cs.LGOct 14, 2025
SaveDemystifying Hybrid Thinking: Can LLMs Truly Switch Between Think and No-Think?
Organizations: Case Western Reserve University · Meta AI
Abstract
Hybrid thinking enables LLMs to switch between reasoning and direct answering, offering a balance between efficiency and reasoning capability. Yet our experiments reveal that current hybrid thinking LLMs only achieve partial mode separation: reasoning behaviors often leak into the no-think mode. To understand and mitigate this, we analyze the factors influencing controllability and identify four that matter most: (1) larger data scale, (2) using think and no-think answers from different questions rather than the same question, (3) a moderate increase in no-think data number, and (4) a two-phase strategy that first trains reasoning ability and then applies hybrid think training. Building on these findings, we propose a practical recipe that, compared to standard training, can maintain accuracy in both modes while significantly reducing no-think output length (from 1085 to 585 on MATH500) and occurrences of reasoning-supportive tokens such as "wait" (from 5917 to 522 on MATH500). Our findings highlight the limitations of current hybrid thinking and offer directions for strengthening its controllability. The code is available at: https://github.com/SR-A-W/demystifying-hybrid-thinking
Figures & tables
Figure 1: Case study on an AIME24 problem. We compare the responses of Qwen3-8B under no-think and think modes. In the no-think mode, Qwen3-8B still performs reasoning outside the no-think constraint (e.g., generating reasoning-supportive words such as Wait ), indicating that its hybrid thinking ability remains imperfect and cannot achieve full control.
| Model | Acc. (%) | Len. | #Wait | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Think | No-think | Think | No-think | Think | No-think | ||||
| MATH500 | |||||||||
| Instruct | – | 59.94 | – | 703.11 | – | 0 | |||
| Hybrid | 92.82 | 82.90 | +22.96 | 4384.35 | 958.31 | +255.20 | 83703 | 646 | +646 |
| AIME24 | |||||||||
| Instruct | – | 6.67 | – | 1729.22 | – | 0 | |||
Table 1: Performance on MATH500, AIME24, and GPQA under think and no-think modes. We report accuracy (Acc.), output length (Len.), #Wait count (i.e., occurrences of reflection words such as “ wait ”, “ hmm ”, “ alternatively ”, aggregated over all responses in the evaluation), and no-think differences ( ) between Hybrid (Qwen3-8B) and Instruct (Qwen2.5-7B-Instruct). Notably, Hybrid model in the no-think mode produce much longer outputs than the Instruct model, and even generate reflection words.
Figure 2: Comparison of the performance of no-think mode of Hybrid model (Qwen3-8B) and Instruct model (Qwen2.5-7B-Instruct) on MATH500, AIME24, and GPQA. We show bar plots of accuracy, average output length and wait count across these three datasets.
| Benchmark | Model | Mode | Output Len. | #Refl. | Judge verdict (agreement) |
|---|---|---|---|---|---|
| MATH500 | Qwen3-4B | No-think | 969 | 210 | Implicit reasoning (100%) |
| Qwen3-4B | Think | 4750 | 163160 | Explicit reasoning (98%) | |
| Qwen3-8B | No-think | 1044 | 113 | Implicit reasoning (92%) | |
| Qwen3-8B | Think | 4419 | 154670 | Explicit reasoning (98%) | |
| Qwen3-14B | No-think | 885 | 131 | Implicit reasoning (98%) | |
| Qwen3-14B | Think | 4468 | 127342 | Explicit reasoning (98%) |
Table 2: Model-based judge validation of #Refl./Ans. as a genuine (not surface-level) leakage signal, on off-the-shelf Qwen3 hybrid baselines. Judge: GPT-OSS-20B, three-way no/implicit/explicit verdict.
Figure 3: Line plots of Qwen2.5-7B-Instruct performance with different training data scales (20k/40k/80k/140k) on MATH500, AIME24, and GPQA. We report accuracy (top) and average output length (bottom) under both think and no-think modes. The results show that while accuracy and output length in the think mode, as well as accuracy in the no-think mode, remain relatively stable across scales, the no-think output length decreases substantially with larger training data scales as expected.
Figure 4: Comparison of accuracy and output lengths under think and no-think modes on MATH500. The bar charts illustrate model behavior under different training settings (pairs vs. no-pairs), highlighting how no-pairs could reduce output length in no-think mode.
Figure 5: Comparison of output lengths under think and no-think modes on MATH500. The bar charts illustrate model behavior under different think-to-no-think data ratios, showing that increasing the proportion of no-think data reduces output length in the no-think mode.
Figure 6: Average output length of models trained with 2-phase and mix strategies across three benchmarks (MATH500, AIME24, and GPQA) under different data scales with no-think mode.
| Model Type | Think | No-think | ||||
|---|---|---|---|---|---|---|
| Acc. | Len. | #Wait | Acc. | Len. | #Wait | |
| MATH500 | ||||||
| Pure think | 86.66 | 4340.62 | 99149 | – | – | – |
| Pure no-think | – | – | – | 53.10 | 430.44 | 0 |
| Hybrid think | 86.12 | 4539.38 | 105655 | 77.42 | 2971.03 | 64622 |
| AIME24 | ||||||
Table 3: Comparison of hybrid, pure-think, and pure-no-think models trained from Qwen2.5-7B-Instruct on MATH500 and AIME24 under think and no-think modes. We report accuracy (Acc.), output length (Len.), and #Wait count (i.e., occurrences of reflection words such as “ wait ”, “ hmm ”, “ alternatively ”). Results show that in the no-think mode, hybrid models still produce much longer outputs than pure no-think models and generate frequent reflection words.
| Model | Mode | MATH500 | AIME24 | ||||
|---|---|---|---|---|---|---|---|
| Acc. | Len. | #Wait | Acc. | Len. | #Wait | ||
| Qwen3-8B | Think | 92.82 | 4384.35 | 83703 | 63.33 | 11394.54 | 12184 |
| No-think | 82.90 | 958.31 | 646 | 24.00 | 4061.67 | 184 | |
| Qwen3-4B | Think | 92.02 | 4679.54 | 97998 | 61.67 | 11595.51 | 13754 |
| No-think | 82.22 | 1004.13 | 611 | 20.67 | 4636.37 | 762 | |
| Qwen3-14B | Think | 93.96 | 4450.98 | 65320 | 67.67 | 11401.06 | 11091 |
Table 4: Performance of Qwen3 models on MATH500 and AIME24 under think and no-think modes. We report accuracy (Acc.), output length (Len.), and #Wait count. Results show that even open-source models still produce such reflection words in the no-think mode.
| MATH500 | ||||||
| Model | Think | No-think | ||||
| Acc. | Len. | #Wait | Acc. | Len. | #Wait | |
| Pure-think | 86.66 | 4340.62 | 99149 | – | – | – |
| Instruct | – | – | – | 75.42 | 640.91 | 0 |
| Original Recipe | 85.88 | 4539.53 | 116663 | 63.16 | 1085.99 | 5917 |
| Our Recipe | 86.78 | 4481.74 | 103335 | 63.60 | 585.63 | 522 |
Table 5: Performance of different training settings on MATH500 and MMLU-STEM under think and no-think modes. We report accuracy (Acc.), output length (Len.), and #Wait count (i.e., occurrences of reflection words such as “ wait ”, “ hmm ”, “ alternatively ”). Our recipe maintains accuracy while substantially reducing no-think verbosity and reflective tokens.
| Model | Mode | MATH500 | MMLU-STEM | ||||
|---|---|---|---|---|---|---|---|
| Acc. | Len. | #Wait | Acc. | Len. | #Wait | ||
| Qwen2.5-7B | Pure-think | 86.06 | 4361.15 | 94997 | 85.79 | 2991.11 | 54345 |
| Instruct | 75.42 | 640.91 | 0 | 66.25 | 427.01 | 18 | |
| Our Recipe-think | 86.50 | 4488.40 | 113183 | 85.82 | 3099.89 | 49397 | |
| Our Recipe-no-think | 63.56 | 593.09 | 1535 | 59.44 | 774.42 | 2334 | |
| Llama3.1-8B | Pure-think | 87.34 | 3814.88 | 96024 | 66.95 | 2089.36 | 43584 |
Table 6: The performance of proposed recipe across different models. We reported the performance of our recipe and the baseline pure think and pure no_think models for Qwen2.5-7B, Llama3.1-8B, and Phi-4-14B. The results shows that our recipe consistently enhances performance across various model architectures (Qwen, Llama, and Phi) and scaling sizes (ranging from 7B to 14B), confirming its robustness and cross-architecture effectiveness. These results are from a different evaluation run than those in Table 5 .
Appendix figures & tables41 assets
Supplementary material from the paper’s appendix.
Appendix
| Data Scale | Accuracy (%) | Avg. Output Len. | ||
|---|---|---|---|---|
| Think | No-think | Think | No-think | |
| Instruct | – | 74.96 | – | 608.85 |
| 20k | 83.18 | 60.12 | 4704.91 | 2214.08 |
| 40k | 85.46 | 62.10 | 4589.04 | 1437.72 |
| 80k | 85.88 | 63.16 | 4539.53 | 1086.00 |
| 140k | 86.58 | 63.90 | 4442.49 | 775.67 |
Table 7: Performance of Qwen2.5-7B-Instruct with different data scales on MATH500 . “Instruct” refers to the original Qwen2.5-7B-Instruct model, while 20k/40k/80k/140k denote the number of training samples used. All training sets maintain a nearly 1:1 ratio of think to no-think data. We report accuracy (%) and average output length under both modes for each model.
| Data Scale | Accuracy (%) | Avg. Output Len. | ||
|---|---|---|---|---|
| Think | No-think | Think | No-think | |
| Instruct | – | 13.33 | – | 1272.64 |
| 20k | 18.33 | 7.00 | 13397.91 | 5654.04 |
| 40k | 19.33 | 7.00 | 13586.36 | 2584.13 |
| 80k | 27.67 | 5.33 | 12799.13 | 2086.05 |
| 140k | 36.00 | 5.00 | 12507.64 | 1293.08 |
Table 8: Performance of Qwen2.5-7B-Instruct with different data scales on AIME24 . “Instruct” refers to the original Qwen2.5-7B-Instruct model, while 20k/40k/80k/140k denote the number of training samples used. All training sets maintain a nearly 1:1 ratio of think to no-think data. We report accuracy (%) and average output length under both modes for each model.
| Data Scale | Accuracy (%) | Avg. Output Len. | ||
|---|---|---|---|---|
| Think | No-think | Think | No-think | |
| Instruct | – | 31.01 | – | 977 |
| 20k | 40.00 | 39.50 | 9444.03 | 5503.32 |
| 40k | 40.61 | 38.99 | 9571.43 | 5330.81 |
| 80k | 40.25 | 38.89 | 9712.00 | 4811.29 |
| 140k | 41.01 | 34.95 | 9826.74 | 4583.18 |
Table 9: Performance of Qwen2.5-7B-Instruct with different data scales on GPQA . “Instruct” refers to the original Qwen2.5-7B-Instruct model, while 20k/40k/80k/140k denote the number of training samples used. All training sets maintain a nearly 1:1 ratio of think to no-think data. We report accuracy (%) and average output length under both modes for each model.
| Data Scale | Accuracy (%) | Avg. Output Len. | ||
|---|---|---|---|---|
| Think | No-think | Think | No-think | |
| Instruct | – | 49.32 | – | 2426.36 |
| 20k | 69.10 | 49.12 | 6008.2 | 1111.1 |
| 40k | 73.40 | 53.92 | 5685.3 | 1118.5 |
| 80k | 78.12 | 55.22 | 5263.7 | 899.7 |
| 140k | 82.00 | 57.72 | 4896.8 | 780.9 |
Table 10: Performance of Llama3.1-8B-Instruct with different data scales on MATH500 . “Instruct” refers to the original Llama3.1-8B-Instruct model, while 20k/40k/80k/140k denote the number of training samples used. All training sets maintain a nearly 1:1 ratio (an approximate proportion of 5:4) of think to no-think data. We report accuracy (%) and average output length under both modes for each model.
| Data Scale | Accuracy (%) | Avg. Output Len. | ||
|---|---|---|---|---|
| Think | No-think | Think | No-think | |
| Instruct | – | 6.0 | – | 7153.73 |
| 20k | 8.33 | 5.67 | 14182.8 | 2949.1 |
| 40k | 10.00 | 4.00 | 14088.2 | 2995.5 |
| 80k | 20.33 | 4.00 | 13253.2 | 2108.0 |
| 140k | 23.67 | 2.67 | 13141.8 | 2229.5 |
Table 11: Performance of Llama3.1-8B-Instruct with different data scales on AIME24 . “Instruct” refers to the original Llama3.1-8B-Instruct model, while 20k/40k/80k/140k denote the number of training samples used. All training sets maintain a nearly 1:1 ratio (an approximate proportion of 5:4) of think to no-think data. We report accuracy (%) and average output length under both modes for each model.
| Data Scale | Accuracy (%) | Avg. Output Len. | ||
|---|---|---|---|---|
| Think | No-think | Think | No-think | |
| Instruct | – | 29.29 | – | 3190.01 |
| 20k | 36.41 | 32.53 | 9119.5 | 2814.4 |
| 40k | 36.52 | 30.35 | 10144.5 | 1957.3 |
| 80k | 37.58 | 31.16 | 10004.7 | 987.2 |
| 140k | 34.95 | 31.67 | 10190.1 | 3352.6 |
Table 12: Performance of Llama3.1-8B-Instruct with different data scales on GPQA . “Instruct” refers to the original Llama3.1-8B-Instruct model, while 20k/40k/80k/140k denote the number of training samples used. All training sets maintain a nearly 1:1 ratio (an approximate proportion of 5:4) of think to no-think data. We report accuracy (%) and average output length under both modes for each model.
| Scale | Setting | Think | No-think | ||
|---|---|---|---|---|---|
| Acc. | Len. | Acc. | Len. | ||
| 20k | pairs | 83.18 | 4704.91 | 60.12 | 2214.08 |
| no-pairs | 83.44 | 4733.91 | 54.26 | 1597.64 | |
| 40k | pairs | 85.46 | 4589.04 | 62.10 | 1437.72 |
| no-pairs | 84.40 | 4560.66 | 61.76 | 942.87 | |
| 80k | pairs | 85.88 | 4539.53 | 63.16 | 1086.00 |
Table 13: Comparison between pairs and no-pairs on MATH500 under think and no-think modes for Qwen2.5-7B-Instruct . Pairs means each question has both think and no-think responses; no-pairs means responses come from different questions. We report accuracy (%) and average output length. The no-pairs setting yields shorter no-think outputs across scales while maintaining comparable accuracy.
| Scale | Setting | Think | No-think | ||
|---|---|---|---|---|---|
| Acc. | Len. | Acc. | Len. | ||
| 20k | pairs | 18.33 | 13397.91 | 7.00 | 5654.04 |
| no-pairs | 23.00 | 12913.75 | 5.33 | 2560.70 | |
| 40k | pairs | 19.33 | 13586.36 | 7.00 | 2584.13 |
| no-pairs | 24.00 | 13308.04 | 7.67 | 1912.82 | |
| 80k | pairs | 27.67 | 12799.13 | 5.33 | 2086.05 |
Table 14: Comparison between pairs and no-pairs on AIME24 under think and no-think modes for Qwen2.5-7B-Instruct . Pairs means each question has both think and no-think responses; no-pairs means responses come from different questions. We report accuracy (%) and average output length. No-pairs setting yields shorter no-think outputs across scales while maintaining accuracy.
| Scale | Setting | Think | No-think | ||
|---|---|---|---|---|---|
| Acc. | Len. | Acc. | Len. | ||
| 20k | pairs | 69.10 | 6008.17 | 49.12 | 1111.11 |
| no-pairs | 69.50 | 6187.14 | 51.70 | 1159.26 | |
| 40k | pairs | 73.40 | 5685.25 | 53.92 | 1118.49 |
| no-pairs | 73.52 | 5679.92 | 54.34 | 1096.61 | |
| 80k | pairs | 78.12 | 5263.71 | 55.22 | 899.72 |
Table 15: Comparison between pairs and no-pairs on MATH500 under think and no-think modes for Llama3.1-8B-Instruct . Pairs means each question has both think and no-think responses; no-pairs means responses come from different questions. We report accuracy (%) and average output length. The no-pairs setting yields shorter no-think outputs across scales while maintaining comparable accuracy.
| Scale | Setting | Think | No-think | ||
|---|---|---|---|---|---|
| Acc. | Len. | Acc. | Len. | ||
| 20k | pairs | 8.33 | 14182.81 | 5.67 | 2949.06 |
| no-pairs | 11.33 | 13880.53 | 3.33 | 2850.43 | |
| 40k | pairs | 10.00 | 14088.24 | 4.00 | 2995.47 |
| no-pairs | 13.33 | 13926.53 | 3.00 | 3203.56 | |
| 80k | pairs | 20.33 | 13253.21 | 4.00 | 2108.03 |
Table 16: Comparison between pairs and no-pairs on AIME24 under think and no-think modes for Llama3.1-8B-Instruct . Pairs means each question has both think and no-think responses; no-pairs means responses come from different questions. We report accuracy (%) and average output length. The no-pairs setting yields shorter no-think outputs across scales while maintaining comparable accuracy.
| Think:No-think | Think | No-think | ||
|---|---|---|---|---|
| Acc. | Len. | Acc. | Len. | |
| 1:4 | 83.14 | 4843.01 | 61.16 | 788.70 |
| 1:2 | 84.70 | 4577.90 | 66.80 | 761.30 |
| 1:1 | 85.88 | 4539.53 | 63.16 | 1086.00 |
| 2:1 | 86.6 | 4452.42 | 62.48 | 1121.09 |
Table 17: Effect of different think-to-no-think data ratios on MATH500 under think and no-think modes for Qwen2.5-7B-Instruct . Ratios denote the proportion of think to no-think samples, with the total training size fixed at 80k. Increasing the proportion of no-think data effectively reduces no-think output length while largely preserving accuracy in both modes. Note: The “1:1” ratio is an approximate proportion ( ) due to the design for dataset construction.
| Think:No-think | Think | No-think | ||
|---|---|---|---|---|
| Acc. | Len. | Acc. | Len. | |
| 1:4 | 20.56 | 13229.06 | 4.33 | 1453.21 |
| 1:2 | 25.00 | 13233.21 | 3.00 | 1592.96 |
| 1:1 | 27.67 | 12799.13 | 5.33 | 2086.05 |
| 2:1 | 31.33 | 12524.66 | 3.33 | 2233.13 |
Table 18: Effect of different think-to-no-think data ratios on AIME24 under think and no-think modes for Qwen2.5-7B-Instruct . Ratios denote the proportion of think to no-think samples, with the total training size fixed at 80k. Increasing the proportion of no-think data effectively reduces no-think output length while largely preserving accuracy in both modes. Note: The “1:1” ratio is an approximate proportion ( ) due to the design for dataset construction.
| Think:No-think | Think | No-think | ||
|---|---|---|---|---|
| Acc. | Len. | Acc. | Len. | |
| 1:4 | 69.56 | 6184.32 | 50.40 | 802.80 |
| 1:2 | 74.32 | 5743.64 | 53.04 | 811.43 |
| 1:1 | 78.12 | 5263.71 | 55.22 | 899.72 |
| 2:1 | 77.96 | 5147.29 | 55.16 | 1025.80 |
Table 19: Effect of different think-to-no-think data ratios on MATH500 under think and no-think modes for Llama3.1-8B-Instruct . Ratios denote the proportion of think to no-think samples, with the total training size fixed at 80k. Increasing the proportion of no-think data effectively reduces no-think output length while largely preserving accuracy in both modes. Note: The “1:1” ratio is an approximate proportion ( ) due to the design for dataset construction.
| Think:No-think | Think | No-think | ||
|---|---|---|---|---|
| Acc. | Len. | Acc. | Len. | |
| 1:4 | 5.33 | 14416.15 | 2.00 | 1234.35 |
| 1:2 | 13.33 | 13767.91 | 3.33 | 1774.01 |
| 1:1 | 20.33 | 13253.21 | 4.00 | 2108.03 |
| 2:1 | 19.33 | 13328.44 | 4.67 | 2229.22 |
Table 20: Effect of different think-to-no-think data ratios on AIME24 under think and no-think modes for Llama3.1-8B-Instruct . Ratios denote the proportion of think to no-think samples, with the total training size fixed at 80k. Increasing the proportion of no-think data effectively reduces no-think output length while largely preserving accuracy in both modes. Note: The “1:1” ratio is an approximate proportion ( ) due to the design for dataset construction.
| Think:No-think | Think | No-think | ||
|---|---|---|---|---|
| Acc. | Len. | Acc. | Len. | |
| 1:4 | 32.73 | 10886.36 | 30.81 | 1470.06 |
| 1:2 | 33.23 | 10493.00 | 31.11 | 1039.15 |
| 1:1 | 37.58 | 10004.75 | 31.16 | 987.24 |
| 2:1 | 38.48 | 9885.08 | 31.92 | 1359.05 |
Table 21: Effect of different think-to-no-think data ratios on GPQA under think and no-think modes for Llama3.1-8B-Instruct . Ratios denote the proportion of think to no-think samples, with the total training size fixed at 80k. Increasing the proportion of no-think data effectively reduces no-think output length while largely preserving accuracy in both modes. Note: The “1:1” ratio is an approximate proportion ( ) due to the design for dataset construction.
| Think:No-think | Think | No-think | ||
|---|---|---|---|---|
| Acc. | Len. | Acc. | Len. | |
| 1:4 | 75.45 | 4474.87 | 50.02 | 568.52 |
| 1:2 | 77.74 | 4181.22 | 49.60 | 540.94 |
| 1:1 | 79.16 | 3774.97 | 48.84 | 546.10 |
| 2:1 | 79.80 | 3542.41 | 49.67 | 584.47 |
Table 22: Effect of different think-to-no-think data ratios on MMLU-STEM under think and no-think modes for Llama3.1-8B-Instruct . Ratios denote the proportion of think to no-think samples, with the total training size fixed at 80k. Increasing the proportion of no-think data effectively reduces no-think output length while largely preserving accuracy in both modes. Note: The “1:1” ratio is an approximate proportion ( ) due to the design for dataset construction.
| Scale | Setting | Think | No-think | ||
|---|---|---|---|---|---|
| Acc. | Len. | Acc. | Len. | ||
| 20k | 2-phase | 83.38 | 4797.40 | 47.26 | 870.50 |
| mix | 83.18 | 4704.91 | 60.12 | 2214.08 | |
| 40k | 2-phase | 85.18 | 4670.88 | 43.52 | 798.87 |
| mix | 85.46 | 4589.04 | 62.10 | 1437.72 | |
| 80k | 2-phase | 85.86 | 4626.42 | 51.86 | 639.60 |
Table 23: Comparison of 2-phase and mix training strategies on MATH500 under think and no-think modes for Qwen2.5-7B-Instruct . Scale denotes the number of samples (e.g., 20k = 20,000). We report accuracy (%) and average output length. The 2-phase strategy first trains on pure-think data before fine-tuning with mixed data, while the mix strategy directly trains on mixed data. Across all scales, 2-phase strategy yields shorter no-think outputs compared to mix training.
| Scale | Setting | Think | No-think | ||
|---|---|---|---|---|---|
| Acc. | Len. | Acc. | Len. | ||
| 20k | 2-phase | 20.00 | 13620.71 | 4.33 | 1847.35 |
| mix | 18.33 | 13397.91 | 7.00 | 5654.04 | |
| 40k | 2-phase | 22.67 | 13562.19 | 1.67 | 1635.34 |
| mix | 19.33 | 13586.36 | 7.00 | 2584.13 | |
| 80k | 2-phase | 30.00 | 12962.41 | 3.00 | 1398.48 |
Table 24: Comparison of 2-phase and mix training strategies on AIME24 under think and no-think modes for Qwen2.5-7B-Instruct . Scale denotes the number of training samples (e.g., 20k = 20,000). We report accuracy (%) and average output length. The 2-phase strategy first trains on pure-think data before fine-tuning with mixed data, while the mix strategy directly trains on mixed data. Across all scales, 2-phase strategy yields shorter no-think outputs compared to mix training.
| Scale | Setting | Think | No-think | ||
|---|---|---|---|---|---|
| Acc. | Len. | Acc. | Len. | ||
| 20k | 2-phase | 68.56 | 6300.03 | 47.18 | 1180.40 |
| mix | 69.10 | 6008.17 | 49.12 | 1111.11 | |
| 40k | 2-phase | 72.52 | 6033.99 | 48.50 | 1170.26 |
| mix | 73.40 | 5685.25 | 53.92 | 1118.49 | |
| 80k | 2-phase | 76.90 | 5475.04 | 50.00 | 870.21 |
Table 25: Comparison of 2-phase and mix training strategies on MATH500 under think and no-think modes for Llama3.1-8B-Instruct . Here, Scale denotes the number of training samples (e.g., 20k means 20,000 samples). We report both accuracy (%) and average output length. The 2-phase strategy first trains on pure-think data before fine-tuning with mixed think and no-think data, while the mix strategy directly trains on think and no-think mixed data. Notably, across all scales, 2-phase strategy consistently yields shorter output lengths under the no-think mode compared to mix training.
| Scale | Setting | Think | No-think | ||
|---|---|---|---|---|---|
| Acc. | Len. | Acc. | Len. | ||
| 20k | 2-phase | 7.00 | 13737.77 | 4.33 | 2735.59 |
| mix | 8.33 | 14182.81 | 5.67 | 2949.06 | |
| 40k | 2-phase | 9.67 | 14034.31 | 4.33 | 2692.68 |
| mix | 10.00 | 14088.24 | 4.00 | 2995.47 | |
| 80k | 2-phase | 16.00 | 13690.04 | 5.00 | 1776.30 |
Table 26: Comparison of 2-phase and mix training strategies on AIME24 under think and no-think modes for Llama3.1-8B-Instruct . Here, Scale denotes the number of training samples (e.g., 20k means 20,000 samples). We report both accuracy (%) and average output length. The 2-phase strategy first trains on pure-think data before fine-tuning with mixed think and no-think data, while the mix strategy directly trains on think and no-think mixed data. Notably, across all scales, 2-phase strategy consistently yields shorter output lengths under the no-think mode compared to mix training.
| Scale | Setting | Think | No-think | ||
|---|---|---|---|---|---|
| Acc. | Len. | Acc. | Len. | ||
| 20k | 2-phase | 36.31 | 10182.25 | 26.67 | 966.86 |
| mix | 36.41 | 9119.54 | 32.53 | 2814.42 | |
| 40k | 2-phase | 35.15 | 10626.91 | 29.60 | 975.13 |
| mix | 36.52 | 10144.51 | 30.35 | 1957.28 | |
| 80k | 2-phase | 37.22 | 10100.31 | 27.98 | 705.01 |
Table 27: Comparison of 2-phase and mix training strategies on GPQA under think and no-think modes for Llama3.1-8B-Instruct . Here, Scale denotes the number of training samples (e.g., 20k means 20,000 samples). We report both accuracy (%) and average output length. The 2-phase strategy first trains on pure-think data before fine-tuning with mixed think and no-think data, while the mix strategy directly trains on think and no-think mixed data. Notably, across all scales, 2-phase strategy consistently yields shorter output lengths under the no-think mode compared to mix training.
| Scale | Setting | Think | No-think | ||
|---|---|---|---|---|---|
| Acc. | Len. | Acc. | Len. | ||
| 20k | 2-phase | 77.26 | 4056.91 | 53.38 | 572.71 |
| mix | 76.82 | 3632.27 | 59.88 | 1127.23 | |
| 40k | 2-phase | 79.10 | 3973.26 | 53.98 | 592.56 |
| mix | 78.50 | 3866.03 | 55.22 | 765.63 | |
| 80k | 2-phase | 79.10 | 3980.86 | 46.02 | 448.93 |
Table 28: Comparison of 2-phase and mix training strategies on MMLU-STEM under think and no-think modes for Llama3.1-8B-Instruct . Here, Scale denotes the number of training samples (e.g., 20k means 20,000 samples). We report both accuracy (%) and average output length. The 2-phase strategy first trains on pure-think data before fine-tuning with mixed think and no-think data, while the mix strategy directly trains on think and no-think mixed data. Notably, across all scales, 2-phase strategy consistently yields shorter output lengths under the no-think mode compared to mix training.
| Setting | Think | No-think | ||
|---|---|---|---|---|
| Acc. | Len. | Acc. | Len. | |
| Baseline | – | – | 74.96 | 608.85 |
| Demo (w/o pairs) | 37.08 | 650.35 | 31.68 | 390.63 |
| 20k-2phase | 83.38 | 4797.40 | 47.26 | 870.50 |
| 20k-mix | 83.18 | 4704.91 | 60.12 | 2214.08 |
| 40k-2phase | 85.18 | 4670.88 | 43.52 | 798.87 |
Table 29: Performance of Qwen2.5-7B-Instruct under different training settings on MATH500 . We report accuracy (Acc.) and output length (Len.) for both think and no-think modes.
| Setting | Think | No-think | ||
|---|---|---|---|---|
| Acc. | Len. | Acc. | Len. | |
| 20k-2phase | 20.00 | 13620.71 | 4.33 | 1847.35 |
| 20k-mix | 18.33 | 13397.91 | 7.00 | 5654.04 |
| 40k-2phase | 22.67 | 13562.19 | 1.67 | 1635.34 |
| 40k-mix | 19.33 | 13586.36 | 7.00 | 2584.13 |
Table 30: Performance of Qwen2.5-7B-Instruct under different training settings on AIME24 . We report accuracy (Acc.) and output length (Len.) for both think mode and no-think mode.
| Setting | Think | No-think | ||
|---|---|---|---|---|
| Acc. | Len. | Acc. | Len. | |
| 20k-2phase | 41.16 | 9872.89 | 26.72 | 1404.46 |
| 20k-mix | 40.00 | 9444.03 | 39.50 | 5503.32 |
| 40k-2phase | 41.62 | 9903.88 | 32.12 | 2892.41 |
| 40k-mix | 40.61 | 9571.43 | 38.99 | 5330.81 |
Table 31: Performance of Qwen2.5-7B-Instruct under different training settings on GPQA-Diamond . We report accuracy (Acc.) and output length (Len.) for both think mode and no-think mode.
| Model | Think | No-think | ||
| Acc. | Len. | Acc. | Len. | |
| Math500 | ||||
| w/o Sys. Prompt | 86.1 | 4539 | 77.4 | 2971 |
| w/ Sys. Prompt | 84.6 | 4383 | 76.6 | 2840 |
| AIME24 | ||||
| w/o Sys. Prompt | 29.3 | 12615 | 23.3 | 5744 |
Table 32: Comparison of Qwen 2-phase training with and without system prompt on MATH500 , AIME24 , and GPQA-Diamond .
| Setting | Acc. | Len. | #Refl. |
|---|---|---|---|
| Instruct | 46.17% | 267.60 | 13 |
| Reasoning | 75.24% | 3723.06 | 516808 |
| Our Recipe (think) | 76.93% | 2822.63 | 274499 |
| Our Recipe (no-think) | 57.06% | 1547.63 | 9073 |
Table 33: Generalization beyond math for Qwen on full MMLU (57 subjects; not the MMLU-STEM subset used elsewhere in this paper): accuracy, output length, and reflective-token count.
| Setting | Acc. | Len. | #Refl. |
|---|---|---|---|
| Instruct | 69.0% | 17.2 | 0 |
| Reasoning | 42.8% | 22283.3 | 32220 |
| Our Recipe (think) | 61.5% | 6474.3 | 437 |
| Our Recipe (no-think) | 56.5% | 735.6 | 80 |
Table 34: Generalization beyond math for Qwen on TruthfulQA : accuracy, output length, and reflective-token count.
| Setting | Acc. | Len. | #Refl. |
|---|---|---|---|
| Instruct | 64.32% | 578.48 | 13 |
| Reasoning | 61.32% | 1869.46 | 242607 |
| Our Recipe (think) | 70.89% | 3748.36 | 491453 |
| Our Recipe (no-think) | 52.12% | 531.77 | 14858 |
Table 35: Generalization beyond math for Llama on full MMLU (57 subjects; not the MMLU-STEM subset used elsewhere in this paper): accuracy, output length, and reflective-token count.
| Setting | Acc. | Len. | #Refl. |
|---|---|---|---|
| Instruct | 49.5% | 9.2 | 0 |
| Reasoning | 54.2% | 6210.8 | 8276 |
| Our Recipe (think) | 58.8% | 3564.1 | 3916 |
| Our Recipe (no-think) | 41.0% | 1256.9 | 0 |
Table 36: Generalization beyond math for Llama on TruthfulQA : accuracy, output length, and reflective-token count.
| Setting | Acc. | Len. | #Refl. |
|---|---|---|---|
| Instruct | 70.47% | 933.33 | 21 |
| Reasoning | 76.05% | 7485.83 | 32478 |
| Our Recipe (think) | 87.44% | 1881.09 | 158644 |
| Our Recipe (no-think) | 65.36% | 365.22 | 2906 |
Table 37: Generalization beyond math for Phi on full MMLU (57 subjects; not the MMLU-STEM subset used elsewhere in this paper): accuracy, output length, and reflective-token count.
| Setting | Acc. | Len. | #Refl. |
|---|---|---|---|
| Instruct | 75.0% | 25.5 | 0 |
| Reasoning | 74.8% | 257.6 | 0 |
| Our Recipe (think) | 70.5% | 4335.6 | 6447 |
| Our Recipe (no-think) | 67.0% | 159.0 | 0 |
Table 38: Generalization beyond math for Phi on TruthfulQA : accuracy, output length, and reflective-token count.
| Setting | #Refl. | Len. |
|---|---|---|
| Instruct | ||
| Reasoning | ||
| Our Recipe (think) | ||
| Our Recipe (no-think) |
Table 39: Statistical rigor for Qwen on MATH500 : mean std over 10 independent random seeds for reflective-token count (#Refl.) and total output length (Len.).
| Setting | #Refl. | Len. |
|---|---|---|
| Instruct | ||
| Reasoning | ||
| Our Recipe (think) | ||
| Our Recipe (no-think) |
Table 40: Statistical rigor for Qwen on AIME24 : mean std over 10 independent random seeds for reflective-token count (#Refl.) and total output length (Len.).
| Setting | #Refl. | Len. |
|---|---|---|
| Instruct | ||
| Reasoning | ||
| Our Recipe (think) | ||
| Our Recipe (no-think) |
Table 41: Statistical rigor for Llama on MATH500 : mean std over 10 independent random seeds for reflective-token count (#Refl.) and total output length (Len.).
| Setting | #Refl. | Len. |
|---|---|---|
| Instruct | ||
| Reasoning | ||
| Our Recipe (think) | ||
| Our Recipe (no-think) |
Table 42: Statistical rigor for Llama on AIME24 : mean std over 10 independent random seeds for reflective-token count (#Refl.) and total output length (Len.).
| Setting | #Refl. | Len. |
|---|---|---|
| Instruct | ||
| Reasoning | ||
| Our Recipe (think) | ||
| Our Recipe (no-think) |
Table 43: Statistical rigor for Phi on MATH500 : mean std over 10 independent random seeds for reflective-token count (#Refl.) and total output length (Len.).
| Setting | #Refl. | Len. |
|---|---|---|
| Instruct | ||
| Reasoning | ||
| Our Recipe (think) | ||
| Our Recipe (no-think) |
Table 44: Statistical rigor for Phi on AIME24 : mean std over 10 independent random seeds for reflective-token count (#Refl.) and total output length (Len.).
| Setting | Time (s) | Tok/s |
|---|---|---|
| Instruct | ||
| Reasoning | ||
| Our Recipe (think) | ||
| Our Recipe (no-think) |
Table 45: Statistical rigor for Qwen on MATH500 : mean std over 10 independent random seeds for wall-clock inference time (s/instance) and throughput (tokens/s). Latency profiling was conducted on MATH500 only.
| Setting | Time (s) | Tok/s |
|---|---|---|
| Instruct | ||
| Reasoning | ||
| Our Recipe (think) | ||
| Our Recipe (no-think) |
Table 46: Statistical rigor for Llama on MATH500 : mean std over 10 independent random seeds for wall-clock inference time (s/instance) and throughput (tokens/s). Latency profiling was conducted on MATH500 only.
| Setting | Time (s) | Tok/s |
|---|---|---|
| Instruct | ||
| Reasoning | ||
| Our Recipe (think) | ||
| Our Recipe (no-think) |
Table 47: Statistical rigor for Phi on MATH500 : mean std over 10 independent random seeds for wall-clock inference time (s/instance) and throughput (tokens/s). Latency profiling was conducted on MATH500 only.