Facts Don't Speak Louder than Words: The Behavioral Essence of Long-CoT Distillation
Authors: Yongcan Yu, Jian Liang, Lingxiao He, Kuangpu Guo, Yanbo Wang, Shuo Lu, Meng Wang, Ran He
Organizations: NLPR & MAIS, Institute of Automation, Chinese Academy of Sciences · School of Artificial Intelligence, University of Chinese Academy of Sciences · Meituan · University of Science and Technology of China
While long chain-of-thought (CoT) distillation significantly improves the reasoning abilities of language models, its underlying mechanism remains poorly understood. Current pipelines generally rely on rejection sampling to gather reasoning traces across diverse prompts, assuming that factual correctness and broad problem coverage are indispensable. Surprisingly, we find that training exclusively on flawed reasoning trajectories or a restricted prompt set yields nearly comparable performance. Driven by this counterintuitive finding, we propose the Behavioral Hypothesis: the essence of Long-CoT distillation is behavioral alignment with structured reasoning patterns, rather than factual knowledge memorization. We then validate this by demonstrating substantial reasoning gains even when models are fine-tuned exclusively on previously mastered problems-effectively isolating behavioral alignment from novel knowledge injection. Having established that reasoning patterns are the true bottleneck, we investigate how to learn them across varying levels of complexity optimally. We reveal a critical interplay: while the recent probability-based loss excels at learning simple patterns, the standard cross-entropy loss is essential for scaling to complex CoTs. We believe these insights demystify CoT distillation and provide a principled foundation for the future development of reasoning models. Code is available on https://github.com/yuyongcan/Long-CoT-Distillation.
Figures & tables
Figure 1: Incorrect Trajectories Teach Long-CoT Behavior Almost as Effectively as Correct Ones. We compare models fine-tuned on positive versus negative CoT trajectories under two training objectives. Across models and benchmarks, negative trajectories retain most of the distillation gains achieved by positive trajectories.
Method
Data
Qwen3-1.7B-Base
Method
Data
Qwen3-4B-Base
MMLUPro
GPQA-D
LCBv2
Average
MMLUPro
GPQA-D
LCBv2
Average
Base
-
28.1
14.4
8.9
17.1
Base
-
46.1
16.2
19.8
27.4
-logp
P
35.3
21.3
13.8
23.5
-logp
P
52.9
29.6
29.4
37.3
-logp
N
34.3
23.0
14.3
23.9 (+0.4)
-logp
N
56.4
31.5
28.8
38.9 (+1.6)
-p
P
34.9
15.7
9.3
20.0
-p
P
54.3
34.3
24.8
37.8
-p
N
34.7
14.7
7.9
19.1 (-0.9)
-p
N
52.6
33.5
24.4
36.8 (-1.0)
Table 1: The Negligible Impact of CoT Correctness Extends Beyond Math Benchmarks. We evaluate whether the weak dependence on CoT correctness generalizes to non-math domains, including general reasoning, scientific reasoning, and coding tasks. Across models and training objectives, negative CoT trajectories achieve average performance nearly identical to positive trajectories. P and N denote positive and negative CoT trajectories, respectively.
Figure 2: Negative CoTs Effectively Mitigate the Scarcity of Correct Data. We train Qwen3-1.7B-Base with different positive sample bases and varying ratios of positive to negative CoT trajectories. Adding negative trajectories consistently improves performance when positive data is scarce.
Figure 3: Prompt Diversity Is Not the Bottleneck Under a Fixed Trajectory Budget. We fix the total number of CoT trajectories and vary the source prompt diversity, ranging from a small prompt set with many sampled trajectories per prompt ( 500×128 ) to a large prompt set with fewer trajectories per prompt ( 16k×4 ).
Model
Loss
Acc (Gains) (%)
Positive
Negative
Qwen3 1.7B-Base
-logp
14.3 (+7.4)
13.5 (+6.6)
-p
17.3 (+10.4)
15.7 (+8.8)
Qwen3 4B-Base
-logp
36.4 (+23.3)
34.6 (+21.5)
-p
35.4 (+22.3)
34.1 (+21.0)
Table 2: Models Avoid Overfitting to Flawed Facts on the Training Set. Numbers in parentheses indicate performance gains relative to the base model.
Figure 4: Substantial Gains on Previously Solvable Problems. Fine-tuning on easy subsets that the base model can already solve (Easy-643/444) yields improvements comparable to training on a larger, randomly sampled dataset (Random-3k) across math benchmarks. This reduces the role of new problem-specific answers as an explanation for the gains.
Figure 5: CoT Complexity Dictates the Appropriate Distillation Objective. We compare four base models fine-tuned with −logp loss (solid lines) and −p loss (dashed lines) across varying CoT complexities. The results reveal a clear dichotomy: while the −p loss excels on simpler CoTs, it suffers from pronounced degradation on highly complex reasoning traces. Conversely, the standard −logp loss scales robustly with complexity.
Appendix figures & tables14 assets
Supplementary material from the paper’s appendix.
Appendix
✓Positive Sample
✗Negative Sample
(Correct Fact & Perfect Behavior)
(Flawed Fact, but Same Behavior)
Step 1: Understand the pattern The terms are: 48,812,…,20042008 . Each term has the general form: 4n4(n+1)=nn+1 So the product becomes: ∏n=1501nn+1 — Correct boundary condition —
Step 1: Understand the pattern The terms are: 48,812,…,20042008 . Let the general term be: 4k4(k+1)=kk+1 So the product becomes: ∏k=2502kk+1 [!] Factual Error: Hallucinated starting index ( k=2 instead of k=1 ).
Step 2: Telescoping Product Write out the product explicitly: 12⋅23⋅34⋯501502 Observe that this is a telescoping product . Most terms cancel out…
Step 2: Telescoping Product This is a telescoping product . Let’s write out the product: 23⋅34⋅45⋯502503 We can see that most terms cancel out…
Final Answer: 502
Final Answer: 2503
Appendix
Figure 6: Factual Flaws vs. Behavioral Alignment in Long-CoT Distillation. Given the same initial problem, the negative sample hallucinated an incorrect starting index ( k=2 ), leading to a wrong final answer, yet it perfectly replicated the core, step-by-step reasoning behaviors of the positive sample. This structurally intact deduction demonstrates why incorrect CoT trajectories still provide high-quality behavioral supervision.
Figure 7: Token Length Distribution Across Reasoning Complexity Tiers. The boxplot illustrates the scaling of response lengths across Simple, Medium, and Complex datasets.
Figure 8: Word Cloud Analysis Reveals Lexical Shifts Across CoT Complexities. The lexical distribution shows a transition from concrete task-oriented words in the Simple dataset, through exploratory terms in the Medium dataset, to meta-cognitive markers in the Complex dataset.
Student
Training
Math avg.
SuperGLUE
GPQA-D
MMLU-Pro
Non-math avg.
Qwen3-1.7B-Base
Base
6.9
10.6
15.9
27.3
17.9
SFT-P
27.2
18.0
22.0
34.9
25.0
SFT-N
26.8
18.3
24.5
34.0
25.6
Qwen3-4B-Base
Base
19.1
8.5
16.0
45.6
23.4
SFT-P
44.6
29.1
34.8
49.0
37.6
SFT-N
43.7
29.8
36.4
49.4
38.5
Appendix
Table 3: Cross-domain evaluation after science QA (GURU) training. The base models are evaluated without fine-tuning; P/N distinguish final-answer correctness of the training trajectories. Values are percentages.
Teacher / mode
Student
Base
SFT-P
SFT-N
Gemma3-12B-it
Qwen3-1.7B-Base
6.9
22.8
22.2
Qwen3-4B-Base
19.1
38.5
38.4
Qwen3-4B / thinking
Qwen3-1.7B-Base
6.9
20.9
20.4
Qwen3-4B-Base
19.1
46.5
44.4
Appendix
Table 4: Teacher and sampling-mode controls: avg@16 accuracy (%) across the five mathematical benchmarks. Base is the corresponding student before fine-tuning.
Loss
Training data
AIME 2026
LiveCodeBench-v6
–
Base
1.3
9.3
−logp
P
5.5
16.6
N
5.6
16.9
−p
P
6.2
16.0
N
7.1
16.0
Appendix
Table 5: Correct vs. incorrect trajectory distillation on newer evaluation sets; percentages averaged over four student architectures (rounded to one decimal place).
Qwen3-4B model pair
Linear CKA
Base vs. SFT-P
0.383
Base vs. SFT-N
0.397
SFT-P vs. SFT-N
0.998
SFT-P vs. SFT-numina
0.412
Appendix
Table 6: Linear CKA between late-layer response-token representations on the same held-out MATH inputs and reference traces (128 problems). SFT-numina is fine-tuned on NuminaMath-CoT.
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
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.
As language models are increasingly deployed for complex autonomous tasks, their ability to reason accurately over longer horizons becomes critical. An essential component of this ability is planning and managing a long, complex chain-of-thought (CoT). We introduce LongCoT, a scalable benchmark of 2,500 expert-designed problems spanning chemistry, mathematics, computer science, chess, and logic to isolate and directly measure the long-horizon CoT reasoning capabilities of frontier models. Problems consist of a short input with a verifiable answer; solving them requires navigating a graph of interdependent steps that span tens to hundreds of thousands of reasoning tokens. Each local step is individually tractable for frontier models, so failures reflect long-horizon reasoning limitations. At release, the best models achieve <10% accuracy (GPT 5.2: 9.8%; Gemini 3 Pro: 6.1%) on LongCoT, revealing a substantial gap in current capabilities. Overall, LongCoT provides a rigorous measure of long-horizon reasoning, tracking the ability of frontier models to reason reliably over extended periods.
Sumeet Ramesh Motwani, Daniel Nichols, Charles London +17
University of Oxford · Lawrence Livermore National Laboratory (LLNL) · MBZUAI +4