our work. All datasets used in our experiments are standard benchmarks that are publicly available. We provide full details of the training setup, model architectures, and evaluation metrics the main paper and appendix. We have also released our codebase anonymous repository, including scripts for preprocessing, training, and evaluation, along with configuration files and documentation to facilitate exact reproduction of our results. Random seeds and hyperparameters will also be included to further ensure reprodueibility.
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A LIMITATIONS
Budget Constraints:
Due budget constraints, models like GPT-o4 were not included in experiments. Moreover, migrating to other benchmarks also incurs substantial API costs. Therefore, for agentic task similar to many related papers /hhou et al. (202)), focus solely the WERARENA Zhou al. (2023) framework. However, our method is simple and efficient, without any benchmark-speaaie optimizations, making easily transferable other models.
Hardware and Time Constraints: Extending distillation to more and larger models is highly challenging due to hardware and time limitations. Therefore, we selected some student models for our distillation experiments.
B BROADER IMPACT
The DC-CoT benchmark is poised to significantly impact AI by fostering the development of smaller, more accessible, and powerful reasoning models. By systematically evaluating data-centric CoT distillation strategies, DC-CoT offers crucial insights and standardized testbed, steering research towards resource- efficient Al and enabling advanced reasoning in computationally constrained environments. This research can yield broad societal and technological benefits:
1. Democratization of AI: Lowering computational barriers allows wider access to innovate with Mtateoofthh-an AI.
2. Educational Advancements: Accessible reasoning models can be integrated into educational tools, supporting personalized learning.
3. Application of Al: Broader deployment of reasoning Al can aid complex problem-solving in research, healthcare, finance, and other industries.
The insights from DC-CoT will also guide practitioners in optimizing distillation pipelines, promoting data-aware and sustainable Al by reducing the computational footprint of large models. By facilitating more efficient reasoning systems, DC-CoT contributes to future of more equitably accessible and sustainably developed advanced AI.
EXPERIMENT SETTING
C.I. DISTILLATION TRAINING
We conduct the distillation training on 8 A1100 GPUs and 16 A6000 GPUs, using LoRA fine-tuning for the student models. The LoRA rank we set is 32, and the lora alpha we set is 64. For an agentic task, the training process spans epochs, with a learning rate of 5 10-5 and context length of 10, 000. For the visual task, the training process spans epoch, with learning rate of 5 * 10-5, The distillation methodology follows the guidelines provided in Llama Factory et al. 2024). For Textual tasks, we train for 10 epochs for each dataset.
C.2 INFERENCE PIPELINE
For inference, employ the vLLM framework, running 8 A100 GPUs. The WEBARENA framework is deployed on 4 CPU machines. To enhance efficiency, we leverage the official task-parallel Bash script for parallel execution, rather than processing tasks sequentially by task ID.
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C.3 EXPERIMENTAL SETTINGS FOR GENERALIZATION EXPERIMENT
For all experiments, we use Llama-3.1 1--8BB as our student model. OOD Datasets were chosen as follows: BoolQ CClak et al. 2019) was used for SQA, OBQA (iihaylov et al. 2018) for ARC, ESNLI (Camburu et al. 2018) for ANLI, GSM8K-Rev (Guo et al. 2024) and MATH for GSM8K, GSM8K for MATH, Webarena-easy for Webarena hard and vice versa, Ok VQA for Visual-CoT and vice versa.
D RELATED WORK
D.I REASONING LLMS
The ability of LLMs to perform complex reasoning has been significantly enhanced by techniques that encourage explicit, step-by-step thinking. Foremost among these is Chain-of-Thought (CoT) prompting (Wei etal. 2022 Kojima et al. 2022. Nye et al. 2021), which elicits intermediate reasoning steps from LLMs before arriving at a final answer. This approach makes the model's inference process more transparent by providing human-readable explanations (Joshi et al. 2023 Lanham et al. (023) and substantially improves performance on tasks requiring multi-step deduction, such as arithmetic, commonsense, and symbolic reasoning (Wei et al.) 2022). By breaking down complex problems into manageable intermediate computations, CoT helps LLMs navigate intricate logical pathways and arrive at more accurate conclusions (Madaan & Yazdanbakhshi 2022]
Wang al. 2023a Dziri al. (023). Integrating self-generated rationales through CoT effectively boosts
the reasoning capabilities inherent in these models (Kojima et al., 2022).
Building upon the foundational CoT paradigm, recent research has explored more sophisticated "deep- thinking" or "Iong-CoT CoT" approaches to push the boundaries of LLM reasoning further. These methods often involve generating more elaborate or structured reasoning pathways. For example, Thhought (Yao et 2023aa) prompting allows models to explore multiple reasoning paths in parallel, evaluating intermediate thoughts to decide the most promising direction. Other techniques focus on iterative refinement (Wang et 2022b) and self-correction, such as Self-Reflection (Madaan et al. [003 Yao et al. 2023b Shinn et al. 2023 where models critique and improve their own generated thoughts.
D.2 KNOWLEDGE DISTILLATION IN LLMS
Knowledge distillation is a potent technique for transferring knowledge from a large, often cumbersome, "teacher" model to a smaller, more efficient "student" model. This process is increasingly relevant in the context of LLMs due to their substantial size and computational demands. The fundamental concept, introduced in early works (Buciluá et al. 2006; Hinton et al.) 2015), involves training the student model to mimic the teacher model's output distribution (soft labels), thereby minimizing the divergence between their respective distributions. This approach has found applications across various tuning techniques for LLMs. For instance, LLM --geerrrtteed annotations. including instructions, responses, and rationales, are leveraged in supervised fine-tumie site-tuning, i.e., where smaller model learns from the synthetic data produced by a larger teacher
LLM (Kim et al. 2023 Tong et al.) [024]] [Huang al. 2023) Wang et al.) 2023b 2025
Lu et al. 2023).
This is earticularly useful for enhancing specific capabilities (Josifoski et al. 2023] Zhang et al. 2023 Zhao
et al.
2023)
or imparting
knowledge efficiently (Taoii et al. 2023 Xu et al. 2023 Zheng
ct al.
2023 Wang et al. 2022a). Furthermore, distillation techniques are employed in alignment tuning. One
example includes Reinforcement Learning from Human Feedback (RLHF) (Ouyang et al. 2022). ) where
synthetic data from LLMs can aid in reward modeling and policy training align model outputs with human preferences and intentions.
While classical knowledge distillation learns from the teacher model's 's distributions, and the objective is to minimize the difference between the student's distribution and the teacher's (Chen et al.) 2020), recent advancements in LLMs have brought particular focus to distilling their complex reasoning capabilities,
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especially CoT processes, into smaller student model's (Kojima al. addressing architectural differences or significant capacity gaps between teacher and student LLMs, as merely
2022) CoT is also crucial when
mimicking the final output might be insufficient for the student to learn effectively. Teacher models provide
CoT rationales in various ways: (1) Sampled directly from the teacher (Hsieh et 2003 Fu et al.
2023 Li
et al. 2023a West et al. 2022] Magister et al.
2023
Mukherjee et al. 2023 Mitra et 2023). (2) Generated
via bootstrapping (Li et al. [023bb Ding et al.
2024
Zelikman et al. [022 Lewkowycz et al. 2022 Yu et al.
2023 [i et al. 2024al] Yuan et al.
2023 Guo et al.
2024; CCen et 2024b). or (3) Obtained via multiple
teacher models You et al. 2017
(0224a). The rationale, reflecting the detailed thought process Chen et al.
and reasoning pathway, serves as valuable auxiliary information for the student model to predict the final answer more accurately and robustly. While CoT distillation shows promise (Mukherjee et al., 2023 Ho et al. 2022). it remains unclear which methods, teacher models are most effective for a specific student model and how they perform in various settings. This calls for data-centric study of how the generation, selection, and combination of distillation data impact student reasoning and generalization.
TASK DESCRIPTIONS
It assesses a model's ability to make logical inferences from text, often through multi- step reasoning. Each instance includes question Q, rationale R, and answer A. The student model So learns to predict A using Q and R. Tasks span commonsense, science, math, and table reasoning, with performance measured by answer accuracy.
Textual Reasoning:
This task tests an LLM agent vy in the WEBARENA browser sandbox, where it must follow instruction by navigating real websites. At each step, the agent observes o, takes action a, and explains its reasoning r. A large LLM (ML) selects actions based on the interaction history. Performance is measured by Success Rate (SR)-the fraction of tasks where the agent reaches the correct goal state.
Agentic Reasoning:
Visual Reasoning: Extends chain-of-thougle to multi-modal inputs, requiring models to interpret visual content and answer related questions. Each instance is a tuple (v, 9, a. r): an image v, a question 4. an answer a, and a rationale r outlining reasoning steps linking to a. Unlike text-only reasoning, vi- sual reasoning demands interpretable grounding-4 often points to specific image regions that justify the answer. This keeps the reasoning process transpar- ent, testing the model's ability to connect visual cues with logical steps across multiple reasoning hops.
Vanilta SQA
Reverse
SQA
sn
20
Dote
in
3D
20
ARC
Date
20
10
ARC
10g
GSMNK
CS WIKK
0.58
1.58
3B
7B
Figure 6: Qwe (0.5B-7B) distilled with Vanilla- CoT Reverse
F IMPACT OF STUDENT MODEL SIZE
This section examines how the scale of the student model influences the efficacy of CoT distillation, with a particular focus on learnability from different augmentation strategies. The experiments, summarized in Figure 6 are performed Qwen-2.5 models of varying sizes (0.5B, 1.5B, 3B, 7B) when distilled with Vanilla CoT and Reverse augmentation, using Gemini-1.5 1.5-Pro the teacher.
Q11. How does the student model size generally affect reasoning performance with standard Vanilla CoT, and how does it interact with more complex augmentations like Reverse? As shown in Figure 6 performance with Vanilla CoT clearly scales with student model size: (wen-225-0.55 achieves an average of 32.86% which improves 45.72 45.72% for 1.5B, 50.89% for 3B, and 55.58% for the 7B model. This confirms
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that larger models better leverage standard teacher CoTs. The introduction of Reverse presents a more nuanced picture. On average across all four textual tasks, the impact is mixed; the 1.5B model shows a modest gain, while others see slight average decreases. However, these averages mask strong task-speeific effects. Reverse significantly boosts performance on SQA and Date for all student sizes. Conversely, it markedly degraded performance on ARC and GSM8K compared to Vanilla COT. This demonstrates that the utility of this complex augmentation is highly task-dependent in our specific student-feacher setup, instead of being a universal benefit.
Q12. Do smaller student models (0.5B, 1.5B) exhibit the small model learnability gap when faced with complex augmentations like Reverse? The small model learnability gap suggests smaller models struggle with overly complex reasoning. Analyzing (0.5B, 1.5B) achieve substantial gains. However, their absolute scores remain below those of larger students, indicating capacity limitation in reaching peak performance.
results: On tasks where Reverse is beneficial, smaller models
G EFFICIENCY AND CODE ANALYSIS
Efficiency is an important consideration for data-centric pipeline designed for broad adoption. While wall-clock time can be a useful metric, often varies significantly depending on the hardware, batch sizes, and API latencies. To offer more hardware-independen and reproducible measure of computational cost, we instead report token-level costs for data generation. The token usage for several key prompting techniques is summarized in the Table g
Moreover, these costs are incurred once during data generation, with no inference-tinee overhead or change to the student model architecture. This design choice deliberate: aimed to make DC-CoT practical for both academic and applied ML use cases.
Table Token-level cost comparison for data generation methods.
Method
Prompt Type
Avg. Prompt Tokens
Avg. Output Tokens
'ooal Tokens per Sample
Standard CoT
Forward CoT Prompt
60
180
240
Rephrased CoT
Question Rewriting
75
180
255
Reverse Thinking
Answer-First Reverse CoT
110
200
310
To quantify the computational benefits of DC-CoT, we measured the throughput of our distilled students on single NVIDIA A100-80GB GPU using vL..M. As shown in Table 9 the distilled Qwen-2.5-31 achieves performance competitive with larger vanilla ceelines-offen ~6-9x speedup relative to the 8B baseline, validating the "Efficient Reasoning" claim of our benchmark.
Table 9: Efficiency profile of distilled student models measured on A100-80GB.
Model
VRAM (GB)
Throughput (tok/s)
Relative Speedup
Llama-3. 1-B (Student)
16.2
115.4
1.0x
Qwen-2.5 2.5--B (Student)
7.8
184.2
~1.6
Owen-2.5511511 (Student)
4.2
245.1
~2.1
H CONFIDENCE INTERVALS AND SIGNIFICANCE TESTING
While we reported average accuracy over 3 seeds for all experiments, we acknowledge that confidence intervals help contextualize gains that appear small. Some of these results are summarized in the Table 10
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We report 95% confidence intervals for core reasoning tasks (ARC, MATH, GSM8K) across Mistral-7B, LLaMA-3.1188 and Gemma-7B models. As shown below, Reverse CoT consistently and significantly outperforms No CoT, with non-overlapping intervals in nearly all cases, confirming the robustness of the gains. These results suggest that improvements are statistically significant, not noise.
Table 10: Accuracy with 95% confidence intervals core reasoning tasks.
Model
Task
Method
Accuracy + CI
No CoT
68.26 + 0.75 76.96 + 1.45
ARC
Reverse CoT
Mistral-7B
CoT
7.98 + 0.39 16.12 # 0.38
MATH
Reverse CoT
31.11 # 1.80 59.21 # 0.85
GSM8K
Reverse CoT
No CoT Reverse CoT
60.41 # 1.37 82.17 # 1.20
ARC
LLaMA-3.1-8B
No CoT Reverse CoT
7.39 0.13 35.52 + 0.26
MATH
No CoT Reverse CoT
20.74 + 1.04 76.35 + 1.98
GSM8K
No CoT Reverse CoT
68.09 + 1.17
ARC
73.46 + 1.06
Gemma-7B
No CoT Reverse CoT
7.24 0.34 16.54 + 0.83
MATH
No CoT
26.22 + 0.83
GSM8K
Reverse CoT
53.45 # 1.75
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I THINKING EXAMPLE
Instruction
You need to issue an action, interaction history summary for this step. when you thinking need have OBSERVATION DESCRIPTION, OBSERVATION HIGHLIGHT, REASON.
You ONLY allowed the given format.
the following action commands. Strictly adheres
{click [id]: To click on an element with its numerical ID on the webpage. E.g., click [7]"
type [id] [content] arress_enter_aftereee
To type content into a field with a specific ID. By default, the "EEnter\" key is pressed after typing unless "ress_enter_afte"" is set to 0. E.g., "type [15] [Carnegie Mellon University [1]'
stop [answer]: To stop interaction and return response. Present your answer within the brackets. If the task doesn't 't require a textual answer or appears insurmountable, additional reasons and all relevant information gather the answer. E.g., stop [N/A ...
note [content]: To take note of all important info w.r.t. t. completing the task to enable reviewing it later. E.g., "note [Spent $10 on 4/1/2024]";
go back: To return the previously viewed page.
Input
OBJECTIVE: Which US states border Vermont?
LASTACTION: first step, no last action
LAST INTERACTION HISTORY SUMMARY: This is the initial interaction. We are on the OpenStreetMap homepage and need to search for Vermont to begin our task of identifying its bordering states.
CURRENT OBSERVATION:
RootWebArea "OpenStreetMap"
link [41] 'OpenStreetMap logo OpenStreetMap'
link [482] 'Edit'
button [403]
link [373] 'History'
link [374] 'Export'
1ink [487] 'GPS Traces'
link [488] 'User Diaries'
link [489]
'Communities"
link [410] 'Copyright'
link [411] 'Help'
link [412] 'About'
link [382] 'Log In'
link [383] 'Sign Up'
link [515] 'where is this?'
textbox [35] 'Search' [required: False]
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button [516] 'Go'
link [503] 'Find directions between two points'
heading Welcome to OpenStreetMap!' button [469] 'close'
text 'OpenStreetMap
a map world, created by people like you free to use under an open license."
text 'Hosting is supported by"
link [475] 'UCL'
link [477] 'Fastly'
link [479] 'Bytemark Hosting'
text ', and other'
link [481] 'partners'
link [485] 'Learn More'
link [486] 'Start Mapping'
generic [15] 'Zoom In Zoom Out Show My Location Layers Share 50 km 50
OpenStreetMap contributors Make Donation. Website and API terms' 1ink [19] 'Zoom In'
link [20] 'Zoom Out'
button [22] 'Show My Location'
link [24] 'Layers'
link [296]
link [26] 'Share"
link [389] "epenStreetMap contributors'
link [311] 'Make Donation'
link [313] 'Website and API terms'
Output
"<think>
OBSERVATION DESCRIPTION: The current page is the OpenStreetMap homepage. It contains a search box (ID: 35) where we can enter our query. There are various navigation links and buttons, but the most relevant element for our task is the search functionality. The map view (ID: 15) is also present, which will crucial visualizing Vermont and its neighboring states once we perform the search.
OBSERVATION HIGHLIGHT: 35, 15, 516, 19, 20, 24, 26
REASON: To locate Vermont on the map, we need to use the search functionality.
</think>
ACTION: type [35] [Vermont] [1]
INTERACTION HISTORY SUMMARY: We have searched for \Veermott" on OpenStreetMap and are now looking the search results page with view of Vermont."
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Published as conference paper ICLR 2026
J DATASET STATISTICS
Dataset
Domain
License
Train (Original)
Train (Filtered)
Test
SQA Geva et al. 22021
Commonsense
MIT
2,061
1,544
229
CSQA Talmor al.
2019
Commonsense
MIT
9,741
6,478
1,140
ARC Clark el 2018
Commonsense
CC BY-SA 4.0
1,199
1,035
1,172
Bool Clark all (2019)
Commonsense
CC BY-SA 3.0
9,427
3,270
OpenbookQA Mihaylov et al
2018
Commonsense
Apache
4957
500
MATH Hendrycks et aL. (2021)
Math
MIT
7,500
2,511
5,000
GSM8K Cobbe ef al. (202T)
Math
MIT
7,379
4,293
1,339
GSM8K-Rev Guo
2024
Math
Apache
777
ANLI (r3) Nie et al. 2020
CC BY-NC 4.0
100,459
883
1,200
e-SNLI Camburu et al 20188
NLI
CC BY-NC 4.0
549,367
9,824
Date Srivastava et al. 2022
Logic
Apache
200
169
Webarena Zhou
2023
Agentic
Apache
0
812
Visual- ColallCCollo Shao ct a.l 2024
Visual
Apache
132,000
943,000
12,500
OK-VQA Marino al. 2019))
Visual
CC 4.0
5,046
9,009
5,000
Table 11: The datasets used in our Experimental Setup.
K THE USE OF LARGE LANGUAGE MODELS (LLMs)
To enhance clarity and readability, we employed OpenAl's GPT-5 and GPT-5-thinking models exclusively language polishing tools. Their role was limited proofreading, grammatical correction, and stylistic refinement-functionn comparable to those of conventional grammar checkers and dictionaries. These tools did not contribute any new scientific content or ideas, their usage consistent with standard practices manuscript preparation.
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Reviews:
[{"review_id": "WmFu4o0amT", "reviewer": "Reviewer_qqBm", "summary": "This paper introduces DC-CoT, the first benchmark and framework specifically designed for systematically evaluating Data-Centric approaches in Chain-of-Thought (CoT) Distillation. The authors address the lack of standardized evaluation methods by investigating how data manipulations (e.g., augmentation, selection, and mixing) influence the reasoning capabilities of smaller, efficient student Large Language Models (LLMs). The DC-CoT benchmark comprehensively assesses the performance of various teacher models (e.g., GPT-4-mini, Gemini-Pro, Claude-3.5) and student architectures (e.g., 3B, 7B) across In-Distribution (IID), Out-of-Distribution (OOD), and Transfer Learning tasks.", "questions": "1. Given the concerns about SOTA methods, did the authors experiment with or consider advanced data selection techniques, such as methods based on student model uncertainty or influence estimation, rather than just simple teacher correctness filtering? If not, why were these omitted?\n\n2.  Among the data-centric strategies (augmentation, selection, mixing), which one provided the most reliable and significant performance uplift for OOD and transfer tasks? A deeper theoretical explanation is requested as to why the CoT rationales generated by a specific teacher model generalize better to unseen or out-of-domain data.\n3. To fully validate the paper's core claim of efficient reasoning, a quantitative comparison of inference efficiency is essential. Please provide explicit performance metrics for the final distilled 3B and 7B student models—specifically tokens per second throughput, actual latency (e.g., time to first token and time to completion), and peak GPU memory utilization—compared against the original teacher models (or a similarly sized, non-distilled baseline model).", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. DC-CoT addresses a timely research gap by focusing on data-centric strategies in CoT distillation. \n\n2. The evaluation structure is comprehensive, spanning different teacher models, various student model scales, and multiple evaluation settings (IID, OOD, Transfer).\n\n3. The study directly confronts the challenge of making robust reasoning accessible to smaller models, which is paramount for reducing inference costs in real-world applications.", "weaknesses": "1. The exploration of specific data-centric strategies (augmentation, selection, mixing) appears superficial. The current implementation is limited to basic methods, failing to incorporate or evaluate more advanced, state-of-the-art (SOTA) data selection or augmentation techniques (e.g., based on model uncertainty or influence). \n\n2. The study fails to clearly articulate the generalizability of the optimal data strategies. The results seem highly task-dependent, yet the authors do not provide a rigorous, nuanced discussion on when a strategy offers a universal benefit versus when it is specific to a task domain (e.g., math vs. commonsense). \n3. While the paper's core objective is to achieve \"efficient reasoning\" during the inference phase, the evaluation relies primarily on coarse metrics like model size (3B, 7B). The benchmark critically lacks explicit, quantitative analysis of the achieved inference efficiency. Crucial metrics such as throughput (tokens/second), actual latency, or GPU memory consumption for the final distilled models are absent.", "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": "KURa7KiwDy", "reviewer": "Reviewer_wMDH", "summary": "The paper introduces DC-CoT, a novel benchmark aimed at systematically evaluating data-centric distillation approaches (augmentation, selection, mixing) for chain-of-thought (CoT) reasoning. This work conducts a large empirical study across various teacher–student model pairings including teacher models like GPT-4, Gemini, Claude-3.5, and student sizes of ~3B to ~7B, and multiple reasoning datasets, measuring IID, OOD, and cross‐domain generalization. Their findings show that augmentation (such as question or answer rephrasing, reverse thinking) typically provides the strongest gains, selection (filtering by teacher correctness or student error) and mixing (blending data from different domains/lengths) offer more nuanced benefits depending on teacher/student compatibility and data regime.", "questions": "1. What does the “IID OOD” contribute to in Figure 1? Training/test data, or domain-specific data distribution?\n2. Maybe it’s better to explain what $L$ is from the start of section 3? I only see that in the third part (Answer Augmentation) in the data augmentation subsection. However, $L$ is also used before that.\n3. Can you explain one or two sentences more on how Consistency Filtering works for Reverse Thinking Augmentation? I was wondering this when I read this paragraph\n4. I have a naive question about “Answer Augmentation”. How do methods avoid the model from generating arbitrary reasoning traces and then the correct answer? The assumption behind this question is that if the teacher model ‘memorizes’ the answer, and is asked to generate diverse reasoning traces, then it will try to follow the prompt by generating true and false reasoning traces. This question is not in the scoop of this work itself, but it would be great if the authors could answer this.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "1. In general, this contributes to the community by having such a controllable and comprehensive benchmark. I feel this work, in the long term, will support the data-centric distillation in reasoning.\n2. Figures explaining different components of data-centric distillation are very clear.\n3. The experiments are designed in a fine-grained and comprehensive manner.", "weaknesses": "1. The improvement of the teacher models is very fast, the observations found in this paper might not hold.\n2. Following the previous, it would be great if the authors could consider expanding the diversity of teacher models. For example, clustering teacher models by architectural differences such as MoE/full activation, linear/full/sparse attention, etc. The observations might be more generalizable if we analyze from a perspective of architectural differences, instead of picking the strongest teacher models.\n3. One more sentence needed explaining $\\mathcal{M}$ in section 3.1 would be appreciated. Currently, I was confused about whether $\\mathcal{M}$ is a framework or a network.\n4. Though the figures 1-4 are great, there are no explicit references to them over the main text.\n5. Line 112-113, typo: should be $D^{\\text{target}}$", "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": "oe9UAqL57h", "reviewer": "Reviewer_tyeG", "summary": "This paper introduces **DC-CoT**, a comprehensive benchmark for evaluating **data-centric approaches to Chain-of-Thought (CoT) distillation**, spanning three axes: (1) data augmentation (e.g., reverse thinking, answer rephrasing), (2) data selection (e.g., teacher-correct filtering, LLM-as-judge), and (3) data mixing (e.g., by length or teacher source). The authors conduct extensive experiments across diverse reasoning tasks (textual, mathematical, agentic, visual), multiple teacher models (e.g., GPT-4, Claude 3.5, Gemini-1.5-Pro), and student architectures (e.g., Llama-3.1-8B, Mistral-7B). Key findings include: augmentation (especially reverse thinking) generally outperforms selection or mixing; the existence of a “learnability gap” where smaller students may not benefit from the strongest teachers; and strong out-of-distribution (OOD) generalization after CoT distillation. The benchmark is well-documented and accompanied by a public codebase.", "questions": "see weakness", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. **High practical relevance**: Efficient reasoning via CoT distillation is a critical direction for deploying capable yet lightweight LLMs. The focus on *data-centric* methods—rather than architectural or training tricks—is timely and underexplored.\n2. **Systematic design**: DC-CoT offers a unified framework to compare augmentation, selection, and mixing strategies across modalities, tasks, and model pairs—something missing in prior work.\n3. **Empirical rigor**: The paper includes large-scale experiments, ablations, statistical significance tests (Appendix H), and cross-dataset generalization analysis (Table 5).\n4. **Actionable insights**: Findings like “reverse thinking boosts math reasoning” or “small students may learn better from moderately strong teachers” provide concrete guidance for practitioners.", "weaknesses": "1. **Significance of Research Question**\n\nThe core problem—improving CoT distillation via data manipulation—is undeniably important for efficient reasoning. However, the paper does not clearly demarcate what constitutes a *data-centric* CoT distillation method versus general data synthesis or instruction tuning. For instance, “question augmentation” blurs the line with self-instruct-style data generation. This conceptual fuzziness slightly weakens the benchmark’s focus.\n\n2. **Problematic construction of benchmark**\n\n- All CoT traces are generated by **closed-source API models** (GPT-4, Claude, etc.), with limited transparency on prompt templates, temperature settings, or consistency checks. This raises reproducibility concerns.\n- The **LLM-as-a-Judge** filtering method, while common, is not validated against human judgments. Given known issues with LLM evaluators (e.g., length bias, preference leakage), this may introduce hidden noise.\n- **Visual and agentic tasks are underrepresented**: only one visual (Visual-CoT) and one agentic (WebArena) benchmark are used, limiting generalizability in these domains.\n- The OOD transfer pairs (e.g., SQA → BoolQ) are reasonable but **not systematically justified** (e.g., no measure of task similarity), making it hard to interpret generalization patterns.\n\n3. **Potential of benchmark**\n\nThe paper offers valuable heuristics (e.g., prefer reverse thinking for math, avoid over-strong teachers for small students). However:\n- Many conclusions are **tied to specific teacher–student pairs** (e.g., Gemini → Llama-3.1-8B). It’s unclear how well they generalize to new architectures (e.g., MoE, multimodal-native models).\n- No comparison to **non-data-centric distillation** (e.g., logits distillation, representation matching), making it hard to assess whether data manipulation is truly the most promising path.", "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)