Instance-adaptive Zero-shot Chain-of-Thought Prompting

Thank you for the constructive advice and comments, which have greatly improved our manuscript, and we are glad to reply to your invaluable suggestions and questions.

Response to Weaknesses

Weakness 1: The proposed method is not clearly explained, some details are missing.

Response to Weakness 1: For IAP-ss, we obtained threshold values with regard to distinct LLMs on different training sets, we computed the overall synthesized scores (defined in eq (4) in Section 3) to divide up the good and bad reasoning paths and adopted the thresholds whose classify reasoning well. Such as, the threshold of LLaMA-3 8B on GSM8K is 5.5e-6, and the identification of the thresholds of different LLMs on different datasets is the same and it is simple and doesn't not need much time. In practice, we considered reasoning with a value higher than the threshold as good, otherwise bad. We have tried different thresholds, and the best performance is shown in the following table.

We can see that an improper threshold can affect the performance of the IAP-ss, whether higher or lower. It comes from that higher thresholds tend to recognize some good reasoning instances as bad ones, and lower thresholds may overlook some bad reasoning.

As for the IAP-mv, we selected top-k (hyper-parameter, k=3) values and adopted the majority result as the final result, we also tried other k values and k=3 is the best among all other values with LLaMA-3 8B and picked some results on 3 datasets in the following table.

The k=3 achieves the best performance on most datasets, therefore, we selected the hyper-parameter k=3 as the default value in the paper. We are sorry for confusing you in this part and we have elaborated these details in the new version.

Weakness 2: The experimental setup is unfair.

Response to Weakness 2: We are sorry for not introducing the comparable approaches thoroughly in the baseline paragraph of Section 4.1, and we would like to replace the current version with the new one:

In practice, the OPPR optimizes a meta prompt on different datasets with distinct LLMs for multiple rounds to guide LLMs to produce better prompts, requiring numerous optimization steps (i.e., inferences). As for Self-Discover, it consists of selecting, adapting, implementing, and reasoning, which also needs multi-round inference in every step.

Given the above description, we think that comparing the IAP with the above methods is not unfair.

The profits of IAP-mv didn't simply come from the multiple reasoning path, we computed the synthesized saliency scores (defined in eq (4)., as an application of former analysis) of all prompt candidates, and conducted a majority vote based on these synthesized scores. For a considerable proportion of questions, the LLM could be guided to generate wrong results with most prompts but only a few right results and our IAP-mv can handle it, thereby outperforming the majority final results vote. We compared the IAP-mv and direct majority results vote results in the following table:

The results show that the majority vote approach performs poorly, and our IAP-mv outperforms it by a large margin, demonstrating that most prompts can lead the LLM to generate wrong answers for a given question, reaching only a few correct answers, i.e., such methods cannot recognize good/bad reasoning. Our IAP-mv can handle that with the analysis for information flow in reasoning, i.e., IAP-mv can differentiate good and bad reasoning, validating the effectiveness of our proposed strategy, rather than benefiting from multiple reasoning paths.

Weakness 3: Some experimental conclusions are missing or somewhat unreasonable.

Response to Weakness 3: We apologize for not providing an extensive explanation of the consistency and complementary experiments, we have discussed adding the following part to the 1st paragraph of Section 4.3 in our new manuscript:

We can observe that the great performance of the instructive group outperforms our groups, which comes from the base of all instructive prompts. Furthermore, the combination of the instructive group and the other two can continue to improve the performance of both, demonstrating that complementary is critical for IAP-mv, and IAP-mv can take advantage of these complementary prompts.

In the Efficacy part, we intended to express that IAP-ss and IAP-mv can be chosen with different time budgets, and we are sorry for selecting an improper figure to confuse you. In fact, the IAP-ss outperforms all the task-level optimal prompts of most LLMs and datasets, as shown in Table 1, showing that people can still employ different strategies to achieve better zero-shot prompting. We have also conducted other time experiments, and plan to replace the current figure with the new one in the updated manuscript.

For some common questions, we made a unified reply in the Author Rebuttal part (see at top) which you can look up.

Thank you for your review,

The authors responded to your initial review. Please be sure to read it and reply indicating the extent to which the authors have addressed your initial questions and concerns.

Best,

AC

Thanks for your detailed explanation. My major concern2 has been solved, and I have already corresponding adjusted my score.

Thanks a lot for your valuable reviews, and we appreciate the time and effort you have taken. Regarding the weaknesses and questions, we would like to elaborate and address your concerns on this work.

Response to Weaknesses

Weakness 1: Limited Scope of Neuron Saliency Score Analysis: The neuron saliency score analysis in Section 2 is conducted on only one LLM (not stated in the paper, personal guess) and one dataset, GSM8K. More evidence and diverse datasets are needed to support this analysis comprehensively. Additionally, Section 2.3, "Head Analysis," lacks a comparative study between good and bad reasoning instances.

Response to Weakness 1: In our investigation, we analyzed the information flow with the same method in different LLMs on various datasets and found that the phenomena of saliency scores for all LLMs on most datasets are quite similar, so we put the analysis process of Qwen-14B on GSM8K to maintain consistency in the narrative subject and present our analysis conclusion. Similarly, the head analysis results for good and bad reasoning are consistent, we are sorry for not elaborating on that in this subsection. We apologize for not putting more figures in the Appendix to make our analysis more complete and well-supported, and we have updated our manuscript. We also put a few samples of the analysis process in the pdf file attached in the Author Rebuttal (see at top).

Weakness 2: Insufficient Experimental Details

Response to Weakness 2: Your understanding of IAP is correct, and your suggestion of supplementing answers to the majority vote experiment would make our work more complete. The results comparison between our IAP-mv and the direct answers majority vote is as follows:

The results show that the majority vote approach performs poorly, and our IAP-mv outperforms it by a large margin, demonstrating that most prompts can lead the LLM to generate wrong answers for a given question, reaching only a few correct answers, i.e., such methods cannot recognize good/bad reasoning. Our IAP-mv can handle that with the analysis for information flow in reasoning, i.e., IAP-mv can differentiate good and bad reasoning, validating the effectiveness of our proposed strategy.

The most adopted prompts in IAP-mv of distinct LLMs on different datasets are the former task-level optimal (among all prompt candidates) since they are suitable for most instances in corresponding datasets, respectively. We display the top-3 prompts for different LLMs on different datasets in the table below:

We can observe that the most adopted prompt candidates are the former task-level optimal ones, which is consistent with our analysis in the paper.

Weakness 3: Figure 1 Inconsistency: Figure 1 does not align with the rest of the paper.

Response to Weakness 3: Figure 1 offered a representative case to illustrate that: the worst task-level prompt can beat the optimal prompt for some instances, which is counterintuitive as we discussed in the 2nd paragraph in the Introduction section, such a case encouraged us to detect the inner mechanism for zero-shot CoT, further trigged us to propose instance-level prompting strategy.

Weakness 4: More Model Variants.

Response to Weakness 4: In this paper, we conducted experiments on 8B, 13B, and 14B LLMs with different architectures (LLaMA-2, LLaMA-3, and Qwen), and the results validated our initiative observation and analysis. The current evaluation across model sizes has provided a broad view of how different scales of models may perform under various prompt candidates. However, your suggestion is also valuable, and we conducted the experiments with LLaMA-3 70B using the same 9 prompts as the main experiments and IAP-mv, the table below shows the results:

In this table, IAP-mv demonstrates its effectiveness on LLaMA-3 70B, consistent with the results on LLaMA-3 8B and Qwen 14B, broadening the model scale impact of the IAP-mv.

Weakness 5: In Figure 3, the terms "Good reasoning" and "Bad reasoning" are used, while in Figure 4, the terms change to "Good prompt" and "Bad prompt."

Response to Weakness 5: We are sorry for not using the same statement in different figures, and we have rectified such issues to keep the claims consistent in the updated manuscript.

For some common questions, we made a unified reply in the Author Rebuttal part (see at top) which you can look up.

Thank you for your review,

The authors responded to your initial review. Please be sure to read it and reply indicating the extent to which the authors have addressed your initial questions and concerns.

Best,

AC

Thanks a lot for the time and effort you invested in providing the detailed reviews. Regarding the current weaknesses and questions you pointed out, we are glad to give our responses.

Response to Weaknesses

Weakness 1: Experiments only covered 7B and 13/14B models, involving larger models in the experiments would be more marvelous.

Response to Weakness 1: In this work, we conducted experiments on 8B, 13B, and 14B LLMs with different architectures (LLaMA-2, LLaMA-3, and Qwen), and empirical results validated our initiative observation and assumption. The current evaluation across model sizes has provided a broad view of how different scales of models may perform under various prompt candidates.

We conducted the experiments with LLaMA-3 70B using the same 9 prompts as the main experiments and IAP-mv, the table below shows the results:

The empirical results of the LLaMA-3 70B with IAP-mv are better than any task-level hard prompt, which demonstrates the effectiveness of the IAP-mv under broader model scales.

Weakness 2: In Section 4.3, the authors didn’t interpret the results of consistency and complementary results in detail.

Response to Weakness 2: In the ablation studies, we conducted the consistency and complementary experiment to detect which type of prompt combination contributed to the performance. Table 2 shows the results, and referring to the main results in Table 1, we can observe that each pair of combinations can improve the performance, and instructive and irrelevant combinations achieve better outcomes than others, which comes from the base performance of instructive prompts.

Response to Questions

Question 1: Why did the authors choose the saliency score instead of the widely used attribution score as the information flow analysis method?

Response to Question 1: There are two reasons that we didn't employ the attribution score: (1) the attribution score is designed for knowledge-oriented tasks, which have been discussed in the related work section; (2) the saliency score is more suitable for the in-context learning scenario, and may not perform well on the reasoning tasks. These two reasons had been demonstrated by [1][2][3][4]. [1] Dai, D., L. Dong, Y. Hao, et al. Knowledge neurons in pretrained transformers. [2] Hao, Y., L. Dong, F. Wei, et al. Self-attention attribution: Interpreting information interactions inside transformer. [3] Wang, L., L. Li, D. Dai, et al. Label words are anchors: An information flow perspective for understanding in-context learning. [4] Li, J., P. Cao, C. Wang, et al. Focus on your question! interpreting and mitigating toxic cot problems in commonsense reasoning.

Question 2: What did some results with underlines in Table 1 mean?

Response to Question 2: In Table 1, we underlined some numbers which means these results are task-level optimal prompts among all candidates, we are sorry for not elaborating on this, and we have explained in the new version.

Question 3: Should the colon after the “remains” in line 44 be removed?

Response to Question 3: Thank you for your detailed review, we have removed the colon after the “remains” in line 44 in the updated manuscript.

Question 4: Should the “and” in the “, and Tracking Shuffled Objects …” in line 258 be removed?

Response to Question 4: We have removed the “and” in the “, and Tracking Shuffled Objects …”, and we have checked all the grammar issues in the new manuscript.

Question 5: In Table 3 in the Appendix, why didn’t the authors highlight the best results and explain the results more?

Response to Question 5: Since Table 3 in the Appendix is the supplement of Table 1, and the IAP shows similar performance on LLaMA-2 13B with LLaMA-3 8B and Qwen 14B, thus we didn’t repeat similar explanations. Also, we have highlighted the best results as we did in Table 1 in the updated manuscript.

For some common questions, we made a unified reply in the Author Rebuttal part (see at top) which you can look up.

Thank you for your review,

The authors responded to your initial review. Please be sure to read it and reply indicating the extent to which the authors have addressed your initial questions and concerns.

Best,

AC

We deeply appreciate the time and effort you invested in reviewing our paper, and we are glad to answer your questions.

Responses to Weaknesses

Weakness 1: As the number of available prompts grows, the strategy for selecting the best prompt could become increasingly complex.

Response to Weakness 1: For IAP-ss, we obtained threshold values with regard to distinct LLMs on different training sets, we computed the overall synthesized scores (defined in eq (4) in Section 3) to divide up the good and bad reasoning paths and adopted the thresholds whose classify reasoning well. Such as, the threshold of LLaMA-3 8B on GSM8K is 5.5e-6, and the identification of the thresholds of different LLMs on different datasets is the same and it is simple and doesn't not need much time. In practice, we considered reasoning with a value higher than the threshold as good, otherwise bad. We have tried different thresholds, and the best performance is shown in the following table.

We can see that an improper threshold can affect the performance of the IAP-ss, no matter higher or lower. It comes from that higher thresholds tend to recognize some good reasoning instances as bad ones, and lower thresholds may overlook some bad reasoning.

As we discussed in the last paragraph in Section 3 and Section 4, IAP-mv can achieve better performance with more computing, while IAP-ss can be a choice under the resource-limited scenario, and it would be faster if the order of prompt candidates were arranged properly. We conducted the time experiments with LLaMA-3 8B on SVAMP under different orders of prompt candidates, and the results are shown in the table below (The numbers in the order column represent the prompt candidates as we introduced in Section 4.1 Zero-shot CoT prompts paragraph.):

Where #9 is the worst task-level prompt, and #6 is the best task-level prompt, achieving the highest accuracy among all the prompt candidates while consuming the least time. The prompt order of the 3rd row is accuracy-decreased on SVAMP, the 4th row is accuracy-increased, and the last row is our default setting, which obtains the best performance. This table shows that IAP-ss can cost less time with fewer prompt candidates but may obtain limited results, however, even fewer improper candidates could take a lot of computing time. Therefore, we think that the time cost of IAP-ss is not a major issue if prompt candidates are in an appropriate order.

Weakness 2: The titles of some figures are verbose (e.g. Figure 2).

Response to Weakness 2: Thanks for your meticulous reviews and suggestions, we have moved that verbose explanation from the figures to the main body in the new version. Now, the explanation of Figure 2 and Figure 4 are as follows:

(Figure 2) The visualization comparison of the saliency matrices between good and bad reasoning instances with two prompts, the darker the color of the pixel point in the image represents a larger saliency score. (a) and (b) are good and bad reasoning instances under "Let's think step by step.", and so as (c) and (d) under "Don't think. Just feel.", respectively. The red, blue, and green boxes in each subfigure depict the question-to-prompt, question-to-rationale, and prompt-to-rationale information flow, respectively.

(Figure 4) Saliency scores of question-to-prompt, question-to-rationale, and prompt-to-rationale across layers. The yellow lines represent prompts that effectively guide the LLMs to generate the correct answer, indicating good prompts. Conversely, the blue lines denote ineffective prompts.

And we have moved the previous definitions of the saliency matrices to the main body in the new version to make the presentation more clear.

Response to Questions

Question 1: How were the saliency score thresholds determined, and how do these thresholds affect the results?

Response to Question 1: For the IAP-ss, we obtained threshold values with regard to distinct LLMs on different training sets, we computed the overall synthesized scores (defined in eq (4) in Section 3) to divide up the good and bad reasoning paths and adopted the thresholds whose classify reasoning well. In practice, we considered reasoning with a value higher than the threshold is good, otherwise bad. From this, it is evident that an improper threshold may lead to inaccurate judgment for good and bad reasoning, thereby hurting the overall performance. The current threshold of LLaMA-3 8B on GSM8K we adopted is 5.5e-6, we also tried other thresholds while keeping other settings, and the results are shown in the table below.

Table caption LLaMA 3 on GSM8k, different thresholds from repeating the experiment on other LLMs and datasets. (validation selection, fast)

We can see that an improper threshold can affect the performance of the IAP-ss, whether it is higher or lower. It comes from that higher thresholds tend to recognize some good reasoning instances as bad ones, and lower thresholds may overlook some bad reasoning. Therefore, a proper threshold benefits the IAP-ss a lot, and vice versa.

Question 2: In some paragraphs, full stops are missing.

Response to Question 2: We appreciate your careful review of our paper, and we have revised all full stops missing issues in the new version and checked the entire manuscript to avoid any similar issues.

For some common questions, we made a unified reply in the Author Rebuttal part (see at top) which you can look up.

Thank you for your review,

The authors responded to your initial review. Please be sure to read it and reply indicating the extent to which the authors have addressed your initial questions and concerns.

Best,

AC