Paper: Active Prompting with Chain-of-Thought for Large Language Models (ICLR-2024)

Reviewer comment (Experiments):
Need for Additional Corpora: One significant advantage of CoT is its ability to leverage the model's generalization capabilities, requiring only a minimal number of task-related samples to teach the model the paradigm for solving tasks. In scenarios without corpora of the same distribution, such as ASDiv, SVAMP, and SingleEq, Active Prompt still needs to capitalize on the model's generalizability. However, it struggles to achieve the same performance boosts as datasets with training corpora like GSM8K and AQuA.

Author response:
From the Table 1, we find that the generalization performance is correlated to the backbone models. If we look into text-davinci-002 and code-davinci-002, we will find the performance boost on GSM8K and AQuA is larger than asdiv, svamp, and singleeq. However, If we look into text-davinci-003 and gpt-3.5-turbo, we will find the performance improvement is similar. For example, with gpt-3.5-turbo, the improvement is around 1.5 for these two scenarios. Therefore, considering the generalization, we can still take the prompts selected by a similar domain / task and then apply them to unseen domains / tasks.

| Model / Dataset | GSM8K | AQuA | Average-1| ASDiv | SVAMP | SingleEq | Average-2 |
| ----------- | ----------- | ----------- | ----------- | ----------- | ----------- | ----------- |----------- |
| text-davinci-003 (CoT) | 61.7 | 46.0 | 53.9 | 78.2 | 77.6 | 91.5 | 82.4 |
| text-davinci-003 (Active-Prompt) | 65.6 | 48.0 | 56.8 | 79.8 | 80.5 | 93.1 | 84.5 |
| gpt-3.5-turbo (CoT) | 74.2 | 50.0 | 62.1 | 82.5 | 83.8 | 95.0 | 87.1 |
| gpt-3.5-turbo (Active-Prompt) | 77.1 | 50.0 | 63.6 | 83.6 | 85.5 | 96.0 | 88.4 |

Reviewer comment (Evaluation):
Differences in Uncertainty Measurement Methods: The authors introduced four methods of uncertainty measurement but did not delve deep into their differences. It appears that “Entropy” has better generalizability on datasets like StrategyQA compared to “Disagreement”. However, “Disagreement” outperforms on datasets like SVAMP and CSQA using code-davinci-002, as discussed in Question 2.

Author response:
Thank you so much for your question! We strongly agree with your observation. In addition, we find entropy-based methods are generally better than disagreement-based methods. For example, across 8 downstream tasks and two models (text-davinci-002 and code-davinci-002), Active-Prompt (E) outperforms Active-Prompt (D) 11 times out of 16. Active-Prompt (D) is better at SVAMP and CSQA. Because the calculation of entropy takes the frequency into consideration, it provides a more accurate estimation for uncertainty.
For the performance disparities between Active-Prompt (E) and Active-Prompt (D) across different datasets, it is because entropy could capture more fine-grained information to help estimate the uncertainty. Let’s take an example for illustration.
We query the model 5 times and obtain the follow results:

For question 1, answers A1 = {2, 3, 3, 3, 6}

For question 2: answers A2 = {2, 2, 3, 3, 6}

The disagreement of A1 is 3 and the disagreement of A2 is also 3. However, the entropy is different. The entropy of A1 is 1.37 while the entropy of A2 is 1.52. This explains why entropy-based methods are better than disagreement-based methods across 11 out of 16 tasks. Because of the fine-grained information, entropy could distinguish the uncertainty of different questions better.

Reviewer comment (Experiments):
Concerns Over Costs: Active Prompt seems to require an additional 1000*k API calls. Given the recommended value of k = 10, an extra 10,000 API calls seems to be a considerably high cost. Additionally, there's the cost associated with extra data annotation, as outlined in Question 3.

Author response:
For the cost of selection, compared with selecting questions by humans, our proposed method is more efficient. For a new task, users need to do trials and errors a lot of times which costs a lot of human effort with unstable performance. Even so, the selected questions are still suboptimal.
Second, as mentioned in Section 3.3, we limit the size of candidate instances to 1,000 which greatly reduce the cost. 1,000 is a good balance between cost and performance. We verified that with more than 1,000 instances, the performance would converge. Doing uncertainty estimation 10 times with a pool of 1,000 questions is acceptable. The cost is smaller than self-consistency, which usually requires 40 times inference, although it is an orthogonal technique and can be complementary to ours. In addition, inspired by the new experimental results requested by reviewer Wb4R, we are excited to find that questions selected by smaller models (e.g., Llama) perform well with larger models (e.g., gpt-3.5-turbo). Considering models like Llama are open-source which does not cause API cost, one may use it (with GPU) to replace black-box API. 


For the cost of annotation, annotating 8 questions is not costly. Humans could finish it in several minutes. Furthermore, like you suggested, one can use ChatGPT or GPT-4 for annotation, which is much more easier. We tried some examples and found the GPT-4 annotations make a lot of sense and we believe they work well as human’s annotation. We are doing this and will add this experiment very soon (before Nov. 22). Thanks!

Reviewer comment (Experiments):
Active learning is an iterative process. However, the method in the article undergoes only a single iteration. The authors also observed that 'the existing annotation of GSM8K is of high quality.' A concerning scenario arises when modifying prompt exemplars causes the model to become uncertain about samples it was previously confident about.

Author response:
Thanks for your questions! Conventional active learning is indeed an iterative process, but now some work feels that the iterative method is costly. So, there are also some recent studies that are one-pass [1,2].
To explore the effects of modification, we conduct more analysis by comparing the changes in terms of confident questions set before and after modification. Here, the confident question set is defined as a set of questions that the model is highly consistency (uncertainty is 0). With gpt-3.5-turbo, using the unmodified CoT, there are 325 questions in the confident question set (set X_1). After modification, with the modified CoT, there are also 325 questions (set X_2). Over 70 % questions in X_1 appear in set X_2. Although the uncertainty has increased in a small number of questions, we find that their uncertainty still remains very low.

Reviewer comment (Evaluation):
What leads to the performance disparities between Active-Prompt (E) and Active-Prompt (D) across different datasets?

Author response:
Thank you so much for your question! We strongly agree with your observation. In addition, we find entropy-based methods are generally better than disagreement-based methods. For example, across 8 downstream tasks and two models (text-davinci-002 and code-davinci-002), Active-Prompt (E) outperforms Active-Prompt (D) 11 times out of 16. Active-Prompt (D) is better at SVAMP and CSQA. Because the calculation of entropy takes the frequency into consideration, it provides a more accurate estimation for uncertainty.
For the performance disparities between Active-Prompt (E) and Active-Prompt (D) across different datasets, it is because entropy could capture more fine-grained information to help estimate the uncertainty. Let’s take an example for illustration.
We query the model 5 times and obtain the follow results:

For question 1, answers A1 = {2, 3, 3, 3, 6}

For question 2: answers A2 = {2, 2, 3, 3, 6}

The disagreement of A1 is 3 and the disagreement of A2 is also 3. However, the entropy is different. The entropy of A1 is 1.37 while the entropy of A2 is 1.52. This explains why entropy-based methods are better than disagreement-based methods across 11 out of 16 tasks. Because of the fine-grained information, entropy could distinguish the uncertainty of different questions better.

Reviewer comment (Evaluation):
From a cost perspective, does Active Prompt hold any advantages over methods like AutoCoT?

Author response:
Auto-CoT applies Sentence-BERT to encode all the questions into vector representation and then adopts k-means clustering to produce k clusters of questions. Active-Prompt does not require CPU and GPU computation because it is purely based on ChatGPT API which costs money. Although there is a clear performance advantage compared with Auto-CoT (as shown in Appendix D), there is no clear advantage compared with Auto-CoT because of the different implementations. Thank you for your question!

Reviewer comment (Evaluation):
Logically, the larger the value of k, the more accurate the model's uncertainty assessment should be. However, on the SingleEq dataset, a k value of 15 led to a noticeable performance decline. The reason given, 'In careful observation of the dataset, when k > 10, the number of the most uncertain questions is scarce, where confusion is no longer a problem,' is perplexing.

Author response:
Your observation about the accuracy decrease in the SingleEq dataset is astute. We attribute this to potential gaps during the transfer process from GSM8K to SingleEq, likely caused by noise and fluctuation in the inference process. To address this, we conducted additional experiments and updated Figure 2 with more stable and consistent results. Due to the unavailability of the code-davinci-002 model, we switched to the text-davinci-003 model for these experiments. The revised figure now reflects a more consistent increase and convergence in accuracy, which we believe more accurately represents the performance of our method.

Once again, thank you for your valuable feedback, which has significantly contributed to the refinement of our work.

Reviewer comment (Experiments):
Many current studies have adopted GPT-4 for label generation. For uncertain samples from datasets, can GPT-4 replace human annotation and achieve similar results?

Author response:
For the cost of selection, compared with selecting questions by humans, our proposed method is more efficient. For a new task, users need to do trials and errors a lot of times which costs a lot of human effort with unstable performance. Even so, the selected questions are still suboptimal.
Second, as mentioned in Section 3.3, we limit the size of candidate instances to 1,000 which greatly reduce the cost. 1,000 is a good balance between cost and performance. We verified that with more than 1,000 instances, the performance would converge. Doing uncertainty estimation 10 times with a pool of 1,000 questions is acceptable. The cost is smaller than self-consistency, which usually requires 40 times inference, although it is an orthogonal technique and can be complementary to ours. In addition, inspired by the new experimental results requested by reviewer Wb4R, we are excited to find that questions selected by smaller models (e.g., Llama) perform well with larger models (e.g., gpt-3.5-turbo). Considering models like Llama are open-source which does not cause API cost, one may use it (with GPU) to replace black-box API. 


For the cost of annotation, annotating 8 questions is not costly. Humans could finish it in several minutes. Furthermore, like you suggested, one can use ChatGPT or GPT-4 for annotation, which is much more easier. We tried some examples and found the GPT-4 annotations make a lot of sense and we believe they work well as human’s annotation. We are doing this and will add this experiment very soon (before Nov. 22). Thanks!

Reviewer comment (Experiments):
Some details in the paper are missing. For example, how is the variance based approach applied to textual answers? There are no results presented with the self-confidence approach and only an example is given, etc.

Author response:
Regarding the variance-based method, its applicability is indeed limited to arithmetic tasks, as it struggles with textual responses. For the self-confidence-based metric, as discussed in Section 5.1 [Effects of Uncertainty Metrics], we observed its tendency towards overconfidence, leading to suboptimal performance. Consequently, our focus shifted to disagreement and entropy metrics, which demonstrated more reliable results. We have clarified these points in our manuscript to ensure a better understanding of our methodological choices. Thanks!

Reviewer comment (Evaluation):
How will the approach generalize to new tasks?

Author response:
Active-Prompt is designed to be versatile and can be effectively utilized even with a limited number of unlabeled questions. This flexibility allows for efficient generalization to similar tasks. For situations where collecting new questions is feasible, our uncertainty estimation method facilitates the selection of high-quality examples. In cases where question collection is challenging, transferring questions from a similar domain is a viable alternative. Our results in Table 1, showcasing the transferability of selected questions from GSM8K to other datasets like ASDiv, SVAMP, and SingleEq, illustrate this point effectively. This evidence supports the notion that Active-Prompt is not only effctive but also generalizable to new tasks.

Reviewer comment (Reproducibility):
How is the variance based approach applied to textual response?

Author response:
Regarding the variance-based method, its applicability is indeed limited to arithmetic tasks, as it struggles with textual responses. For the self-confidence-based metric, as discussed in Section 5.1 [Effects of Uncertainty Metrics], we observed its tendency towards overconfidence, leading to suboptimal performance. Consequently, our focus shifted to disagreement and entropy metrics, which demonstrated more reliable results. We have clarified these points in our manuscript to ensure a better understanding of our methodological choices. Thanks!

Reviewer comment (Evaluation):
In Figure 2, what is the intuition for accuracy decreasing with more number of predicted answers?

Author response:
Your observation about the accuracy decrease in the SingleEq dataset is astute. We attribute this to potential gaps during the transfer process from GSM8K to SingleEq, likely caused by noise and fluctuation in the inference process. To address this, we conducted additional experiments and updated Figure 2 with more stable and consistent results. Due to the unavailability of the code-davinci-002 model, we switched to the text-davinci-003 model for these experiments. The revised figure now reflects a more consistent increase and convergence in accuracy, which we believe more accurately represents the performance of our method.

Reviewer comment (Experiments):
**Baselines are too weak, leading to a misunderstanding of the effectiveness of the proposed method.** I would like to urge the authors to include more powerful baselines in the experiment rather than hide them. ALL the reviewers are experts in this domain and familiar with the state-of-the-art performance of LLMs on these benchmarks in this domain. In the experiment section, the authors only include the CoT annotations from [1] as the most important baseline. It is widely acknowledged and studied that the complexity (i.e., the length or reasoning steps of the CoT annotations) significantly influences the performance of the LLMs. The annotations from [1] are very simple and short, only including some easy examples as in-context examples. In comparison, if we look at Page 17, the actual annotations from the authors are very long and detailed. Previous work [2] has already shown that by selecting the most complex examples from the training dataset, the performance can be largely improved compared to the original annotations from [1]. For example, by selecting the most complex examples, the performance of ChatGPT (i.e., gpt-3.5-turbo) can easily achieve more than 80% accuracy (without self-consistency) compared to the number 77.1% in Table 1. One may also refer to https://opencompass.org.cn/leaderboard-llm for the performance of LLMs (I acknowledge that the performance of ChatGPT on GSM8K from that website is possibly still underestimated). Without comparison with SOTA's performance, I will try my best to reject this paper. Please do not try to hide the best baselines.

Author response:
**Q1. Performance in Table 1** 

Thank you for highlighting the discrepancies in the performance of gpt-3.5-turbo on GSM8K as reported in different sources. We acknowledge the variation in results across different papers. For example, according to chain-of-thought hub [3] (https://github.com/FranxYao/chain-of-thought-hub), the performance is 74.9 which is similar to our reported 74.2. But indeed, we find some papers reporting higher performance [4,5], which is about 80.8. We checked Opencompass [6] as well, they reported 78.2. All of these three sources have a much higher performance than our reported 74.2. This leads to an interesting question which motivates us to take a deep investigation. 

First of all, we are very certain that the results we reported are not deliberately understated.
We take a careful look into [4] who reported 80.8 and find they are using a different version of gpt-3.5-turbo. Our initial results were based on gpt-3.5-turbo-0613, while some of the higher performances reported in other studies utilized gpt-3.5-turbo-0301. We conduct experiments with gpt-3.5-turbo-0301 and surprisingly find that the baseline CoT is indeed above 80! We never expect such a situation although there are several papers observing and discussing similar phenomenons [7]. Therefore, we add the results with gpt-3.5-turbo-0301 as well to provide a more comprehensive evaluation. The results are shown below.

| Model / Dataset | GSM8K | AsDiv | SVAMP | SingleEq |
| ----------- | ----------- | ----------- | ----------- | ----------- |
| gpt-3.5-turbo-0613 (original CoT)| 74.2 | 82.5 | 83.8 | 95.0 |
| gpt-3.5-turbo-0613 (active-prompt) | 77.1 | 83.6 | 85.5 | 96.0 |
| gpt-3.5-turbo-0301 (original CoT) | 80.1 | 86.7 | 82.0 | 91.3 |
| gpt-3.5-turbo-0301 (active-prompt) | 83.5 | 87.4 | 83.0 | 93.3 | 

These results confirm a consistent improvement with our proposed Active-Prompt approach, irrespective of the GPT-3.5 version. We list the results with different versions in the same table for people to reproduce the results. We are grateful for your comment which helps us have a deeper understanding. In addition, the 0613 version is likely based on the continued training from 0301, which reveals a very interesting phenomenon — the forgetting issue of LLMs as training progresses. This has sparked our interest in conducting more in-depth research in the future. Thank you very much!

Reviewer comment (Experiments):
**More ablation study is required.** Again, the performance improvement may come from two aspects. The first is selecting the most uncertain examples, and the second is making the CoT annotations longer. The annotations in baseline [1] are much shorter compared to the annotations by the authors. Without the ablation studies on these two aspects, we cannot determine whether the performance improvement truly comes from the author's contribution or just longer CoT annotations.

Author response:
**Q2. Ablation Study of Longer CoT Annotations**

Thank you for suggesting an ablation study to differentiate the impacts of longer CoT annotations from our method. To explore this, we extended the length of the original CoT [1] annotations to an average of 155 words, comparable to our average length of 160 words. Here are the comparative results:


| Model / Dataset | GSM8K | AsDiv | SVAMP | SingleEq |
| ----------- | ----------- | ----------- | ----------- | ----------- |
| gpt-3.5-turbo (original CoT) | 74.2 | 82.5 | 83.8 | 95.0 |
| gpt-3.5-turbo (longer CoT) | 69.4 | 69.2 | 70.4 | 83.2 |
| gpt-3.5-turbo (active-prompt) | 77.1 | 83.6 | 85.5 | 96.0 |

Our findings show that merely increasing the length of CoT annotations does not lead to improved performance, and in some cases, even reduces it. In contrast, our Active-Prompt method consistently demonstrates superior performance. This suggests that the selection of questions, rather than their length, contributes significantly to the improved results. Our approach effectively identifies and utilizes more informative examples for annotations.

Reviewer comment (Novelty):
**The method is simple with limited contribution, while performance improvement is not significant.** The method is quite intuitive and can be regarded as an in-context example selection method (followed by annotations). The authors should discuss the relationship with other in-context example selection methods and compare the performance. Existing performance improvement is quite limited. Once more baselines are included, it is very possible that the performance will be surpassed.

Author response:
**Q3. Performance improvement and more baselines** 

We appreciate your emphasis on comparing our method with diverse baselines. We have included comparisons with both diversity-based (Auto-CoT [8]) and complexity-based (Complex-CoT [2]) methods.
First, the comparison with Auto-CoT is as follows. 

| Model / Dataset | GSM8K | MultiArith | AddSub |
| ----------- | ----------- | ----------- | ----------- | 
| Complex-CoT | 62.8 | 93.2 | 91.9 | 
| Active-Prompt (D) | 67.0 | 95.5 | 93.2 | 

Because Auto-CoT only reported the results on GSM8K, MultiArith, and AddSub with code-davinci-002 without self-consistency, we compare our method with it on these three datasets in the same setting, and we find Active-Prompt outperforms Auto-CoT by a large margin.

Second, we test the performance of Complex-CoT and compare it with Active-Prompt, and the results are shown in the following table. All the results are based on gpt-3.5-turbo-0613. The prompts for Complex-CoT are directly taken from their paper.

| Model / Dataset | GSM8K | AsDiv | SVAMP | SingleEq |
| ----------- | ----------- | ----------- | ----------- | ----------- | 
| Complex-CoT | 76.3 | 82.4 | 79.9 | 93.3 |
| Active-Prompt (D) | 77.1 | 83.6 | 85.5 | 96.0 |

We find that Active-Prompt outperforms Complex-CoT across all tasks, demonstrating the effectiveness of uncertainty-based methods.

Note that diversity, complexity, and uncertainty are useful for selecting the most informative questions, and they are complementary. We consider the combination of them as an important future direction.

Reviewer comment (Experiments):
[Major] An important and very relevant baseline is missing: https://arxiv.org/abs/2210.00720. Their method is very similar to Active Prompt and simply selects the longest training instances. I would be curious to see how it compares to this work.

Author response:
**Q1. Performance of Complex-CoT**

We sincerely appreciate your suggestion to compare the performance of Complex-CoT with our proposed Active-Prompt methodology. As recommended, we conducted a detailed evaluation using the GPT-3.5-turbo-0613 model. The prompts for Complex-CoT were sourced directly from the original paper to maintain consistency in comparison.


| Model / Dataset | GSM8K | AsDiv | SVAMP | SingleEq | Average |
| ----------- | ----------- | ----------- | ----------- | ----------- | ----------- |
| Complex-CoT | 76.3 | 82.4 | 79.9 | 93.3 | 82.97 |
| Active-Prompt (D) | 77.1 | 83.6 | 85.5 | 96.0 | 85.5 |

We find that Active-Prompt consistently outperforms Complex-CoT across all tasks. In addition, we can combine the uncertainty and the complexity together to achieve a better performance, and we look forward to exploring the combination in future work. We have updated our draft with these new results in Appendix E. Thanks very much for your constructive suggestion!

Reviewer comment (Experiments):
[Major] One can imagine that if the model is reasonably good, the demonstrations selected by Active-Prompt will be more useful. I wonder whether this is still the case for “weaker” models. If the model does not know too much about the task, will the prompts selected by its uncertainty still be useful? This can be tested out by trying Active-Prompt on, e.g., one of the smaller Llama models.

Author response:
**Q2. Performance of Weaker Models** 

We acknowledge the importance of evaluating performance across models of varying capabilities. Therefore, we conduct new experiments with Llama2-13b-chat and Lllama2-70b-chat. The results are shown as follows.

| Model / Dataset | GSM8K | AsDiv | SVAMP | SingleEq | Average |
| ----------- | ----------- | ----------- | ----------- | ----------- | ----------- |
| CoT (Llama2-13b-chat) | 29.1 | 57.4 | 45.7 | 75.4 | 51.9 |
| Active-Prompt (Llama2-13b-chat) | 27.2 | 53.9 | 47.4 | 68.2 | 49.2 |
| CoT (Llama2-70b-chat) | 54.8 | 73.2 | 77.4 | 84.6 | 72.5 |
| Active-Prompt (Llama2-70b-chat) | 56.9 | 74.9 | 82.5 | 83.2 | 74.4 |
| CoT (gpt-3.5-turbo-0613) | 74.2 | 82.5 | 83.8 | 95.0 | 83.8 |
| Active-Prompt (gpt-3.5-turbo-0613) | 77.1 | 83.6 | 85.5 | 96.0 | 85.6 |


Firstly, because smaller models do not have a good chain-of-thought ability, it is difficult for Llama2-13b-chat to understand the chain-of-thought prompting, with poor performance of both CoT and Active-Prompt. Especially, we find that the more complex the prompt, the poorer performance. However, with Llama2-70b model, our proposed Active-Prompt outperforms CoT by a large margin, demonstrating this method is still useful for weaker models.

Note that we are using the instruction-tuned version of Llama2-70b in all our experiments (i.e., Lllama2-70b-chat) because it is able to understand complex chain-of-thought prompting and follow human instructions.

Reviewer comment (Experiments):
[Major] The conclusion drawn on the transferability of prompts found by Active-Prompt in 5.3 needs more evidence. All the models tested are from the GPT-3 family, which are finetuned from the same base model. It is unclear whether, e.g., the prompts found by GPT-3.5 perform well for Llama. This concern is important since it directly determines how useful Active-Prompt is in practice. If the prompts do not transfer across different model families, it will have a huge overhead annotating a new set of instances for a different model. Besides, it makes it impossible to do fair comparisons among models controlling the prompts. I suggest adding an experiment studying the transferability between GPT and Llama models.

Author response:
**Q3. Transferability between GPT and Llama models**
 
Thanks for your suggestion! Your suggestion prompted us to investigate the transferability between GPT and Llama models. Because smaller Llama models perform poorly on reasoning tasks, we conduct experiments with Llama2-70b-chat. 
We conduct two types of experiments: (1) select questions by gpt-3.5-turbo and infer by Llama2-70b-chat and (2) select questions by Llama2-70b-chat and infer by gpt-3.5-turbo. Note that we are using the 0613 version of gpt-3.5-turbo.
The results are shown as follows:

| Model / Dataset | GSM8K | AsDiv | SVAMP | SingleEq | Average |
| ----------- | ----------- | ----------- | ----------- | ----------- | ----------- |
| gpt-3.5-turbo  | 74.2 | 82.5 | 83.8 | 95.0 | 83.8 |
| gpt-3.5-turbo -> gpt-3.5-turbo  | 77.1 | 83.6 | 85.5 | 96.0 | 85.6 | 
| Llama2-70b-chat -> gpt-3.5-turbo  | 78.7 | 85.9 | 83.1 | 91.5 | 84.8 |
| Llama2-70b-chat | 54.8 | 73.2 | 77.4 | 84.6 | 72.5 |
| Llama2-70b-chat -> Llama2-70b-chat | 56.9 | 74.9 | 82.5 | 83.2 | 74.4 |
| gpt-3.5-turbo -> Llama2-70b-chat | 58.9 | 74.7 | 81.2 | 86.0 | 76.0 |

The model before the arrow denotes the model for actively selecting questions while the model after the arrow denotes the model for inference. The results demonstrate the feasibility of selecting questions with smaller models (Llama2-70b-chat) and applying the selected questions to larger models (gpt-3.5-turbo). In addition, selecting questions with larger models and applying them to smaller models has better performance.

Reviewer comment (Experiments):
To draw conclusions on the transferability of the prompts, Table 3 should compare, e.g., CD-002->TD-002 (SC) with TD-002->TD-002 (SC), instead of the non-Active-Prompt baseline.

Author response:
**Q4. Transferability Results in Table 3** 

Thanks for your suggestions! We add the experimental results of TD-003 -> TD-003 (CoT) in Table 3. TD-003-> TD-003 (CoT) outperforms CD-002 -> TD-003 (CoT) by a large margin (on average 2%). Due to the high inference cost of SC, we did not include the results of TD-002 -> TD-002 (SC). In the transferability analysis, our original intention is not to prove that transfer is better than non-transfer, but to demonstrate that the method of selecting questions through transfer is superior to not selecting them. Transfer will certainly lead to a decrease in results, and we have already updated these results in the paper. Thank you!

| Model / Dataset | GSM8K | CSQA | Letter (4) | Average |
| ----------- | ----------- | ----------- | ----------- | ----------- |
| TD-002 (CoT) | 46.9 | 73.5 | 56.6 | 59.0 |
| TD-002 -> TD-002 (CoT) | 48.4 | 74.7 | 57.7 | 60.3 |
| TD-002 (SC) | 58.2 | 72.9 | 57.6 | 62.9 |
| CD-002 -> TD-002 (SC) | 73.2 | 76.6 | 67.7 | 72.5 |
| TD-003 (CoT) | 61.7 | 76.2 | 70.2 | 69.4 |
| CD-002 -> TD-003 (CoT) | 65.6 | 78.9 | 71.2 | 71.9 |
| TD-003 -> TD-003 (CoT) | 67.2 | 80.8 | 73.7 | 73.9 |

Reviewer comment (Writing):
Some of the wordings are confusing, even misleading. Please see the details below.

Author response:
**Q6. Wordings** 

Thank you for pointing out the need for clearer wordings. We have thoroughly revised the manuscript to address this following your suggestions, with significant changes highlighted in **blue** for ease of review.

Thank you again for your valuable suggestions! We have included all these new results in our revised version.

Reviewer comment (Experiments):
A clear limitation of Active-Prompt is the high cost associated with doing inference runs over the training set. A discussion about this would be nice.

Author response:
**Q5. the high cost associated with doing inference runs over the training set**

Thanks for your question!
Compared with selecting questions by humans, our proposed method is more efficient. For a new task, users need to do trials and errors a lot of times which costs a lot of human effort with unstable performance. Even so, the selected questions are still suboptimal.
Second, as mentioned in Section 3.3, we limit the size of candidate instances to 1,000 which greatly reduces the cost. 1,000 is a good balance between cost and performance. We verified that with more than 1,000 instances, the performance would converge. Doing uncertainty estimation 10 times with a pool of 1,000 questions is acceptable. The cost is smaller than self-consistency, which usually requires 40 times inference, although it is an orthogonal technique and can be complementary to ours. 
In addition, inspired by the new experimental results requested by you, we are excited to find that questions selected by smaller models (e.g., Llama) perform well with larger models (e.g., gpt-3.5-turbo). Considering models like Llama are open-source which does not cause API cost, one may use it (with GPU) to replace black-box API.  We included this discussion into Section H.
Thank you very much for your suggestions!