Reasoning distillation requires chain-of-thought (CoT) data with correct answers, but obtaining such data efficiently remains challenging. Forward CoT generation (FCG) followed by rejection sampling (RS) produces verified, question-only responses, yet may require many teacher calls for difficult problems. Reverse CoT generation (RCG) is cheaper because it conditions on the known answer, but access to this answer can lead to post-hoc rationalization and a mismatch with the student's answer-free inference setting. We propose CoTranslator, which learns to translate reverse CoT responses toward the distribution of verified forward responses. Trained on a small set of paired reverse and rejection-sampled forward responses, it supports large-scale generation and verification of student training data. Across six student models evaluated on six mathematics benchmarks, CoTranslator improves average accuracy over semantic suppression by up to 5.82 percentage points. For two 4B students, it retains 95.0% of rejection sampling's average accuracy while using 35.9% of its estimated compute. Without retraining, the same translator transfers to a new mathematics dataset, a different teacher, and STEM problems, improving average STEM accuracy by 4.88 and 4.31 percentage points for 4B and 8B students, respectively. These results show that CoTranslator offers an efficient and transferable approach to reasoning distillation.
Figures & tables
Figure 1: Math benchmark accuracy of Qwen3-4B-Base under SSR, SUP, and CoTranslator , using the same queries from Nemotron-SFT-Math-v4 .
Figure 2: Overview of CoTranslator . FCG generates reasoning from questions alone; rejection sampling keeps correct responses but may require many attempts. RCG conditions on both the question and answer, reducing sampling cost but risking post-hoc rationalization. Trained on paired RCG and accepted FCG responses from a small subset, CoTranslator translates RCG responses at scale for training the student.
Method
AIME25
AIME26
HMMT25
HMMT26
Omni
IMO
pass@64_1
pass@64_1
pass@64_1
pass@64_1
pass@1_1
pass@8_1
Avg.
Qwen3-4B-Base
RS
32.55
33.80
19.38
20.12
41.55
15.88
27.21
SSR
6.77
5.42
3.28
2.89
22.27
5.44
7.68
SUP
27.45
27.45
15.16
16.90
31.44
11.62
21.67
SUP-AUG
23.85
23.44
13.70
14.73
30.19
11.03
19.49
Table 1: Math performance across student models. HMMT25 and HMMT26 refer to HMMT November 2025 and HMMT February 2026 . Omni and IMO refer to Omni-MATH and IMO-AnswerBench . The highest average scores are bold.
Method
AIME25
AIME26
HMMT25
HMMT26
Omni
IMO
pass@64_1
pass@64_1
pass@64_1
pass@64_1
pass@1_1
pass@8_1
Avg.
Qwen3-4B-Base ; DeepSeek-V4-Pro ; ODA-Math-460k
SUP
26.30
28.18
18.96
17.14
36.11
14.72
23.57
CoTranslator
30.83
34.27
23.44
21.59
42.25
17.62
28.33
Qwen3-8B-Base ; DeepSeek-V4-Pro ; ODA-Math-460k
SUP
33.33
36.77
25.99
23.67
42.48
19.44
30.28
Table 2: Math performance when changing the dataset or the teacher model. The blue rows specify the student model, teacher model, and dataset for each setting. CoTranslator transfers across datasets and teacher models.
Method
Olympiad
SciBench
OmniScience
pass@1_1
pass@1_1
pass@1_1
Avg.
Qwen3-4B-Base
SUP
24.35
22.43
9.68
18.82
Ours
24.35
37.93
8.83
23.70
Qwen3-8B-Base
SUP
37.68
24.71
12.33
24.91
Table 3: Student performance on STEM benchmarks. Olympiad and OmniScience refer to OlympiadBench and AA-Omniscience , respectively.
Figure 3: Similarity to RS responses by teacher attempts. Top: semantic features. Bottom: full-text lexical features. CoTranslator brings responses closer to RS in both semantic and lexical features across difficulty levels.
Figure 4: Post-hoc rationalization. CoTranslator reduces answer and suppression mentions and shortcuts.
Figure 5: First-answer position in the full saved data. Translated responses mention the answer later.
Figure 6: Math accuracy by translator size and paired training-data size. 4B and 8B show gains.
Figure 7: Computational cost and performance relative to RS. CoTranslator reduces compute by 64.1% and 4B students achieve 95.0% accuracy in main experiment.
Appendix figures & tables8 assets
Supplementary material from the paper’s appendix.
Appendix
Hyperparameter
Value
Qwen3-1.7B
lr
5e-5
num_train_epochs
3
lr_warmup_fraction
0.1
weight_decay
0.1
clip_grad
1.0
Appendix
Table 4: Training hyperparameters for the translator.
Hyperparameter
Value
Qwen2.5-Math-{7B, 7B-Instruct}
lr
5e-5
num_train_epochs
3
lr_warmup_fraction
0.1
weight_decay
0.1
clip_grad
1.0
Appendix
Table 5: Training hyperparameters for the student models.
Hyperparameter
Value
teacher model
temperature
1.0
reasoning_effort
high
max_out_token
32768
top_p
DeepSeek-V4-Pro
1.0
Appendix
Table 6: Inference hyperparameters for teacher models and translators.
Setting
AIME25
AIME26
HMMT25
HMMT26
Omni
IMO
pass@64_1
pass@64_1
pass@64_1
pass@64_1
pass@1_1
pass@8_1
Avg.
SUP
21.88
21.15
10.57
13.07
28.88
10.25
17.63
Qwen3-1.7B
1/8
10.63
9.53
3.91
5.02
23.62
4.91
9.60
1/4
12.81
7.92
4.32
6.58
24.73
5.19
10.26
1/2
13.39
11.15
5.78
8.48
28.00
6.19
12.17
Appendix
Table 7: Detailed math results for the translator size and training-data analysis. The fractions denote paired training subsets of the cot data in nvidia/Nemotron-SFT-Math-v4 : 1/8 , 1/4 , and 1/2 correspond to 35.7k , 71.4k , and 142.8k examples, respectively. The 0 setting uses no paired training examples.
Figure 8: Mean NLL under the teacher. Left: all response sets. Right: six groups by teacher attempts.
Distilling large reasoning models is essential for making Long-CoT reasoning practical, as full-scale inference remains computationally prohibitive. Existing curation-based approaches select complete reasoning traces post-hoc, overlooking collaboration among heterogeneous teachers and lacking dynamic exploration, which leads to redundant sampling and missed complementary reasoning. We introduce CoRD, a collaborative multi-teacher decoding framework that performs step-wise reasoning synthesis guided by predictive perplexity-based scoring and beam search. This enables heterogeneous LRMs to jointly construct coherent reasoning trajectories while efficiently preserving diverse, high-potential hypotheses. Experiments show that CoRD produces higher-quality reasoning data and achieves near teacher-level student performance with fewer, structured supervision signals, without substantial efficiency overhead. CoRD further generalizes well to out-of-domain and open-ended settings. The dataset and model are available at https://github.com/DISL-Lab/CoRD.
Reasoning capabilities are critical for advancing Large Language Models, yet current approaches either require massive computational budgets or struggle to effectively distill reasoning to smaller models. Standard distillation methods rely on outcome-based rewards, failing to distinguish between sound reasoning and lucky guesses. We propose Collaborative Reasoning Distillation (CRD), a framework that enhances reasoning in compact models through three innovations: (1) interactive cross-feedback where teachers iteratively critique each other's reasoning, (2) fine-grained step-wise quality assessment capturing logical validity independent of final answers, and (3) coherence-aware step stitching that synthesizes complementary strengths. Students are trained via Reasoning Quality Optimization (RQO) with budget constraints. Our model, CRD-4B, achieves 97.3% on MATH-500 and 70.3% on AIME'25, surpassing baselines while using only 50K training examples, up to 12 times smaller than the datasets of comparable models.
Recent advances in large reasoning models (LRMs) have shown strong performance on complex problems through long chain-of-thought (Long CoT) reasoning. However, distilling such trajectories into smaller student models remains challenging: direct Long CoT supervision often provides limited gains and can be less effective than concise Short CoT rationales. In this work, we investigate this phenomenon from a gradient-centric perspective. Our analysis shows that Long CoT induces larger gradient magnitudes and more concentrated update directions than Short CoT, with this effect becoming more pronounced as student model capacity increases. These findings suggest that effective Long CoT distillation requires balancing the reasoning information density of reasoning trajectories with their distributional alignment to the student model. Motivated by this insight, we propose Model Interporlation Distillation (MI-Distillation), a framework that constructs a continuous Instruct-Reasoning data spectrum through model interpolation. To select suitable trajectories from this spectrum, we further introduce Sequential Learnable Surprisal Score (SeqLSS), which favors reasoning paths that are both informative and learnable for the student. Extensive experiments on reasoning benchmarks show that MI-Distillation consistently improves small model CoT distillation over strong Long CoT baselines.
Yangsong Lan, Renkai Hu, HongKai Zheng +4
College of Artificial Intelligence, Nanjing University of Aeronautics and Astronautics, Nanjing, China · 2The Key Laboratory of Brain-Machine Intelligence Technology, Ministry of Education, Nanjing, China