CoTranslator: Reverse to Forward Chain-of-Thought Translator for Reasoning Distillation

Zinan Tang; Zhuoshi Pan; Kairui Chen; Ze Yan; Shaomian Zheng; Yukun Zhang; Gang Wang; Biqing Huang

cs.CLOct 14, 2026

CoTranslator: Reverse to Forward Chain-of-Thought Translator for Reasoning Distillation

Authors: Zinan Tang, Zhuoshi Pan, Kairui Chen, Ze Yan, Shaomian Zheng, Yukun Zhang, Gang Wang, Biqing Huang

Organizations: Tsinghua University · Ant Group · Xiaomi Corporation

Abstract

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	pass@64_1	pass@64_1	pass@64_1	pass@64_1	pass@1_1	pass@8_1	Avg.
Method	AIME25	AIME26	HMMT25	HMMT26	Omni	IMO
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.

Qwen3-4B-Base ; DeepSeek-V4-Pro ; ODA-Math-460k
Method	AIME25	AIME26	HMMT25	HMMT26	Omni	IMO
Method	pass@64_1	pass@64_1	pass@64_1	pass@64_1	pass@1_1	pass@8_1	Avg.
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.

Qwen3-4B-Base
Method	Olympiad	SciBench	OmniScience
Method	pass@1_1	pass@1_1	pass@1_1	Avg.
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.

Qwen2.5-Math-{7B, 7B-Instruct}
Hyperparameter	Value
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.

Qwen3-1.7B
Setting	AIME25	AIME26	HMMT25	HMMT26	Omni	IMO
Setting	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
$1/8$	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.

Main experiment ( # 285,516 )
Metric ( $10^{20}$ FLOPs)	RS	CoTranslator
Teacher inference	13.888	3.825
Translator training	–	0.310
Translator inference	–	0.855
Total	13.888	4.990
Transfer experiments ( # 942,724 )

Appendix

Table 8: Estimated data construction budgets.

Panel of Figure 9 — Figure 9: Prompt for SUP.

Panel of Figure 12 — Figure 12: Complete Post-hoc rationalization rubric.

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